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全国高等院校土木工程类系列教材 　 　 　 　 　 　 　 　 　

土 木 工 程 英 语

张 　倩 　主编

北 　京

内 　容 　简 　介

　 　本书是根据 ２００４年 ８ 月颁布的枟大学英语课程教学要求（教学大纲）枠（试行）的规定编写的 。本书选材涉及工程力学 、钢筋混凝土结构 、钢结构 、结构抗震 、土质学和土力学 、工程岩土学 、桥梁工程 、路面工程 、路基工程 、道路勘测设计 、工程经济与管理等学科 ，共有 ２２ 个单元 ，每个单元均由课文（Text） 、注解（Notes） 、生词（New Words） 、词组（Phrases and Expressions） 、练习（Exercises）和阅读材料（Reading Material）组成 。本书可作为高等学校土木工程类专业英语教材 ，也可作为土木工程专业

技术人员提高专业英语水平的参考读物 。

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　土木工程英语／张倩主编 ．—北京 ：科学出版社 ，２００８（全国高等院校土木工程类系列教材）　 ISBN 　 ９７８唱７唱０３唱０２２９４８唱９

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全国高等院校土木工程类系列教材编委会

主 　 　任 　白国良副 主 任 （以姓氏笔画为序）

　 　 　 　 　马建勋 　刘伯权 　何明胜 　邵生俊 　陈宗平杨 　勇 　童安齐

秘 书 长 　贾凤云副秘书长 　任加林 　陈 　迅委 　 　员 （以姓氏笔画为序）

　 　 　 　 　马 　斌 　马建勋 　王士川 　王志骞 　王泽军史庆轩 　白国良 　冯志焱 　任加林 　刘伯权苏明周 　杜高潮 　李 　进 　李青宁 　李建峰李惠民 　余梁蜀 　何明胜 　何廷树 　邵生俊张 　荫 　张 　倩 　张志政 　陈 　迅 　陈宗平杨 　勇 　赵 　平 　赵树德 　赵鸿铁 　姚继涛贾凤云 　徐 　雷 　袁伟宁 　郭成喜 　梁兴文韩晓雷 　童安齐 　曾 　珂 　廖红建 　熊仲明薛建阳

前 　 　言

本书结合我国高等教育发展的新趋势 ，按照 ２００４ 年 ６ 月教育部颁布的枟大学英语课程教学要求（教学大纲）枠（试行）的定位和要求编写 。 为了使学生毕业后能更快和更有效地应用英语这一语言工具获取国外与本专业有关的科技信息和进行专业技术交流 ，需通过专业英语课程的学习培养其专业英语基本技能 ，因此学生在完成基础阶段的英语学习任务后 ，须修读专业英语 。专业英语属大学英语学习的应用提高阶段 ，其教学目的是让学生掌握一定量的专业或与专业有关的常用单词和词组 ，培养学生阅读和翻译专业英文文献的能力 。

本书在选材上注意在有限的篇幅下尽可能多地涉及土木工程学科的相关课程 ，如工程力学 、钢筋混凝土结构 、钢结构 、结构抗震 、土质学和土力学 、工程岩土学 、桥梁工程 、路面工程 、路基工程 、道路勘测设计 、工程经济与管理等 。 本书共 ２２ 个单元 ，每个单元均由课文（Text） 、注解（Notes） 、生词（New Words） 、词组（Phrases and Expressions） 、练习（Exercises）和阅读材料（Reading Material）组成 。 课文和阅读材料的题材均选自原版英文资料 ，选材时注意语言的规范性 ，并且配有与文章内容相关的插图和表格 ，以帮助学生加深对文章的理解 。

本书由西安建筑科技大学和长安大学的部分教师编写 。 其中第 １ 、３ 、４ 、６ 、７ 、２１ 单元由长安大学雷自学编写 ，第 ８ 、９ 、１０ 、１１ 、２０ 、２２ 单元由西安建筑科技大学苏立君编写 ，第２ 、５ 、１４ 、１８ 、１９ 单元由西安建筑科技大学王先铁编写 ，第 １２ 、１３ 、１５ 、１６ 、１７ 单元由西安建筑科技大学张倩编写 。全书由张倩统稿 。

由于编者水平所限 ，书中难免存在不妥之处 ，敬请读者批评指正 。

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Contents

Unit 1 1…………………………………………………………………………………………

　 　 C iv ilEngineering 1…………………………………………………………………………

　 　 Sky scraper 6………………………………………………………………………………

Unit 2 9…………………………………………………………………………………………

　 　 Analy sis of P lane Structures 9……………………………………………………………

　 　 D esign of Beams 14………………………………………………………………………

Unit 3 17………………………………………………………………………………………

　 　 Normal stress in beams 17………………………………………………………………

　 　 Structural analy sis 22……………………………………………………………………

Unit 4 26………………………………………………………………………………………

　 　 Shear Stresses in Beams 26………………………………………………………………

　 　 Structural engineering 31…………………………………………………………………

Unit 5 33………………………………………………………………………………………

　 　 Load 33……………………………………………………………………………………

　 　 Combinations of Loads 38………………………………………………………………

Unit 6 42………………………………………………………………………………………

　 　 Basic BehaviorA ssumptions forConcreteM embers 42…………………………………

　 　 Reinforced Concrete 47……………………………………………………………………

Unit 7 51………………………………………………………………………………………

　 　 Axially Loaded Short Columns 51………………………………………………………

　 　 The Elastic BendingM oment D iagram ofConcrete Beams 56……………………………

Unit 8 59………………………………………………………………………………………

　 　 TheNature of So ils 59……………………………………………………………………

　 　 U ltimate BearingCapacity 65……………………………………………………………

Unit 9 68………………………………………………………………………………………

　 　 Foundation Settlement and So ilCompression 68…………………………………………

　 　 Permeability 74……………………………………………………………………………

Unit 10 77………………………………………………………………………………………

　 　 Shear Strength of So il 77…………………………………………………………………

　 　 Contam inated Land 83……………………………………………………………………

Unit 11 87………………………………………………………………………………………

　 　 Rankine's Theory of Earth Pressure 87……………………………………………………

　 　 Geotextile唱Reinforced So ilW alls 92………………………………………………………

Unit 12 96………………………………………………………………………………………

　 　 Prestressed Concrete Bridges 96…………………………………………………………

　 　 Prelim inary design ofCabled Stayed Bridges 102………………………………………

Unit 13 106……………………………………………………………………………………

　 　 D esign of Suspension Bridges 106………………………………………………………

　 　 SteelBridge Construction 112……………………………………………………………

Unit 14 115……………………………………………………………………………………

　 　 Welding and Types ofW elds 115…………………………………………………………

　 　 Cracks in F lexuralM embers 121…………………………………………………………

Unit 15 125……………………………………………………………………………………

　 　 Roadway A lignment 125…………………………………………………………………

　 　 Shoulders 131………………………………………………………………………………

Unit 16 135……………………………………………………………………………………

　 　 F lexible PavementD esign 135……………………………………………………………

　 　 PavementM aterialCharacterization 140…………………………………………………

Unit 17 145……………………………………………………………………………………

　 　 Joints of Concrete Pavements 145………………………………………………………

　 　 PavementD rainage 150……………………………………………………………………

Unit 18 155……………………………………………………………………………………

　 　 Composite Columns 155…………………………………………………………………

　 　 Prestressed Concrete 160…………………………………………………………………

Unit 19 163……………………………………………………………………………………

　 　 GeneralEffects of Earthquakes 163………………………………………………………

　 　 Seism ic Resistance ofOrdinary Construction 167………………………………………

Unit 20 170……………………………………………………………………………………

　 　 Construction ProjectM anagement 170……………………………………………………

　 　 Engineering contracts 176…………………………………………………………………

Unit 21 180……………………………………………………………………………………

　 　 Approaches and Types of Estimate forD irectCost Estimation 180……………………

　 　 Techniques forConstruction Cost Estimation 184………………………………………

Unit 22 188……………………………………………………………………………………

　 　 RockM ass C lassification 188……………………………………………………………

　 　 TheNorw egian TunnelingM ethod 194…………………………………………………

Reference 198…………………………………………………………………………………

　 · iv · 土木工程英语

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Unit 1

Tex tCivil Engineering

C iv il engineering is a pro fessional engineering d iscipline that deals w ith the design andconstruction of the physical and natural built environment, including works such as bridges,

roads, canals, dams and buildings. Civil engineering is the oldest engineering discipline after

military engineering, and it was defined to distinguish it from military engineering. It is

traditionally broken into several sub唱disciplines including environmental engineering,

geotechnical engineering, structural engineering, transportation engineering, water resources

engineering, materials engineering, coastal engineering, surveying, urban planning, and

construction engineering.

· Construction Engineering

Construction engineering invo lves p lann ing and execu tion o f the designs fromtransportation, site development, hydraulic, environmental, structural and geotechnical

engineers. As construction firms tend to have higher business risk than other types of civil

engineering firms, many construction engineers tend to take on a role that is more business唱like

in nature: drafting and rev iew ing con tracts , evaluating logistical operations , and closely唱monitoring prices of necessary supplies.

· Environmental Engineering

Env ironm en tal engineering deals w ith the treatm en t o f chem ical, b io logical, and /o r therm alwaste, the purification of water and air, and the remediation of contaminated sites, due to prior

w aste d isposal o r acciden tal con tam ination . Am ong the top ics covered by env ironm en talengineering are pollutant transport, water purification, sewage treatment, and hazardous waste

management(1 ) . Env ironm ental engineers can be invo lved w ith po llu tion reduction , greenengineering, and industrial ecology. Environmental engineering also deals with the gathering of

information on the environmental consequences of proposed actions and the assessment of

effects of proposed actions for the purpose of assisting society and policy makers in the

decision making process.

Env ironm en tal engineering is the con temporary term fo r sanitary engineering, thoughsanitary engineering traditionally had not included much of the hazardous waste management

and environmental remediation work covered by the term environmental engineering. Some

other terms in use are public health engineering and environmental health engineering.

· Geotechnical Engineering

G eo techn ical engineering is an area o f civ il engineering concerned w ith the rock and so ilthat civil engineering systems are supported by. Knowledge from the fields of geology, material

science and testing,m echan ics , and hydrau lics are app lied by geo techn ical engineers to safelyand economically design foundations, retaining walls, and similar structures. Environmental

concerns in relation to groundwater and waste disposal have spawned a new area of study

called geoenvironmental engineering where biology and chemistry are important.

Som e o f the un ique d ifficu lties o f geo techn ical engineering are the resu lt o f the variab ilityand p roperties o f so il. B oundary cond itions are o ften w ell defined in o ther branches o f civ ilengineering, but with soil, clearly defining these conditions can be impossible. The material

properties and behavior of soil are also difficult to predict due to the variability of soil and

limited investigation. This contrasts with the relatively well唱defined material properties of steel

and concrete used in o ther areas o f civ il engineering. So ilm echan ics ,w h ich defines the behav io ro f so il, is comp lex due to stress唱 dependen t m aterial p roperties such as vo lum e change, stress唱strain relationship, and strength(2 ) .· Hydraulic Engineering

H ydrau lic engineering is concerned w ith the flow and convey ance o f flu ids , p rincipallywater. This area of civil engineering is intimately related to the design of pipelines, water

distribution systems, drainage facilities (including bridges, dams, channels, culverts, levees,

storm sewers), and canals. Hydraulic engineers design these facilities using the concepts of fluid

p ressure, flu id statics , flu id dynam ics, and hydrau lics , am ong o thers . W ater resourcesengineering is concerned with the collection and management of water (as a natural resource).

As a discipline it therefore combines hydrology, environmental science, meteorology, geology,

conservation, and resource management. This area of civil engineering relates to the prediction

and management of both the quality and the quantity of water in both underground (aquifers)

and above ground (lakes, rivers, and streams) resources. Water resource engineers analyze and

model very small to very large areas of the earth to predict the amount and content of water as

it flow s in to , through , o r ou t o f a facility although the actual design o f the facility m ay be leftto o ther engineers .· Materials Science

C iv il engineering also includes elem en ts o f m aterials science. C onstruction m aterials w ithbroad applications in civil engineering include ceramics such as Portland cement concrete (PCC)

and ho t m ix asphalt concrete, m etals such as alum inum and steel, and po lym ers such as

·２· 土木工程英语

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polymethylmethacrylate (PMMA) and carbon fibers. Current research in these areas focus

around increased strength, durability, workability, and reduced cost.

· Structural Engineering

Structural engineering is concerned w ith the structural design and structural analy sis o fbuildings, bridges, and other structures. This involves calculating the stresses and forces that

act upon or arise within a structure, and designing the structure to successfully resist those

forces and stresses. Resistance to wind and seismic loadings, especially performance near

resonant frequencies, which affect the overall stability of a structure, are major design concerns.

O ther facto rs such as durab ility and cost are also considered . In add ition to design o f newbuildings, structural engineers may design a seismic retrofit for an existing structure to mitigate

undesirab le perfo rm ance during earthquakes .· Surveying

Survey ing is the p rocess by w hich a survey o r m easures certain d im ensions that generallyoccur on the surface of the Earth. Modern surveying equipment, such as EDM, total stations,

GPS surveying and laser scanning, allow for remarkably accurate measurement of angular

deviation, horizontal, vertical and slope distances. This information is crucial to convert the

data into a graphical representation of the Earth's surface, in the fo rm o f a m ap . Th isinformation is then used by civil engineers, contractors and even realtors. Elements of a

building or structure must be correctly sized and positioned in relation to each other and to site

boundaries and ad jacen t structures . C iv il engineers are trained in them ethods o f survey ing andm ay seek p ro fessional land survey o r status.· Transportation Engineering

T ranspo rtation engineering is concerned w ith m ov ing peop le and goods efficien tly , safely ,and in a m anner conducive to a v ibran t community . Th is invo lves specify ing, design ing,constructing, and maintaining transportation infrastructure which includes streets, canals,

highways, rail systems, airports, ports, and mass transit. It includes areas such as

transportation design, transportation planning, traffic engineering, urban engineering, queuing

theory, pavement engineering, Intelligent Transportation System (ITS), and infrastructure

management.

Notes(1) Am ong the top ics covered by env ironm en tal engineering are po llu tan t transpo rt ,w ater

purification , sew age treatm en t, and hazardous w aste m anagem ent.此句将 Among置于句首 ，因而采用倒装句式 ，全句可译为 ：环境工程所包含的问题有污染物的运输 、水的净化 、污水

·３·Unit １

处理以及危险废物的处理 。(2) So ilm echan ics , w h ich defines the behav io r o f so il, is comp lex due to stress唱 dependen t

m aterial p roperties such as vo lum e change, stress唱 strain relationsh ip , and strength .句中 w hich… o f so il,为非限定性定语从句 ，修饰 so ilm echan ics。 全句可译为 ：土力学确定土的特性 ，是一门复杂的学科 ，这是由于它涉及到依赖应力的材料性能 ，如体积变化 、应力 - 应变关系和强度 。

New Words1. d iscip line［餐disiplin］ n .纪律 ，学科2. geo techn ical［餐d礒i礑待礟餐teknik待l］ a.岩土的 ，土工技术的3. rem ediation［仓ri仓midi餐ei礏待n］ n .补习 ，补救4. sew age［餐sju（礑）id礒］ n .下水道 ，污水5. hazardous［餐h辈z待d待s］ a.危险的 ，冒险的6. con temporary［k待n餐temp待r待ri］ a.当代的 ，同时代的7. san itary ［餐s辈nit待ri］ a.(有关 )卫生的 , (保持 )清洁的 ，清洁卫生的8. spaw n［sp礎礑n］ v .生产 ，产卵 　 n .(鱼等的 )卵 ， (植物 )菌丝 ，产物9. geoenv ironm ental［餐d礒i礑待礟in仓vai待r待n餐mentl］ a.地质环境的10. cu lvert［餐k礍lv待t］ n .管路 ，涵洞11. levee［餐levi］ n .防洪堤 ，码头 ，大堤12. sew er［餐sju待］ n .下水道 ，缝纫者13. statics［餐st 辈 tiks］ n .［物］静力学14.m eteo ro logy ［仓mi礑tj待餐r礎l待d礒i］ n .气象学15. aqu ifer［餐辈kwif待］ n .含水土层 ，蓄水层16. polymethy lmethacry late［仓p礎lime礕ilme餐礕辈kr待leit］ n.聚甲基丙烯酸甲酯 ，有机玻璃17. durab ility ［仓dju待r待餐biliti］ n .经久性 ,耐久性18. w orkab ility［仓w待礑k待餐biliti］ n .和易性 ，易加工性 ，可加工性19. seism ic［餐saizmik］ a.［地］地震的20. retro fit［餐retr待仓fit］ n .改造 ，改进 ，花样翻新21.m itigate［餐mitigeit］ v .减轻22. realto r［餐ri礑待lt待］ n .房地产经纪人23. conducive［k待n餐dju礑siv］ n .益处 　 a.有益的24. in frastructure［餐infr待餐st r礍kt礏待］ n .基础设施 ，下部构造25. convey ance［k待n餐vei待ns］ n .运输 ，财产让与 ，运输工具26. ceram ics［si餐r 辈miks］ n .制陶术 ，制陶业 ，陶瓷（器）27. v ibran t［餐vaibr待nt］ a.振动的28. po lym er［餐p礎lim待］ n .聚合体

·４· 土木工程英语

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Phrases and E xpressions1. retain ing w all　挡土墙2. geo techn ical engineering　岩土工程3. geoenv ironm ental engineering　地质环境工程4. flu id dynam ics　 流体动力学5. EDM (E lectron ic D istanceM easurem ent)　电子测距6. logistical operation　后勤工作7. therm al w aste　热废料8. sew age treatm en t　污水处理9. san itary engineering　卫生工程10. resonan t frequency　共振频率11. queu ing theo ry　排队理论

E xercises1. T ranslate the fo llow ing paragraph in to Ch inese.Engineering has been an aspect o f life since the beginn ings o f hum an existence. C iv il

engineering might be considered properly commencing between4000 and 2000 BC in A ncien tEgypt and Mesopotamia when humans started to abandon a nomadic existence, thus causing a

need for the construction of shelter. During this time, transportation became increasingly

important leading to the development of the wheel and sailing. The construction of Pyramids in

Egyp t (circa 2700唱 2500 BC ) m igh t be considered the first instances o f large structureconstructions. Other ancient historic civil engineering constructions include the Parthenon by

Iktinos in Ancient Greece (447唱 438 BC ), theA pp ianW ay by Rom an engineers (c. 312 BC ), andthe G reatW all o f Ch ina by G eneralM eng T 'ien under o rders from Ch 'in Empero r Sh iHuang T i(c. 220 BC ).

2 . T ranslate the fo llow ing sen tences in to English .(1)土木工程可分为许多分支 ，如结构工程 、交通工程 、环境工程和岩土工程等 。(2)与其他土木工程分支不同 ，在岩土工程中 ，很难明确定义边界条件 。(3)结构工程涉及计算结构中的应力和内力等作用效应 ，以及确定结构构件的材料 、

尺寸和外形等 。(4)采用 GPS和激光扫描技术可精确测量角度 、水平和垂直距离等 。(5)过去卫生工程基本不涉及当今环境工程所包括的危险废物处理 。

·５·Unit １

Reading Material

SkyscraperA sky scraper is a very tall, con tinuously hab itab le bu ild ing. There is no o fficial defin ition

o r a p recise cu to ff heigh t above w hich a bu ild ing m ay clearly be classified as a sky scraper.However, as per usual practice in most cities, the definition is used empirically, depending on

the relative impact of the shape of a building to a city's overall sky line. Thus , depend ing on theaverage heigh t o f the rest o f the bu ild ings and /o r structures in a city , even a bu ild ing o f 80m eters heigh t (app roxim ately 262 ft) m ay be considered a sky scraper p rov ided that it clearlystands out above its surrounding built environment and significantly changes the overall skyline

o f that particu lar city .The w ord sky scraper o riginally referred to a nau tical term tallm ast o r its m ain sail on a

sailing ship. The term was first applied to buildings in the late19th cen tury as a resu lt o fpublic amazement at the tall buildings being built in Chicago, Detroit and New York City.

The structural defin ition o f the w ord sky scraper w as refined later by arch itecturalhistorians, based on engineering developments of the1880s that had enab led construction o f tallm ulti唱 sto ry bu ild ings . Th is defin ition w as based on the steel skeleton— as opposed toconstructions of load唱bearing masonry, which passed their practical limit in1891 w ith Chicago'sMonadnock Building. Philadelphia's C ity Hall, comp leted in 1901, still ho lds claim as the w orld 'stallest load唱bearing masonry structure at167 m (548 ft). T he steel fram e developed in stages o fincreasing self唱 sufficiency , w ith several bu ild ings in Chicago and N ew York advancing the

technology that allowed the steel frame to carry a building on its own. Today, however, many

o f the tallest sky scrapers are bu ilt alm ost en tirely w ith rein fo rced concrete. Pump s and sto ragetanks m ain tain w ater p ressure at the top o f sky scrapers .

A loose conven tion in the U nited S tates now draw s the low er lim it o f a sky scraper at 150m eters (500 ft).A sky scraper taller than 300m eters (984 ft)m ay be referred to as supertall. Inthe U nited S tates, the supertall conven tion is 100 sto ries , w h ich is equal to 1000 feet. Sho rter

buildings are still sometimes referred to as skyscrapers if they appear to dominate their

surroundings.

The som ew hat arb itrary term sky scraper shou ld no t be con fused w ith the sligh tly lessarbitrary term highrise, defined by the Emporis Standards Committee as "A high唱rise building is

a mu lti唱 sto ry structure w ith at least 12 floo rs o r 35 m eters (115 feet ) in heigh t." A llskyscrapers are highrises, but only the tallest highrises are skyscrapers. Habitability separates

sky scrapers from tow ers and m asts . Som e structural engineers define a h ighrise as any verticalconstruction fo r w h ich w ind is a m o re sign ifican t load facto r than w eigh t is . N o te that th iscriterion fits not only highrises but also some other tall structures, such as towers.

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The w ord sky scraper o ften carries a conno tation o f p ride and ach ievem en t. T heskyscraper, in name and social function, is a modern expression of the age唱old symbol of the

world center or axis mundi: a pillar that connects earth to heaven and the four compass

directions to one another.

M odern sky scrapers are bu ilt w ith m aterials such as steel, glass , rein fo rced concrete andgranite, and routinely utilize mechanical equipment such as water pumps and elevators. Until

the 19th cen tury , bu ild ings o f over six sto ries w ere rare, as hav ing great numbers o f stairs toclimb was impractical for inhabitants, and water pressure was usually insufficient to supply

running water above50m (164 ft ). H ow ever, desp ite the lack o f san itation , the first h ighrisehousing dates back to the1600s in som e p laces. In Edinburgh , Sco tland , fo r examp le, adefensive city wall defined the boundaries of the city. Due to the restricted land area for

development, the houses increased in height instead. Buildings of11 sto ries w ere comm on , andthere are reco rds o f bu ild ings as h igh as 14 sto ries .M any o f the stone唱 built structures can stillbe seen today in the o ld tow n o f Edinburgh .

The o ldest iron fram ed build ing in the w o rld is the F laxm ill (also locally know n as the "Maltings"), in Shrewsbury, England. Built in1797, it is seen as the "grandfather o f sky scrapers" dueto its fireproof combination of cast iron columns and cast iron beams developed into the

modern steel frame that made modern skyscrapers possible. Unfortunately, it lies derelict and

needs much investment to keep it standing. On31 M arch 2005, it w as announced that EnglishH eritage w ou ld buy the F laxm ill so that it cou ld be redeveloped .

The firs t sky scraper w as the ten唱 sto ry H om e Insurance Build ing in Chicago , bu ilt in 1884唱1885.W h ile its heigh t is no t considered unusual o r very im p ressive today , the arch itect,M ajo rW illiam Le B aron Jenney , created the firs t load唱 bearing structural fram e. In th is bu ild ing, a steelfram e supported the en tire w eigh t o f the w alls , instead o f load唱 bearing w alls carry ing the

weight of the building, which was the usual method. This development led to the "Chicago

skeleton" form of construction. After Jenney's accomp lishm ent the sky w as tru ly the lim it asfar as building was concerned.

M ost early sky scrapers em erged in the land唱 strapped areas o f Ch icago , London , and N ewYork tow ard the end o f the 19th cen tury . London bu ilders soon found bu ild ing heigh ts lim iteddue to a comp lain t from Q ueen V icto ria, ru les that con tinued to exist w ith few excep tions un tilthe 1950s . concerns abou t aesthetics and fire safety had likew ise hampered the developm en t o fsky scrapers across con tinen tal Europe fo r the first half o f the tw en tieth cen tury (w ith the

notable exceptions of the26唱 sto rey B oeren to ren in A ntw erp , B elgium , bu ilt in 1932, and the31唱 sto rey T o rre P iacen tin i in G enoa, Italy , bu ilt in 1940). A fter an early competition betw eenNew York City and Chicago for the world's tallest bu ild ing,N ew York took a firm lead by 1895w ith the comp letion o f the Am erican Surety Build ing. D evelopers in Chicago also foundthemselves hampered by laws limiting height to about40 sto rey s , leav ing N ew Yo rk to ho ldthe title of tallest building for many years. New York City developers then competed among

·７·Unit １

themselves, with successively taller buildings claiming the title of "world's tallest" in the 1920sand early 1930s , cu lm inating w ith the comp letion o f the Chry sler Bu ild ing in 1930 and theEmpire State Building in1931, the w orld 's tallest bu ild ing fo r fo rty y ears . F rom the 1930sonwards, skyscrapers also began to appear in Latin America (S本o Paulo, Caracas, Mexico City)

and in A sia (T oky o , Shanghai,H ong K ong, S ingapo re).T oday , sky scrapers are an increasingly comm on sigh t w here land is scarce, as in the

centres of big cities, because of the high ratio of rentable floor space per area of land.

Skyscrapers, like temples and palaces in the past, are considered the symbols of a city'seconomic power.

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Unit 2

Tex tAnalysis of Plane Structures

· Equations of Equilibrium

A sy stem o f fo rces is said to be in equ ilibrium w hen the resu ltan t o f all the fo rces and theresu ltan t o f all the m om ents at one po in t are equal to zero . Fo r a three唱 dim ensional sy stem

with a set of mutually perpendicular axes,x, y and z, six conditions must be satisfied. These

six conditions can be stated in mathematical terms as follows:

∑ Px ＝ ∑ Py ＝ ∑ P z ＝ ０

∑ Mx ＝ ∑ My ＝ ∑ M z ＝ ０

W here Px is the componen t o f any fo rce in the x direction andMx is them om ent o f a fo rcePabou t the x axis.

In fact it is no t necessary fo r the axes to be o rthogonal— any three axes can be chosen fo rthe summ ation o f the fo rces , and any three axes fo r the summ ation o f them om ents. The case o fparallel axes w ou ld o f course be excep ted .

If the sy stem is cop lanar, that is say P z = 0 and ∑ Mx ＝ ∑ My ＝ ０ , then there w ill beon ly three cond itions o f equ ilibrium

∑ Px ＝ ∑ Py ＝ ０

∑ M z ＝ ０

　 　 Several special cases arise fo r a cop lanar sy stem .1. If there are on ly tw o fo rces acting on a body that is in equ ilibrium , then the fo rcesmust

be equal and opposite.2 . If there are on ly three fo rces acting on a body that is in equ ilibrium , then the three

forces must be concurrent.

3.A set o f cop lanar fo rces no t in equ ilibrium can be reduced to a single resu ltan t fo rce o rresu ltan t m om en t.

· Stability and Determinacy of Reactions

If w e consider a tw o唱 dim ensional sy stem w ith know n app lied loads, the free唱 bodydiagram can be drawn showing all the unknown reactions. With the system in static equilibrium

the three cond itions o f equ ilibrium can be app lied , and w ill resu lt in three equations in term s o fthe unknow n reactions . The equations can then be so lved simu ltaneously . Fo r a comp lete

solution there will in general be a limitation of three unknowns.

If there are less than three unknow n independen t reactions , there w ill no t be sufficien tunknowns to satisfy the three equations and the system will not be in equilibrium. It is then

termed statically unstable so far as the external supports are concerned.

If there arem ore than three unknow ns, the equations canno t be comp letely so lved and thesy stem w ill be statically indeterm inate o r redundan t. Fo r examp le if there w ere five unknow ns ,tw o o f them cou ld be assigned any value, the rem ain ing three cou ld then be found from the

equations of equilibrium and would be entirely dependent on the values chosen for the first

two reactions(1 ) . T h is does no t m ean that a statically indeterm inate sy stem is inso lub le, thename implies that the system cannot be solved by the use of statics alone. Additional

information will be required about the manner in which the system deforms under the applied

loading. This type of structure is generally described as redundant and methods of solution will

be d iscussed later.

F ig.2.1　 Tw o唱 dimensional structural sy stemIn F ig.2 .1 several examp les o f d ifferen t structures are show n . T he beam , in F ig.2 .1 (a) , has

on ly tw o unknow n vertical reactions and w ill therefo re be an unstab le sy stem . T he beam , in F ig.2 .1 (b ) , has four unknow n reactions, one at the left唱 hand end and three at the righ t唱 hand end , thebeam is therefo re statically indeterm inate to the first degree, that is there is one m o re reaction

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than can be determined by statics alone. The portal frame, in Fig.2 .1 (c ) , is also staticallyindeterminate to the first degree, as there will be a vertical and horizontal reaction at each

support. The frame, in Fig.2 .1 (d ) , is statically determ inate fo r reactions, bu t it w ill be seen laterthat it is statically indeterm inate so far as the fo rces in them em bers are concerned . It shou ld beno ted that in all cases the question o f statical determ inacy is independen t o f the load ing app liedto the sy stem . Reverting to sy stem a: if vertical external fo rces are app lied itm igh t be temp tingto say that there w ou ld on ly be vertical com ponen ts o f reaction at each support, the suppo rt

system shown is quite capable of sustaining these, hence the system is stable(2 ) . H ow ever aninstability arises if a horizontal force, however, small, is applied. It can be seen that the

question of stability and determinacy of the reactions must be independent of the actual loading

that is app lied to the structure. In effect it w ou ld be no use design ing a structure to w ithstandonly vertical loads, if it collapsed when a small lateral wind load was applied. In in Fig.2 .1 (e)we have a case where the lines of action of three supports, shown dotted, all pass through a

single point. Any loading system that is applied to the beam would have a moment about the

point of intersection and this cannot be resisted by the reactions, hence the beam would tend to

ro tate abou t the po in t. B ased on th is fact a general statem en t can bem ade: the reactionsm ust becapab le o f resisting any sm all d isp lacem ent o r ro tation that is app lied to the structure.· Calculation of Reactions

This can p robab ly best be illustrated by one o r tw o examp les, bu t befo re dealing w ithspecific cases we ought to consider the different types of loading that may be applied. A

concentrated load is assumed to be acting at a point; in actual fact this is an impossibility as

there would have to be an infinite stress in the member at the point directly under the load. In

p ractice the m aterial under the load w ill defo rm and the load w ill then be sp read over a sm allarea hence reducing the stress concentration. However, for the purpose of calculation it will be

sufficien tly accurate to assum e that the load is acting at a po in t.A no ther very comm on type o fload is referred to as a un ifo rm ly d istribu ted load (U .D .L .). A s the nam e suggests , the load is

distributed along the surface of the member with a constant value per unit length, or per unit

area.

A ssum e that the m om en t abou t po in t C is requ ired fo r the un ifo rm ly d istribu ted load pper unit length, extending over length b, see Fig.2.2.C onsider an elem en t dx of the load distant

x from C. the moment of this'concen trated ' load abou t C is p xdx. The total moment is found

by in tegrating th is exp ressionMC ＝∫

a＋ b

ap xd x ＝ pb a ＋ b

２

·１１·Unit ２

Fig.2.2　 Calculation of reactions　 　 It is clear from above equation that the moment can be found by replacing the U.D.L. by

a po in t load , equal in m agn itude to its to tal value, and acting at its cen tro id .If the load w as no t un ifo rm ly d istribu ted bu t w as som e function o f x, the moment could

be found in a similar manner. The load would be replaced by a concentrated load equal to the

total distributed load and acting at the centroid of the load system.

Notes(1) Fo r examp le if there w ere five unknow ns , tw o o f them cou ld be assigned any value, the

rem ain ing three cou ld then be found from the equations o f equ ilibrium and w ould be en tirelydependent on the values chosen for the first two reactions.句中 if引导的从句为条件状语从句 ，chosen引导的过去分词短语作后置定语 ，修饰 values。全句可译为 ：例如 ，如果有五个未知量 ，可以给其中两个指定任意值 ，那么剩余的三个可以由平衡方程得到 ，它们完全取决于前两个反力所选的值 。

(2) Reverting to sy stem a: if vertical external fo rces are app lied it m igh t be temp ting tosay that there would only be vertical components of reaction at each support, the support

system shown is quite capable of sustaining these, hence the system is stable.句中 if引导的从句为条件状语从句 ， it m igh t be temp ting to say that意为“或许可以说 … … ” 。 全句可译为 ：回到系统 a，如果施加竖向外力 ，可以认为每一个支座反力只有竖直分量 ，则所示的支撑系统完全能承受这些荷载 ，因此系统是稳定的 。

New Words1. resu ltan t［ ri餐 z礍 lt待 nt］ n .合力2.mutually ［餐m ju :t∫ u待 li］ a.相互地3. perpend icu lar［仓p待 :p待 n餐d ik jul待］ a.垂直的4. o rthogonal［礎 :餐礕礎 g待 n l］ a.正交的 ，互相垂直的5. parallel［餐p辈 r待 lel］ a.平行的 ，并联的6. cop lanar［ k待 u餐p lein待］ a.共面的7. concurren t［ k待 n餐k礍 r待 nt］ a.同时发生的 ，并存的

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8. static［餐 st辈 tik］ a.静力的9. po rtal［餐p礎 :t待 l］ n .门式框架10. inso lub le［ in餐 s礎 ljub l］ a.不能解决的 ，不能溶解的11. in tegrate［餐 in tigreit］ v .积分12. cen tro id［餐 sen tr礎 id］ n .重心 ，形心 ，质量中心

Phrases and E xpressions1. free唱 body d iagram　隔离体图形2. equations o f equ ilibrium 　平衡方程3. three唱 dim ensional sy stem 　三维系统4. statically indeterm inate sy stem 　静不定系统5. po rtal fram e　门式框架6. in effect　实际上7. deal w ith　涉及8. concen trated load　集中荷载9. stress concen tration　应力集中10. un ifo rm ly d istribu ted load　 均布荷载

E xercises1. T ranslate the fo llow ing paragraph in to Ch inese.C ertain types o f structures, fo r examp le a dam , rely partly on their largem ass to resist the

app lied fo rces ; w e shall no t concern ourselves w ith these types o f structure in th is text. If astructure is stationary or moving with a constant velocity, the resultant of all the applied loads

and reactions w ill be zero , and the structure is said to be in equ ilibrium . If how ever thevelocity is not constant it is necessary to consider inertia forces in addition to the applied

forces. We shall confine our attention to structures that are in static equilibrium. Very often it

w ill be found that w e have to simp lify and idealise a structure in o rder to ob tain a theo reticalsolution that will give us a fairly good idea of the loading in individual members. When the

member loads have been deduced we are able to proceed with the design of each member in

turn.

2. T ranslate the fo llow ing sen tences in to English .(1)当所有力的合力和某一点所有弯矩的合力矩等于零时 ，力系处于平衡状态 。(2)如果未知量超过三个 ，就不能完全求解平衡方程 ，系统为静不定 。(3)反力必需能够抵抗施加在结构上的任何很小的位移和转动 。(4)为了计算 ，假设荷载作用在一点是足够精确的 。(5)可以看出 ，稳定问题和反力的确定必需独立于施加在结构上的实际荷载 。

·３１·Unit ２

Reading Material

Design of Beams

· General Design Principles

P rim ary variab les in design ing beam s include the fo llow ing: spans , m ember spacing,loading types and magnitudes, material type, cross唱sectional sizing and shaping, and assembly

or fabrication techniques. The more a design situation is constrained, the easier it is to design a

specific m ember. The easiest cond ition is w hen every th ing is specified bu t a m ember's size, inwhich case the process can almost be deterministic. As more and more variables are brought

into play, as is the normal case in a true design situation, the process becomes considerably

more difficult and less deterministic. Iterative approaches are common where several beam

designs for different variable sets are developed and compared according to prespecified

criteria.

A ny beam design must m eet specified strength and stiffness criteria fo r safety andserviceability. Design approaches for meeting criteria are highly dependent on the materials

selected for use. Timber, steel and reinforced concrete beams will be discussed extensively in

following sections. Even within a specified material context, however, broadly differing

attitudes may be taken to member design. The size and shape of a member may be determined

on the basis o f them ost critical fo rce state anyw here in the beam , and th is sam e size and shapeused throughou t the length o f the m ember. T he m ember is thus w orked to its m aximumcapacity at one section only. This strategy is used widely for reasons of ease and construction

exped iency .A n attemp t m ay be m ade to vary the size and shape o f a m ember along its lengthin response to the nature and m agn itude o f the fo rce state p resen t at specific locations , w ith

the intent to have the beam equally stressed along its length and commensurate advantages of

material economy. Shaping a beam along its length, however, may prove difficult, depending on

the construction app roach selected . In fo llow ing sections w e exp lo re these and o ther designapproaches.

· Strength and Stiffness Control

Beam s must be sized and shaped so that they are su fficien tly strong to carry app liedloadings without undue material distress or deformations. When the design act is highly limited

to that o f find ing a beam size and shape fo r a given span , load ing and m aterial con text, theproblem reduces to a fairly simple one of finding section properties for a member such that the

actual stresses generated in the beam at any po in t are lim ited to p redeterm ined safe levelsdependent on the properties of the materials used.

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Shear and m om ent d iagram s are typ ically firs t draw n . The m aximum bending m om en t(Mm ax ) is determ ined . Fo r sim p le steel o r timber m embers w ith symm etrical cross sections ,initial member size estimates are made using the concept of a "required" section modulus (S).Thus, S req 'd = Mm ax /F b .A m ember w ith a section m odulus equal to , o r greater than , th is value isselected as a trial s ize.Rem ain ing stresses and deflections are checked . The p rocedure describedstarted w ith a m ember size based on bend ing.D epend ing on the situation , a trialm ember size

may be determined based on deflections or other type of stress.

· Cross唱Sectional Shapes

The m om en t o f inertia (I) and the section modulus (S) are of primary importance in beam

design .A comm on design ob jective is to p rov ide the requ ired I or S for a beam carrying a given

load ing w ith a cross唱 sectional con figuration that has the sm allest possib le area. T he to talvolume of material required to support the load in space would then be reduced. Alternatively,

the ob jective cou ld be stated in term s o f tak ing a given cross唱 sectional area and o rgan iz ing th ism aterial so that the m aximum I or S value is obtained, thus allowing the beam to support the

maximum possible external moment.

The basic p rincip le fo r m axim iz ing the m om ent o f inertia obtainab le from a given area iscontained in the definition of the moment of inertia, which is I= y２ dA. The contribution of a

given element of area (dA) to the total moment of inertia of a section depends on the square of

the d istance o f th is elem ental area from the neu tral axis o f the section . The sensitiv ity to thesquare of the distance is important. This would lead one to expect that for a given amount of

material, the best way to organize it in space is to remove it as far as practically possible from

the neu tral axis o f the section ( i.e., m ake the section deep w ith m ost o f the m aterial at theextremities). Consequently beams with high depth/width ratios are usually more efficient than

ones with shallower proportions.

The d iscussion thus far has focused on w ay s o f increasing the m om ent o f inertia (I) of a

section. It should be recalled, however, that in design of a beam, the measure that is actually of

p rim ary impo rtance is the I／ ym ax value o f a section . In cases w here the section is symm etricabout the neutral axis, increasing theI value automatically increases the section modulus,S. In

nonsymm etric sections such as T beam s, the design must be based on the cond ition that themaximum bending stress at any point on the beam is limited to the allowable stresses. At a

section this point is defined byym ax and occurs on one face o f the section . The o ther face,w itha value o f y less thanym ax , is therefo re understressed .H ence, the use o f such a section is no tadvantageous in beams made of homogeneous materials such as steel. When a composite

material such as reinforced concrete is used, however,T beams can have definite advantageous

p roperties .· Material Property Variations

In add ition to changing the w ay m aterial is d istribu ted at a cross section , it is also

·５１·Unit ２

possible to vary the types of material used within a given cross section so that there is a better

m atch ing betw een the stress state p resen t and the characteristics o f the m aterial used . Th isprinciple finds its manifestation in beams as diverse as those made of laminated wood and

reinforced concrete.

· Shaping a Beam along Its Length

The p rev ious section generally considered w ay s o f design ing beam s o f d ifferen t m aterialsat a single cross section. This section considers the shaping of a beam along its axis as a way of

imp rov ing the overall efficiency o f a beam .The in ten tion beh ind vary ing the shape o f am emberalong its axis is to p rov ide a better fit betw een the characteristics o f a beam and the shears andm om ents w hich typ ically vary along the length o f a beam .· Varying Support Locations and Boundary Conditions

M anipu lating suppo rt cond itions can lead to m ajo r econom ies in the use o f m aterials . T heimm ediate in ten t o f such m anipu lations is usually to reduce the m agn itudes o f the design

moments present or to alter their distribution. A classic way of reducing design moments is to

use can tilever overhangs on beam s. The effect o f can tilevering one end o f a simp ly suppo rtedbeam with uniform loads is to cause a reduction in the positive moment present while a

negative moment develops at the base of the cantilever over the support. The greater the

cantilever, the higher the negative moment becomes and the lower the positive moment

becomes. The cantilever can be extended until the negative moment even exceeds the positive

moment.

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Unit 3

Tex tNormal Stress in Beams

· The Basic Kinematic Assumption

Consider a typ ical elem ent o f the beam betw een tw o p lanes perpend icu lar to the beamaxis, as shown in Fig.3.1. In side v iew , such an elem en t is iden tified in the figure as abcd .W hensuch a beam is sub jected to equal end m om ents M z acting around the z axis , F ig.3 .1 (b ), th is

beam bends in the plane of symmetry, and the planes initially perpendicular to the beam axis

tilt slightly. Nevertheless, the lines such as ad and bc becominga＇d＇ and b＇c＇ rem ain straigh t.This observation forms the basis for the fundamental hypothesis of the flexure theory. It may

be stated thus : p lane sections through a beam taken no rm al to its axis rem ain p lane after thebeam is subjected to bending.

F ig.3.1　 A ssumed behavior o f elastic beam in bendingIn pure bend ing o f a p rism atic beam , the beam axis defo rm s in to a part o f a circle o f rad ius

r, as shown by Fig.3.1(b ). Fo r an elem ent defined by an in fin itesim al angle dθ, the fiber length

ef o f the beam axis is given as ds ＝ r dθ. Hence,

dθd s ＝ １ρ ＝ κ (3 .1)

w here the recip rocal o f r defines the axis curvatureκ.The fiber length gh located on a rad ius (r唱y ) can be found similarly, and the difference

between fiber lengths gh and ef can be expressed as (唱ydθ), which is equal to du, since the

deflection and rotations of the beam axis are very small. Then one obtains the normal strainεx= du/dx, as

εx ＝ － κy (3 .2)　 　 Th is equation estab lishes the exp ression fo r the basic k inem atic hypo thesis fo r the flexuretheo ry : the strain in a ben t beam varies along the beam dep th linearly w ith y .· The Elastic Flexure Formula

By usingH ooke's law , the exp ression fo r the no rm al strain given by Eq .（ 3.2） can be recastin to a relation fo r the no rm al longitud inal stress

σx ＝ Eεx ＝ － Eκy (3 .3)T o satis fy equ ilibrium , the sum o f all fo rces at a section in pure bend ing must van ish ,

∫A

σx d A ＝ ０

w hich can be rew ritten as－ Eκ∫

A

yd A ＝ ０

By defin ition , the in tegral∫A

yd A ＝ y－ A

w here y－ is the d istance from the o rigin to the cen tro id o f an area A . S ince the in tegral equalszero here and area A is not zero, distancey－ must be set equal to zero . Therefo re, the z axis

must pass through the centroid of a section. In bending theory, this axis is also referred to as

the neutral axis of a beam. On this axis both the normal strainεx and the no rm al stress σx arezero. Based on this result, linear variation in strain is schematically shown in Fig.3.1 (c). T hecorresponding elastic stress distribution in accordance with Eq.(3.3 ) is show n in F ig.3 .1 (d ).Both the absolute maximum strainεm ax and the abso lu tem aximum stressσm ax occur at the largestvalue o f y.

Equilibrium requ ires the add itional cond ition that the sum o f the externally app lied andthe internal resisting moments must vanish(1 ) . Fo r the beam segm ent in F ig.3 .1(d ), th is y ields

M z ＝ Eκ∫A

y２ d AIn m echan ics , the last in tegral, depending on ly on the geom etrical p roperties o f a cross唱 sectionalarea, is called the rectangu lar m om ent o f inertia o r the second m om ent o f inertia o f the area Aand is designated byI. Since I must always be determined withrespect to a particu lar axis , it is

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o ften m ean ingfu l to iden tify it w ith a subscrip t co rresponding to such an axis . Fo r the caseconsidered, this subscript isz, that is,

I z ＝∫A

y２ d A (3 .4)　 　 W ith th is no tation , the basic relation giv ing the curvature o f an elastic beam subjected to aspecified m om en t is exp ressed as

κ ＝ M z

E I z(3 .5)

　 　 By substitu ting Eq .(3 .5) in to Eq .(3 .3), the elastic flexure fo rm ula fo r beam s is ob tained :σx ＝ － M z

I zy (3 .6)

It is custom ary to recast the flexure fo rm ula to give the m aximum norm al stress σm ax directlyand to designate the value|y |m ax by c, as in Fig.3.1(c). It is also comm on p ractice to d ispensewith the sign, as in Eq.(3.7 ), as w ell as w ith the subscrip ts on M and I (2 ) . S ince the no rm alstresses must develop a couple statically equivalent to the internal bending moment, their sense

can be determ ined by inspection .O n th is basis , the flexure fo rmu la becom es

σmax ＝ McI (3 .7)

· Elastic Strain Energy in Pure Bending

U sing the section "E lastic S train Energy fo r U niaxial S tress" as the basis , the elastic strainenergy fo r beam s in pure bend ing can be found . B y substitu ting the flexure fo rm ula in to theequation of elastic strain energy and integrating over the volume,V , of the beam, the expression

fo r the elastic strain energy ,U, in a beam in pure bending is obtained:

U ＝∫L

０

M２

２EI d x (3 .8)

· Unsymmetric Bending and Bending with Axial Loads

Consider the rectangu lar beam show n in F ig.3 .2 , w here the app lied m om ents M act in the

p lane abcd .B y using the vecto r rep resen tation fo rM shown in Fig.3.2(b ), th is vecto r fo rm s anangleα with the z axis and can be resolved into the two components,My and M z . S ince thecross section for this beam has symmetry about both axes, Eq.(3.3 ) to Eq .(3 .7 ) are d irectlyapplicable. By assuming elastic behavior of the material, a superposition of the stresses caused

by My and M z is the so lu tion to the p rob lem .H ence, using Eq .(3 .6),σx ＝ － M z y

I２ ＋ My zI y

(3 .9)

·９１·Unit ３

F ig.3.2　 Unsymmetrical bending of a beam w ith doubly symmetric cross section

Fig.3.3　 Bending of unsymmetric cross section　 　 A line of zero stress, i.e., a neutral axis, forms at an angle with thez axis and can be

determined from the following equation:

tanβ ＝ I zI ytanα (3 .10)

In general, the neu tral axis does no t co incide w ith the no rm al o f the p lane in w h ich the app liedm om ent acts .

Superposition can again be emp loy ed to include the effect o f axial loads , lead ing Eq .(3 .9)to be generalized into

σx ＝ PA － M z y

I２ ＋ My zI y

(3 .11)w here P is taken positive for axial tensile forces and bending takes place around the two

principal y and z axes. Further, if an applied axial force causes compression, a member must be

stocky , lest a buck ling p rob lem o f the type considered in a later section arises.

Notes(1) Equ ilibrium requ ires the add itional cond ition that the sum o f the externally app lied and

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the internal resistingm om ents must van ish .句中 that… must van ish为同位语从句 ，其同位语为 the add itional cond ition .全句可译为 :平衡需要进一步的条件 ，即外部施加弯矩和内部抵抗弯矩之和必须为零 。

(2) It is also comm on p ractice to d ispense w ith the sign , as in Eq .(3 .7), as w ell as w ith thesubscrip ts on M and I. 句首的 It为形式主语 ，真正的主语为动词不定式 to d ispense w ith… ，全句可译为 ：而且通常的做法是去掉正负号 ，如在方程 3.7中那样 ，同时也去掉 M和 I的下标 。

New Words1. k inem atic［仓kaini餐m 辈 tik］ a.运动学的 ，运动学上的2. perpend icu lar［仓p待礑p待n餐dikjul待］ a.垂直的 ，正交的 　 n .垂线3. tilt［tilt］ v .(使 )倾斜 ， (使 )翘起4. hypo thesis［hai餐p礎礕isis］ n .假设5. p rism atic［priz餐m 辈 tik］ a.棱镜的 ，棱柱的 ，等截面的6. in fin itesim al［in仓fin待餐tesim待l］ a.无穷小的 ，极小的 　 n .极小量 ，无限小7. deflection［di餐flek礏待n］ n .挠度 ，偏斜 ，偏转8. recast［餐ri礑餐k袋礑st］ v .重铸 ，重做9. longitud inal［l礎nd礒itju礑dinl］ a.经度的 ，纵向的10. cen tro id［餐sentr礎id］ n .质心 ，形心11. designate［餐dezigneit］ v t.指明 ，指派12. coup le［餐k礍pl］ n .力偶 ， (一 )对 ， (一 )双13. un iaxial［餐ju礑ni餐辈ksi待l］ a.单轴的14. superposition［仓sju礑p待p待餐zi礏待n］ n .叠加 ，重叠 ，叠合15. co incide［仓k待uin餐said］ v i.一致 ，符合 ，重合16. no rm al［餐n礎礑m待l］ n .正规 ，常态 ，法线17. stocky ［餐st礎ki］ a.矮壮的 ，短而粗的18. buck ling［餐b礍kli礗］ n .屈曲19. recip rocal［ri餐sipr待k待l］ a.相应的 ，倒数的 　 n .倒数20. van ish［餐v辈ni礏］ v i.消失 ，［数］成为零21. in tegral［餐inti礔r待l］ a.完整的 ，整体的 ，［数学］积分的 　 n .［数学］ 积分

Phrases and E xpressions1. perpend icu lar to　垂直于 … …2. neu tral axis　中性轴3.m om ent o f inertia　惯性矩4. second m om ent o f inertia　二次惯性矩

·１２·Unit ３

5. strain energy　应变能6. co incide w ith　与 … …重合7. axis curvature　轴向曲率8. no rm al strain　正应变9. un iaxial stress　 单轴应力

E xercises1. T ranslate the fo llow ing paragraph in to Ch inese.Th is equation show s that the longitud inal strains Ex are d irectly p ropo rtional to the

curvature and to the distancey from the neutral surface. When the fibre under consideration is

below the neu tral axis , the d istance y is positive and the strain is positive (tension). When the

fibre is above the neu tral surface, bo th y andεx w ill be negative, ind icating that the m aterial isin comp ression . The equation w as derived so lely from the geom etry o f the defo rm ed bar, and

hence it is independent of the properties of the material. Thus, the equation is valid when the

material of the beam has any type of stress唱strain diagram.

2. T ranslate the fo llow ing sen tences in to English .(1)混凝土梁可能会受到弯矩和轴力的共同作用 ，从而使梁中产生正应力和剪应力 。(2)梁受弯变形后 ，与梁轴线垂直的平面仍保持平面 。(3)推导说明中性轴总是通过截面的形心 。(4)通过叠加 ，就可考虑轴力和弯矩的共同影响 。(5)此向量可分解为相应于 x轴和 y 轴的两个分量 。

Reading Material

Structural AnalysisStructural analy sis comp rises the set o f phy sical law s and m athem atics requ ired to study

and p red ict the behav io r o f structures. The sub jects o f structural analy sis are engineeringartifacts whose integrity is judged largely based upon their ability to withstand loads; they

commonly include buildings, bridges, aircraft, and ships. Structural analysis incorporates the

fields of mechanics and dynamics as well as many failure theories. From a theoretical

perspective the primary goal of structural analysis is the computation of deformations, internal

fo rces , and stresses. In p ractice, s tructural analy sis can be v iew ed m ore abstractly as a m ethodto drive the engineering design p rocess o r p rove the soundness o f a design w ithou t a

dependence on directly testing it.

· Analytical Methods

T o perfo rm an accurate analy sis a structural engineermust determ ine such in fo rm ation as

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structural loads , geom etry , suppo rt cond itions and m aterials p roperties . The resu lts o f such ananaly sis typ ically include suppo rt reactions, stresses and d isp lacem ents. Th is in fo rm ation isthen compared to criteria that indicate the conditions of failure. Advanced structural analysis

may examine dynamic response, stability and non唱linear behavior.

There are three app roaches to the analy sis : the m echan ics o f m aterials app roach (alsoknown as strength of materials), the elasticity theory approach (which is actually a special case

o f the m ore general field o f continuum m echan ics ), and the fin ite elem ent app roach . The firs ttwo make use of analytical formulations which apply mostly to simple linear elastic models,

lead to closed唱form solutions, and can often be solved by hand. The finite element approach is

actually a num erical m ethod fo r so lv ing d ifferen tial equations generated by theo ries o fmechanics such as elasticity theory and strength of materials. However, the finite element

method depends heavily on the processing power of computers and is more applicable to

structures of arbitrary size and complexity.

Regard less o f app roach , the fo rm ulation is based on the sam e three fundam ental relations :equ ilibrium , constitu tive, and compatib ility . The so lu tions are app roxim ate w hen any o f theserelations are only approximately satisfied, or only an approximation of reality.

· Limitations

Each m ethod has no tew orthy lim itations . Them ethod o f m echan ics o f m aterials is lim itedto very simp le structural elem en ts under relatively sim p le load ing cond itions. T he structural

elements and loading conditions allowed, however, are sufficient to solve many useful

engineering problems. The theory of elasticity allows the solution of structural elements of

general geometry under general loading conditions, in principle. Analytical solution, however, is

lim ited to relatively sim p le cases . The so lu tion o f elasticity p rob lem s also requ ires the so lu tiono f a sy stem o f partial d ifferen tial equations , w h ich is considerab ly m ore m athem aticallydemanding than the solution of mechanics of materials problems, which require at most the

solution of an ordinary differential equation. The finite element method is perhaps the most

restrictive and most useful at the same time. This method itself relies upon other structural

theories (such as the other two discussed here) for equations to solve. It does, however, make it

generally possib le to so lve these equations , even w ith h ighly comp lex geom etry and load ingconditions, with the restriction that there is always some numerical error. Effective and reliable

use o f th is m ethod requ ires a so lid understand ing o f its lim itations .· Strength of Materials Methods （Classical Methods）

The sim p lest o f the three m ethods here d iscussed , the m echanics o f m aterials m ethod isavailable for simple structural members subject to specific loadings such as axially loaded bars,

p rism atic beam s in a state o f pure bend ing, and circu lar shafts sub ject to to rsion . The so lu tionscan under certain cond itions be superim posed using the superposition p rincip le to analy ze a

·３２·Unit ３

member undergoing combined loading. Solutions for special cases exist for common structures

such as thin唱walled pressure vessels.

For the analy sis o f en tire sy stem s , th is app roach can be used in con junction w ith statics ,giv ing rise to the m ethod o f sections and m ethod o f jo in ts fo r truss analy sis , m om en tdistribution for small rigid frames, and portal frame and cantilever method for large rigid frames.

Excep t fo r m om en t d istribu tion , w h ich cam e in to use in the 1930s , these m ethods w eredeveloped in their current forms in the second half of the nineteenth century. They are still

used for small structures and for preliminary design of large structures.

The so lu tions are based on linear iso trop ic in fin itesim al elasticity and Eu ler唱Bernou llibeam theory. In other words, they contain the assumptions (among others) that the materials in

question are elastic, that stress is related linearly to strain , that the m aterial (bu t no t thestructure) behaves identically regardless of direction of the applied load, that all deformations

are small, and that beams are long relative to their depth. As with any simplifying assumption

in engineering, them ore them odel stray s from reality , the less usefu l (and m ore dangerous) theresu lt.· Elasticity Methods

E lasticity m ethods are availab le generally fo r an elastic so lid o f any shape. Ind iv idualmembers such as beams, columns, shafts, plates and shells may be modeled. The solutions are

derived from the equations of linear elasticity. The equations of elasticity are a system of15partial d ifferen tial equations. D ue to the nature o f the m athem atics invo lved , analy ticalsolutions may only be produced for relatively simple geometries. For complex geometries, a

numerical solution method such as the finite element method is necessary.

M any o f the developm en ts in the m echan ics o f m aterials and elasticity app roaches havebeen expounded or initiated by Stephen Timoshenko.

· Finite Element Methods

F in ite elem en t m ethod m odels a structure as an assemb ly o f elem ents o r componen ts w ithvarious fo rm s o f connection betw een them . Thus , a con tinuous sy stem such as a p late o r shellis m odeled as a d iscrete sy stem w ith a fin ite number o f elem en ts in terconnected at fin ite

number of nodes. The behavior of individual elements is characterised by the element's s tiffnesso r flexib ility relation , w h ich altogether leads to the sy stem 's stiffness o r flexib ility relation . T oestab lish the elem en t 's stiffness o r flexib ility relation , w e can use the m echan ics o f m aterialsapproach for simple one唱dimensional bar elements, and the elasticity approach for more

complex two—and three唱dimensional elements. The analytical and computational development

are best effected throughout by means of matrix algebra.

Early app lications o f m atrix m ethods w ere fo r articu lated fram ew orks w ith truss , beamand column elements; later and more advanced matrix methods, referred to as "finite element

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analysis", model an entire structure with one唱, two唱, and three唱dimensional elements and can be

used fo r articu lated sy stem s together w ith con tinuous sy stem s such as a p ressure vessel,plates, shells and three唱dimensional solids. Commercial computer software for structural

analysis typically uses matrix finite唱element analysis, which can be further classified into two

main approaches: the displacement or stiffness method and the force or flexibility method. The

stiffness m ethod is the m ost popu lar by far thanks to its ease o f im p lem entation as w ell as o ffo rm ulation fo r advanced app lications. The fin ite唱 elem ent techno logy is now soph isticated

enough to handle just about any system as long as sufficient computing power is available. Its

app licab ility includes , bu t is no t lim ited to , linear and non唱 linear analy sis , so lid and flu idinteractions, materials that are isotropic, orthotropic or anisotropic and external effects that are

static, dynam ic, and env ironm ental facto rs . Th is , how ever, does no t im p ly that the computedsolution will automatically be reliable because much depends on the model and the reliability of

the data inpu t.

·５２·Unit ３

Unit 4

Tex tShear Stresses in Beams

· Shear Flow

Consider an elastic beam m ade from several con tinuous longitud inal p lanks w hose crosssection is shown in Fig.4.1(1 ) . T o m ake th is beam act as an in tegralm ember, it is assum ed thatthe planks are fastened at intervals by vertical bolts. If an element of this beam, in Fig.4.1(b ), issub jected to a bend ing m om ent + MA at end A and + MB at end B , bending stresses that act

normal to the sections are developed(2 ) . T hese bend ing stresses vary linearly from the neu tralaxis in accordance with the flexure formulaMy／ I. The top plank of the beam element is

isolated, as shown in Fig.4.1 (c). T he fo rces acting perpend icu lar to the ends A and B o f th isplank may be determined by summing the bending stresses over their respective areas.

Denoting the total force acting normal to the area fghj byFB , and rem embering that, at sectionB ,MB and I are constants, one obtains the following relation:

FB ＝ － MBI ∫area ＝ f g hj

yd A ＝ － MB QI (4 .1)

w hereQ ＝ ∫

area ＝ f g hjyd A ＝ Af g hj y－ (4 .2)

The in tegral defin ing Q is the first , o r static,m om ent o f area fgh j around the neu tral axis . B ydefinition, y is the distance from the neutral axis to the centroid ofA fgh j . S im ilarly , one canexpress the total force acting normal to the area abcd asFA = － MA Q／ I. If MA is not equal to

MB , w h ich is alw ay s the case w hen shears are p resen t at the ad jo in ing sections,FA is no t equalto FB . Equ ilibrium o f the ho rizon tal fo rces in F ig.4 .1(c) m ay be attained on ly by develop ing a

horizontal resisting force in the boltR, as in Fig.4.1 (d ). T ak ing a d ifferen tial beam elem ent o flength dx, MB = MA + dM and dF = |FB |唱 |FA | , and substitu ting these relations in to theexpression forFA and FB found above, one ob tains dF = dM Q／ I. It is more significant to

obtain the force per unit length of beam length, dF/dx, which will be designated byq and

referred to as the shear flow. Then, noting that dM/dx ＝ V , one obtains the following

expression for the shear flow in beams:

q ＝ VQI (4 .3)

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In th is equation , I is the moment of inertia of the entire cross唱sectional area around the neutral

axis , and Q extends only over the cross唱sectional area of the beam to one side, at whichq is

investigated.

F ig.4.1　 Elements for deriv ing shear flow in a beam· Shear唱Stress Formula for Beams

The shear唱 stress fo rmula fo r beam sm ay be ob tained by m odify ing the shear flow fo rmu la.In a so lid beam , the fo rce resisting dF may be developed only in the plane of the longitudinal

cut taken parallel to the axis of the beam, as shown in Fig.4.2. Therefo re, assum ing that theshear stressτ is uniformly distributed across the section of widtht, the shear stress in the

longitudinal plane may be obtained by dividing dF by the areatdx. This yields the horizontal

shear stressτ, which for an infinitesimal element is numerically equal to the shear stress acting

on the vertical p lane［ see F ig.4 .2(b )］ . S ince q = dF/dx, one obtains

τ ＝ VQI t ＝ q

t (4 .4)w here t is the width of the imaginary longitudinal cut, which is usually equal to the thickness

or width of the member. The shear stress at different longitudinal cuts through the beam

assumes different values as the values ofQ and t for such sections differ.

·７２·Unit ４

F ig.4.2　 Derivation of shear stress in a beam　 　 Since the shear唱stress formula for beams is based on the flexure formula, all the limitations

imposed on the flexure fo rm ula app ly . The m aterial is assum ed to be elastic w ith the sam eelastic modulus in tension as in compression. The theory developed applies only to straight

beams. Moreover, in certain cases such as a wide flange section, the shear唱stress formula may

not satisfy the requirement of a stress free boundary condition. However, no appreciable error

is invo lved by using Eq . (4 .4 ) fo r th in唱w alled m embers , and the m ajo rity o f beam s belong tothis group.

· Shear Stresses in a Rectangular Beam

The cross唱 sectional area o f a rectangu lar beam is show n in F ig.4 .3 (a). A longitud inal cu tthrough the beam at a distancey 1 from the neu tral axis iso lates the partial area fgh j o f the crosssection .H ere t ＝ b and the infinitesimal area of the cross section may be conveniently

expressed as bdy. By applying Eq. (4.4), the ho rizon tal shear stress is found at level y 1 o f thebeam .A t the sam e cu t, num erically equal vertical shear stresses act in the p lane o f the crosssection (τxy ＝ τyx ):

τ ＝ VQI t ＝ V

I t∫area

fghi yd A ＝ VI t∫

h／２

y１byd y ＝ V

２ Ih２

２

－ y２１ (4 .5)　 　 This equation show s that in a beam o f rectangu lar cross section , bo th the ho rizon tal andthe vertical shear stresses vary parabolically. The maximum value of the shear stress is

obtained wheny１ is equal to zero . In the p lane o f the cross section , F ig.4 .3 (b ), th is isdiagrammatically represented byτm ax at the neu tral axis o f the beam . A t increasing d istancesfrom the neutral axis, the shear stresses gradually diminish. At the upper and lower boundaries

o f the beam , the shear stresses cease to exist as y 1 = ± h/ 2. These values o f the shear stressesat the various levels o f the beam m ay be rep resen ted by the parabo la show n in F ig.4 .3 (c). A nisometric view of the beam with horizontal and vertical shear stresses is shown in Fig.4.3(d ).

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Fig.4.3　 Shear stresses in a rectangular beamThe m aximum shear stress in a rectangu lar beam occurs at the neu tral axis , and fo r th is

case, the general expression forτm ax m ay be sim p lified by setting y 1 = 0.τ ＝ Vh２

８ I ＝ Vh２

８bh３ ／１２ ＝ ３２

Vbh ＝ ３

２VA (4 .6)

w hereV is the total shear andA is the entire cross唱sectional area. Since beams of rectangular

cross唱sectional area are used frequently in practice, this equation is very useful. It is widely

used in the design of wooden beams, since the shear strength of wood on planes parallel to the

grain is sm all. T hus, although equal shear stresses exist on mu tually perpend icu lar p lanes ,wooden beams have a tendency to split longitudinally along the neutral axis. Note that the

maximum shear stress is1 1/2 tim es as great as the average shear stressV／ A. Nevertheless, in

the analy sis o f bo lts and rivets , it is custom ary to determ ine their shear strengths by d iv id ingthe shear forceV by the cross唱sectional areaA. Such practice is considered justified since the

allowable and ultimate strengths are initially determined in this manner from tests.

Notes(1 ) C onsider an elastic beam m ade from several con tinuous longitud inal p lanks w hose

cross section is shown in Fig.4.1. consider用在句首 ，引导祈使句 ，w hose引导限定性定语从句 ，修饰 beam 。全句可译为 ：让我们研究一下由数个在纵向连续的厚木板所组成的弹性梁 ，其截面如图 4.1所示 。

(2) If an elem ent o f th is beam , in F ig.4 .1(b ), is sub jected to a bend ingm om ent + MA at endA and + MB at end B , bend ing stresses that act no rm al to the sections are developed .句首 if引导条件状语从句 ；句中 that… to the section为限定性定语从句 ，修饰 bend ing stresses。全句可译为 ：如果图 4.1(b )中梁的一个微元两端 A和 B分别受到弯矩 + MA 和 + MB 的作

用 ，便会产生垂直于梁截面的弯曲应力 。

New Words1. p lank［pl辈礗k］ n .厚木板 ，支架 　 v t.铺板

·９２·Unit ４

2. bo lt［b待ult］ n .门闩 ，螺钉 　 v t.上门闩3. static［餐st 辈 tik］ a.静态的 ，静力的4. ad jo in ing［待餐d礒礎ini礗］ a.邻接的 ，隔壁的5. equ ilibrium ［仓i礑kwi餐libri待m］ n .平衡 ，平静 ，均衡6. d ifferen tial［仓dif待餐ren礏待l］ a.微分的 　 n .微分7. num erically ［nju（礑）餐merik待li］ ad .用数字 ，在数字上8. im aginary ［i餐m 辈d礒in待ri］ a.假想的 ，想象的 ，虚构的9. app reciab le［待餐pri礑礏i待bl］ a.可感知的 ，可评估的10. rectangu lar［rek餐t 辈礗礔jul待］ a.矩形的 ，成直角的11. parabo lically ［仓p辈 r待餐b礎lik待li］ ad .以抛物线方式12. d iagramm atically ［仓dai待礔r待餐m 辈 tik待li］ ad .以图表形式13. d im in ish［di餐mini礏］ v .(使 )减少 ， (使 )变小14. sp lit［split］ v .劈开 ， (使 )裂开 　 n .裂开 ，裂痕15. parabo la［p待餐r 辈b待l待］ n .抛物线16. isom etric［餐ais待u餐metrik］ a.等大的 ，等容积的 ，等轴的17. flange［fl辈nd礒］ n .翼缘 ，法兰

Phrases and E xpressions1. in acco rdance w ith　与 … …一致2. th in唱w alled m ember　薄壁构件3. elastic m odulus　弹性模量4. isom etric v iew 　等轴测视图5. boundary cond ition　 边界条件

E xercises1. T ranslate the fo llow ing paragraph in to Ch inese.The p rincip le o f v irtual w o rk , described in the p reced ing article, can be used to derive the

un it唱 load m ethod , w h ich is an im portan t m ethod fo r find ing d isp lacem ents o f structures .W ehave already discussed methods for finding deflections of beams and simple trusses. However,

the un it唱 load m ethod can be used no t on ly fo r beam s, trusses , and o ther sim p le k inds o fstructures, but also for very complicated structures having many members. Furthermore, the

unit唱load method is suitable for finding all types of displacements, including the deflection of a

po in t in the structure, the ro tation o f the axis o f a m ember, the relative d isp lacem ent betw eentwo points, and others. Theoretically, it may be used for either statically determinate or

indeterminate structures, although for practical purposes the method is limited to determinate

structures because its use requires that the stress resultants be known throughout the structure.

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2. T ranslate the fo llow ing sen tences in to English .(1)沿梁纵轴不同断面上的剪应力随着这些断面的剪力和宽度的不同而不同 。(2)根据定义 ，y是中性轴至 abcd面的距离 。(3)以上方程说明矩形截面梁的剪应力在梁高方向上呈抛物线变化 。(4)矩形截面的剪应力在中性轴处为最大 ，在梁上下边缘为零 。(5)因为容许应力和极限应力最初都是以此方法确定的 ，所以认为这种做法是合

适的 。

Reading Material

Structural EngineeringStructural engineering is a field o f engineering that deals w ith the design o f a structural

system with the purpose of supporting and resisting various loads. Though other disciplines

touch on this field, a physical object or system is truly considered a part of structural

engineering, regardless of its central scientific or industrial application, if its main function is

designed to resist loads and dissipate energy.

A structural engineer is m ost comm only invo lved in the design o f bu ild ings and non唱building structures, but also plays an essential role in designing machinery where structural

integrity of the design item impacts safety and reliability. Large man唱made objects, from

furniture to medical equipment to a variety of vehicles, require the input of a structural

engineer.

Structural engineers ensure that their designs satisfy a given "design in ten t", p red icated onsafety (e.g. structures do no t co llap se w ithou t due w arn ing), and on serv iceab ility (e.g. floo r

vibration and building sway do not result in discomfort for the occupants). Structural engineers

are responsib le fo r m ak ing efficien t use o f funds and m aterials to achieve these goals . En try唱level structural engineers may design simple beams, columns, and floors of a new building,

including calculating the loads on each member and the load capacity of building materials such

as (steel, tim ber, m asonry and concrete ). M ore experienced engineers w ou ld render m orecomplex structures, often calculating the physics of moisture, heat and energy as they relate to

build ing componen ts .In the U nited S tates, the structural engineering field is o ften subd iv ided in to bridge

engineering and building engineering. Structural engineers often further specialize into special

structural manufacturing or construction, such as pipeline engineering or industrial structures.

Structural loads on structures are generally classified as live loads and dead loads. L iveloads are the weight of a building's occupan ts and furn iture, the fo rces/w eigh ts o f w ind andwater, and seismic activity. Dead loads are the weight of the structure itself and all major

architectural components, as well as roof loads experienced only during construction. The

·１３·Unit ４

limiting design criteria include forces of nature such as winds, earthquakes and tsunamis. In

recent years, reinforcing structures against terrorism has also taken on increased importance.

Buildings are now designed with anti plane protection, which limit the number of plane crashes

in to bu ild ings v ia the m eans o f a n igh t w atchm an ; w hose job is to b lind the p ilo t in case o fcollision so that the optimal crash doesn't take p lace.· History of Structural Engineering

Structural engineering is one o f the o ldest p ro fessions in the w orld , dating back to at least2700 B .C .A t th is tim e, the stepped py ram id o f K ing D joser w as bu ilt by Imho tep ,w ho m anyregard as the first s tructural engineer. In ancien t tim es , m ost o f structural engineering w orks

were carried out by other professions, such as architect, royal builder and other artisans. No

actual record exists pointing to the first calculations of the strength of structural members or

the behavior of structural material. At that time, structures tended to be a simpler and more

straightforward element compared to today's s tandards.N evertheless , the desire to bu ild higherand longer structures w ith larger in ternal spaces pushed the need to fo rm ulate imp rovedstructural configurations and materials.

H ere is an ou tline o f developm en ts in S tructural Engineering since 1500 A .D .B y the 16th /17th cen turies , an in troduction o f 'Tw o N ew Sciences'by G alileo estab lished

the scien tific app roach fo r structural engineering. Th is is also regarded as the beginn ing o fstructural analysis, the mathematical representation and design of building structures.

Late 19th and early 20th cen turies , s tructural engineering undergoes a trem endousdevelopment. In1868, rein fo rced concrete w as developed by Joseph M onier to strengthencement material that was considered to be too brittle. Russian structural engineer Vladimir

Shukhov developed many new analysis methods in structural engineering which led to new

industrial designs such as the hyperboloid structure, tensile structure and others.

In 1889, the cast唱 iron E iffel T ow er w as bu ilt by G ustave E iffel andM auriceK oech lin , andv isib ly dem onstrated hum an talen t fo r constructing m odern h igh唱 rise structures .

P restressed concrete, inven ted by Eugene F rey ssinet in 1928 (and later standard ized byTung唱Yen Lin) gave a novel approach in overcoming the weakness of concrete structures in

tension.

In 1930, w ith P ro fesso r H ardy C ross 's M om ent D istribu tion M ethod , the stresses o fmany complex structures can be determined quickly and accurately.

M odern structural engineering's ach ievem ents can be seen all over the w o rld in examp lessuch as Akashi唱Kaikyo Bridge, Mega唱Float at Tokyo Bay, Sears Tower, Golden Gate Bridge,

Sydney Harbour Bridge, and the Millennium Dome.

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Unit 5

Tex tLoad

· Introduction

N orm ally , a design specification does no t p rescribe them agn itudes o f the loads that are tobe used as the basic inpu t to the structural analy sis ,w ith the excep tion o f special cases such ascrane design specifications . It is the ro le o f the specification to detail the m ethods and criteriato be used in arriving at satisfactory member and connection sizes for the structural material in

question , given the m agn itudes o f the loads and their effects . The specification therefo rereflects the requirements that must be satisfied by the structure in order that it will have a

response that allows it to achieve the performance that is needed. Loads, on the other hand, are

governed by the type o f occupancy o f the bu ild ing,w h ich in turn is d ictated by the app licab lelocal, regional, and national law s that are m ore comm only know n as bu ild ing codes.

The bu ild ing code loads have trad itionally been given as nom inal values, determ ined on thebasis o f m aterial p roperties (e.g., dead load ) o r load survey s (e.g., live load and snow load ). T obe reasonab ly certain that the loads are no t exceeded in a given structure, the code values havetended to be h igher than the loads on a random structure at an arb itrary po in t in tim e. Th is

may, in fact, be one of the reasons why excessive gravity loads are rarely the obvious cause of

structural failures . B e that as it m ay , the fact o f the m atter is that all o f the various types o fstructural loads exhibit random variations that are functions of time, and the manner of

variation also depends on the type of load(1 ) . Rather than dealing w ith nom inal loads thatappear to be deterministic in nature, a realistic design procedure should take load variability

into account along with that of the strength, in order that adequate structural safety can be

achieved through rational means.

Since the random variation o f the loads is a function o f tim e as w ell as a number o f o therfacto rs , the m odeling, strictly speak ing, shou ld take th is in to accoun t by using stochastic

analysis to reflect the time and space interdependence. Many studies have dealt with this

highly complex phenomenon, especially as it pertains to live load in buildings. In practice,

however, the use of time唱dependent loads is cumbersome at best, although the relationship

must be accounted for in certain cases. For most design situations the code will specify the

magnitude of the loads as if they were static. Their time and space variation are covered

through the use of the maximum load occurring over a certain reference (turn) period, and its

statistics. For example, American live load criteria are based on a reference period of50 y ears ,w h ile C anad ian criteria use a 30 y ear in terval.

The geograph ical location o f the structure p lay s an im portan t ro le fo r certain loads. It isparticularly applicable to snow, wind, and seismic action, the first being of special importance

in no rth唱 cen tral and no rth唱 eastern areas o f the U nited S tates , the second in h igh w ind coastaland mountain areas, and the last in areas having earthquake fault lines.

D esign fo r w ind effects is comp licated by a number o f phenom ena. L ive snow loads andearthquake action, wind loads are given more attention in certain parts of the country. At the

same time wind loads are neither static nor uniformly varying, and are heavily influenced by

geometry of the structure as well as the surrounding structures and the landscape. To a certain

degree th is also app lies to them agn itude o f the snow load .Bu ild ing codes treat these effects asstatic phenom ena and relate them to the actual cond itions through sem iemp irical equation . Th isgives the designer a better hand le on a d ifficu lt p rob lem , but can lead to d ifficu lties w hen thereal structure departs significantly from the bases of the code. For that reason wind loads, and

som etim es earthquake and snow loads, are determ ined on the basis o fm odel tests . In particu lar,w ind tunnel testing has becom e a usefu l and p ractical too l in these endeavo rs .

The loads on the structure are no rm ally assum ed to be independen t o f the type o f thestructure and structural material, with the exception of dead loads. The response of a building,

how ever, w ill be d ifferen t fo r d ifferen t m aterial, depend ing on the type o f load . Fo r examp le,the behavior of a moment唱resistant steel frame will be quite unlike that of a braced frame, when

sub jected to lateral loads , especially those due to an earthquake. O n the o ther hand , theresponse of these two frames to gravity loads will not be all that different.

The size o f a structure (heigh t, floor area) has a sign ificant impact on the m agn itudes o fmost loads. All loads are influenced by the increasing height of a multistory building, for

example. Similarly, the greater the floor area that is to be supported by a single member, the

smaller the floor area that is to be supported by a single member, the smaller will be the

probability that the code live load will appear with its full intensity over the entire area. In

such cases a live load reduction method is used to arrive at more realistic design data.

· Loads on Building Structures

There are m any types o f loads that m ay act on a bu ild ing structure at one tim e o r o ther,and this section provides a general description of the characteristics of the most important

ones.

The fo llow ing loads are o f p rim ary concern to a bu ild ing designer：G rav ity loads:D ead load ; L ive load ; Snow load .Lateral loads:W ind loads ; Seism ic action ; Special loads and load effects .Special loads and load effects include the in fluence o f temperature variations , structural

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foundation settlements, impact, and blast. They are given only a brief description here; the

reader interested in the details is advised to seek out the specialized publications that deal with

th is ty pe o f load ing.Each o f the p rim ary types o f loads can be d iv ided in to several sub types.

· 1 Dead Load

In theo ry , at least, the dead load on a structure is supposed to rem ain constan t. In reality ,the w ord constan t is a relativem easure, because the dead load includes no t on ly the self唱w eigh to f the structure, bu t also the w eigh t o f perm anen t construction m aterials , p artitions , floo r andceiling materials, machinery and other equipment, and so on. Also included in this category are

the load effects o f p restressing fo rces .The w eigh t o f all o f these elem en ts can be determ ined exactly on ly by actually w eigh ing

and/or measuring the pieces. This is almost always an impractical solution, and the designer

will therefore rely on published material data to arrive at the dead loads. Some variation from

consequently will occur in the real structure, accounting for some of the deviation from

constancy. Similarly, there are bound to be differences between otherwise identical structures,

representing the major source of dead load variability. However, compared to the other

structural loads, the dead load variations are relatively small, and the actual mean values are

quite close to the code唱prescribed data.

· 2 Live Load

L ive load , o r m o re accurately the grav ity live load , is the nam e that is comm only used fo rthe loads on the structure that are no t part o f the perm anen t installations. T o that end it

includes the weight of the occupants of the building, furniture and movable equipment, and so

on . The fluctuations in th is load are bound to be substan tial. F rom being essen tially zeroimmediately before the tenants take possession to a maximum value that may be several times

as h igh as the dead load , them agn itude o f the live load at any given tim em ay be qu ite d ifferen tfrom that specified by the bu ild ing code. Th is is one o f the reasons w hy num erous attemp ts

have been made to model the live load and its variations, and why live load measurements in

actual buildings continue to be made.

F ig.5.1　 Variation o f live load w ith time

The live load on the structure at anygiven time is also called the arbitrary

point唱in唱time live load. As shown by Fig.

5.1, th is is the load that is determ ined in alive load survey . Part o f the to tal load m aynow be d irectly attribu tab le to theoccupants of the structure: As soon as the

room is emp tied , the transien t live load

·５３·Unit ５

(TLL) is reduced to zero or near zero. The load that remains, say, due to furniture and the like,

is a sustained live load (SLL ) that changes very little as long as the sam e tenan t occup ies thepremises. Significant variations in the SLL may come about when the occupancy changes: As

one company moves out, the SLL may drop to near zero. It will remain at this level until the

next tenant moves in, at which time it will increase to a level that may be quite different from

the SLL o f the earlier occupan t.A s dem onstrated later, live loads in general are a function o f the size o f the floo r area

under consideration. The larger the area, the smaller is the change that the full code load will

appear over the entire area. This affects the magnitude of the arbitrary point唱in唱time loads as

well as the maximum lifetime live load, which represents the maximum live load that the

structure may experience in its lifetime. In American practice the life of a structure is expected

to be 50 y ears ; hence, a 50唱 y ears reference period fo rm s the basis fo r m any o f the live loadmodels that have been developed.

The live load on the structure at any tim e is no rm ally w ell below the code value; themaximum lifetime (50唱 y ears ) live load m ay be a certain am ount larger. Curren t load statis ticsand code recommendations take these phenomena into account.

Notes(1) B e that as it m ay , the fact o f the m atter is that all o f the various types o f structural

loads exhibit random variations that are functions of time, and the manner of variation also

depends on the type of load. Be that as it may为让步状语从句 。全句可译为 ：尽管如此 ，事实上各种类型的结构荷载都表现为时间函数的随机变量 ，并且变化的方式视荷载类型而定 。

New Words1. p rescribe［ p ris餐kraib］ v t.指示 ，规定2. criterion［ krai餐 ti待 ri待 n］ n .标准 ，规范 ，准则3. d ictate［ d ik餐 teit］ v .规定 ，指示 ，命令4. survey ［ s待礑餐vei］ n .调查 ，测量 　 v t.调查5. variation［仓vε待 ri餐ei∫待 n］ n .变更 ，变化 ，变异6. determ in istic［ di仓 t待礑m i餐n istik］ a.确定性的7. rational［餐 r辈∫待 nl］ a.合理的 ，理性的8. stochastic［ st待 u餐k辈 stik］ n .随机的9. pertain［ p待礑餐 tein］ v .适合 ，属于10. cumbersom e［餐k礍mb待 s待m］ a.讨厌的 ，麻烦的11. landscape［餐 l辈 ndskeip］ n .地形 ，风景

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12. endeavo r［ in餐dev待］ n .努力 　 v i.尽力 ，努力13. occupan t［餐礎 kju :p待 nt］ n .居住者 ，占有者14. fluctuation［仓 fl礍 ktju餐ei∫待 n］ n .波动 ，起伏15. tenan t［餐 ten待 nt］ n .房客 ，承租人 　 v t.出租16. transien t［餐 tr辈 nz i待 nt］ a.瞬时的17. p rem ise［餐p rem is］ n .前提 　 v t.假定

Phrases and E xpressions1. nom inal value　标准值 ，名义值2. in p ractice　实际上3. at best　充其量 ，最好也只不过4. reference period　重现期5. w ind tunnel test　风洞试验6.m ean value　平均值7. transien t live load　瞬时活荷载8. sustained live load　 持续活荷载

E xercises1. T ranslate the fo llow ing paragraph in to Ch inese.The data that have been p rov ided fo r w ind loads are all based on m easured w ind speeds ,

since these are relatively easy to determine. Meteorological data (气象资料 ) from m anylocations throughout the country yield the local wind speed data for daily and annual maxima;

these are then used to m odel long唱 term characteris tics . In particu lar, the m aximum w ind speedis needed for the50唱 y ear reference period . In som e cases th is number is availab le; in o ther casesit m ust be extrapo lated using a statistical m odel.W ind loads are h igh ly dependen t on local

conditions, in the same way that snow loads are. The designer must consult local requirements;

there are no general, national specifications, o ther than a comp ilation o f m eteo ro logical data.2 . T ranslate the fo llow ing sen tences in to English .(1)对于大多数设计情况 ，规范规定的是静力荷载的大小 。(2)对于风作用 ，许多现象使设计复杂化 。(3)类似地 ，单个构件承担的楼板面积越大 ，在整个面积上 ，规范活荷载以全部强度出

现的概率就越小 。(4)然而 ，与其他结构荷载相比 ，恒载变化是相对较小的 ，实际平均值与规范规定的值

很接近 。(5)至少在理论上 ，结构上的恒载被认为是保持不变的 。

·７３·Unit ５

Reading Material

Combinations of LoadsM ost structural loads vary w ith tim e.C alcu lations o f structural perfo rm ance that are used

in check ing safety and serv iceab ility requ ire them aximum combined load effect occurring duringsom e su itab le period o f reference. Th is period T might be on the order of50 to 100 y ears fo r

safety唱related performance criteria, and approximately1 to 10 y ears fo r serv iceab ility . If thestructure or structural component is subjected to a set ofN loadsQi（ t） ， i ＝ １ ，．．．，N ，which

vary in tim e, the designer w ou ld then be concerned w ith determ in ing an app rop riate value o fthe maximum combined load effectQm ax ,

Qmax ＝ maxT

［Q１ （ t） ＋ Q２ （ t） ＋ … ＋ QN （ t）］ (5 .1)w h ich can be used fo r design and detailing purposes.

A s has been show n in earlier sections o f th is chap ter, structural loads are random in spaceand tim e.D uring the past decade, load comb inations have been analy zed using the theo ry o fstochastic processes to take into account the spatial and temporal correlation and variation of

the loads. The discussion herein uses an intuitive approach to arrive at similar conclusions.

F ig.5 .2 gives typ ical samp le functions that show the structural effects o f several comm onloads considered in codes and standards . Perm anen t load effects such as those due to dead loado r p restressing change slow ly w ith tim e and m ay be assum ed to rem ain essen tially constan tduring the period of reference. Occupancy live loads, temperature effects, and snow loads vary

w ith tim e, bu t their effects on the structure are essen tially static. F inally , w ind loads that arestructurally significant and earthquake loads occur relatively infrequently and their durations

are much smaller than the durations of permanent and other variable loads described above.

The load at any po in t in tim e is described by a p robab ility density function f（ x） shown

at the left side o f F ig.5 .2 . Th is po in t唱 in唱 tim e load cou ld be determ ined by m eans o f a loadsurvey. The mean point唱in唱time load usually is much less than the nominal loadQn that isspecified for design purposes in the ANSI A85 Standard and in o ther regu lato ry docum ents .

If the structural componen t is sub jected to on ly one variab le load in add ition to thepermanent load, the load combination analysis is relatively straightforward, since the maximum

comb ined load effect during T occurs when the variable load attains its maximum value. In the

design o f large in terio r slabs o r long唱 span roo fs , fo r examp le, them aximum occupancy live loadon the slab o r them aximum snow load on the roo f during T would be combined with the dead

load .H ow ever, the analy sis is no t so sim p le w hen m ore than one variab le load acts on thestructure at any given time. One may observe from Fig.5.2 that the likelihood is sm all that tw oo r m ore o f the variab le loads in the combination w ill attain their m aximum valuessimultaneously. Accordingly, one would expect that

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Fig.5.2　 Stochastic p rocess models o f structural loads

Qmax ＜ ［maxT

Q１ （ t） ＋ maxT

Q２ （ t） ＋ … ＋ maxT

Q N （ t）］ (5 .2)in w h ich m ax

TQ i（ t） is the maximum value ofQi（ t) to occur duringT. Consequently, structural

m embers m ay be designed fo r a to tal load that is less than the sum o f the peak loads . Curren tstandards recogn ize th is by p rescrib ing p rocedures fo r reducing the effect o f the combination o fpeak load values fo r design purposes.

In allow ab le o r w ork ing stress design , the to tal load effect m ay be mu ltip lied by a loadcombination probability factorψ less than unity to obtain a design loadQd as

Qd ＝ ψ（Qn１ ＋ Qn２ ＋ … ＋ QnN ） (5 .3)In the AN SI A 58 S tandard , the load combination p robab ility facto r is taken as 0.75 w hen the

combination includes two time唱varying loads and0.66 w hen the combination includes threetime唱varying loads. For example, analysis of load combinations involving dead loadD, live load

L, and wind loadW , would require the following combinations to be considered:

Qd ＝ maxD ＋ LD ＋ W０ ．７４（D ＋ L ＋ W）

(5 .4)

　 　 A lternatively , in som e allow ab le stress specifications, the allow able stress is increased fo rsom e load combinations. Fo r examp le, the A ISC Specification perm its the allow ab le stress to

be increased by33% fo r load comb inations invo lv ing w ind load , bu t the combined load effects

·９３·Unit ５

are no t ad justed . Th is app roach is consisten t w ith the treatm en t o f D ＋ L ＋ W in the ANSI

A 58 Standard since 0.75= 1/1.33; how ever, it is no t consisten t fo r D ＋ W , where ANSI A58Standard m akes no ad justm en t because W is the only variable load in the combination.

Apparently, the 33% increase in allow ab le stress perm itted by A ISC fo r combinationsinvolving wind represents more than simply a way to account for the low probability that the

peaks o f the variab ility loads co incide.In strength o r p lastic design , the sm all likelihood o f peak loads co incid ing is treated by

reducing the combined factored loads. This adjustment usually has been consistent with the

treatment of load combinations in allowable stress design, which predated the strength design

procedures. In the ACI Code, the combinations for dead, live, and wind loads are

Qd ＝ max １ ．４D ＋ １ ．７ L０ ．７５（１ ．４D ＋ １ ．７ L ＋ １ ．７W）

(5 .5)N o te that the combination invo lv ing facto red w ind load is multip lied by the facto r 0 .75, just asit had been done in allow ab le stress design . S im ilarly , Part 2 o f the A ISC Specification gives

Qd ＝ max １ ．７（D ＋ L）１ ．３（D ＋ L ＋ W）

(5 .6)In w hich it m igh t be observed that 1 .3/1 .7≈ 0.75.

The C anad ian L im it S tates D esign S tandard takes a sligh tly d ifferen t app roach to loadcombinations, using the following load requirement,

Qd ＝ １ ．２５D ＋ ψ（１ ．５ L ＋ １ ．５W ＋ １ ．２５ T） (5 .7)In w hich ψ is a load combination facto r equal to 1.00 w hen one o f L ， W , or T (temperature

effect) act; 0.7 w hen tw o o f L ， W , or T act; and 0.6 w hen all three act. U n like the loadcombinations in Eq.(5.4 ) through Eq .(5 .6 ), the load combination facto r is no t app lied to thepermanent load D, which is always present. Therefore, Eq.(5.7) p rov ides a better descrip tion o fhow structural loads actually combine in p ractice than do Eqs .（ 5.4） through（ 5.6） .

M ore recen t load combination ru les draw upon resu lts o f the p robab ilis tic loadcombination studies referred to earlier. Such studies have led to the observation that the

maximum effect of a combination of loads usually occurs when one of the loads reaches its

maximum value during time period T while the other loads are equal to their point唱in唱time

values. The maximum load effect then is approximated by,

Qmax ≈ maxN

imax

TQ i（ t） ＋ 钞

j ≠ iQ j（ t） (5 .8)

　 　 The term (m axT

Q i ) is deno ted the p rincipal variab le load , w h ile the Qi are deno tedcompanion actions. It is necessary to considerM distinct load combinations in order to

compute the maximum load effect for structural design purposes, that is, each time唱varying

load must assume, in turn, the position of the principal variable load in Eq.(5.8 ). Eq . (5 .8 )neglects the possibility that two or more variable loads will reach their respective maximum

values at the same time, or that the maximum effect will occur when two of the loads attain

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"near唱maximum " values . Th is in troduces a degree o f unconservatism w hich m ay be sign ifican twhen two of the loads are positively correlated as a consequence of arising from the same

underlying physical phenomenon. However, studies have shown that Eq. (5.8 ) is a goodapproximation for most practical cases involving building structures. It is also consistent with

the observation that structural failures (at least those not due to human error or willful abuse)

usually occur as a consequence o f one load attain ing an extrem e value.

·１４·Unit ５

Unit 6

Tex tBasic Behavior Assumptions for Concrete MembersFour basic assump tions are m ade w hen deriv ing a general theo ry fo r the flexural strength

of reinforced concrete sections:

1. P lane sections befo re bend ing rem ain p lane after bend ing.2 . The stress唱 strain curve fo r the steel is know n .3. The tensile strength o f the concrete m ay be neglected .4 . The stress唱 strain curve fo r concrete, defin ing the m agn itude and d istribu tion o f

compressive stress, is known.

The firs t assump tion , B ernou lli 's p rincip le, im p lies that the longitud inal strain in theconcrete and the steel at the various points across a section is proportional to the distance

from the neutral axis. A large number of tests on reinforced concrete members have indicated

that this assumption is very nearly correct at all stages of loading up to flexural failure,

provided good bond exists between the concrete and steel(1 ) . C ertain ly it is accurate in thecompression zone of the concrete. A crack in the tension zone of concrete implies that some

slip has occurred between the steel reinforcement and the surrounding concrete, and this means

that the assump tion is no t comp letely app licab le to the concrete in the neighbo rhood o f acrack. However, if the concrete strain is measured over a gauge length that includes several

cracks, it is found that Bernoulli's p rincip le app lies to th is average tensile strain . F ig.6 .1 show sthe strain d istribu tionsm easured across sections o f rein fo rced concrete co lumns near the failureregions at various load ing increm ents . The co lumn sections w ere either 10in (254mm ) square o r12in (305mm ) d iam eter round . The strains on the steel w ere m easured over a 1in (25mm ) gaugelength and the strains on the concrete over a6in (150mm ) gauge length . Som e dev iation fromlinearity must be expected because of small inaccuracies in individual strain measurements and

small errors in the location of gauge lines. It is evident from Fig.6.1 that the m easured strainprofiles are reasonably linear. Certainly the assumption of plane sections remaining plane is

sufficiently accurate for design purposes. The assumption does not hold for deep beams or in

regions of high shear.

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F ig.6.1　 Strain distribution across sections of reinforced concrete co lumns at various loading increments　 　 The second assumption means that the stress唱strain properties of the steel are well

defined. Normally a bilinear stress唱strain curve is assumed; hence strain hardening is neglected.

The po int at w h ich strain harden ing begins is no t stipu lated in specifications fo r steel andtherefore it is difficult to include it. Normally it would be unwise to rely on any increase in

strength due to strain hardening because this could be associated with very large ultimate

deformations of the members. When an increase in strength could cause an unfavorable

·３４·Unit ６

condition (e.g., resulting in a brittle shear failure rather than a ductile flexural failure in seismic

design ), the designerm ay take the add itional strength due to strain harden ing in to accoun t byreferring to the actual stress唱strain curve for the steel(2 ) .

T he th ird assump tion is very nearly exact. A ny tensile stress that exists in the concretejust below the neutral axis is small and has a small lever arm.

The fourth assump tion is necessary to assess the true behav io r o f the section . S ince thestrains in the compressed concrete are proportional to the distance from the neutral axis, the

shape of the stress唱strain curves of Fig.6 .1 ind icate the shape o f the comp ressive stress b lock atvarious stages o f load ing. F ig.6 .2 p resen ts the changing shape o f the stress b lock as the bend ingm om ent at a beam section is increased . T he section reaches its flexural strength (m axim ummoment of resistance) when the total compressive force in the concrete multiplied by the

internal lever arm jd is a maximum. The properties of the compressive stress block at the section

o f m axim um m om en t m ay be defined by param eters k１ ， k２ and k３ , as in F ig.6 .3 (a ) . Fo r arectangular section of widthb and effective depthd, the total compressive force in the concrete

becom es k１ k３ f′c bc and the internal level arm isd唱k２ c, wherec is the neutral axis depth. A great

deal o f research has been conducted to determ ine the m agn itude o f these param eters fo runconfined concrete. The most notable work has consisted of the short唱term tests conducted by

H ognestad et al at the Po rtland C em ent A ssociation(PCA)and by Rü sch . T he specim ens usedin the PCA tests w ere like those appearing in F ig.6 .4 . The test region o f the specim en w as

loaded eccentrically by increasing the two thrustsP１ and P２ . T he thrusts P１ and P２ w erevaried independently such that the neutral axis (i.e., fiber of zero strain) was maintained at the

bottom face of the specimen throughout the test; therefore, the stress distribution in the

compression zone of a member with flexure was simulated. By equating the internal and external

fo rces and m om ents, it w as possib le to calcu late the values o f k１ , k２ , and k3 directly , ob tain ingas w ell the stress唱 strain curve fo r the concrete in the specim en . S tress唱 strain curves fo r theconcrete were also determined from axially loaded cylinders and were found to be similar to the

stress唱 strain curves fo r the concrete in the specim ens. Fo r h igher strength concrete, how ever, them axim um stress reached in the specim ens at the flexural strength w as k３ f′c sligh tly less than thecy linder strength . The tests also determ ined the concrete strain εc at the extrem e comp ressionfiber at the flexural strength. The values found for the stress block parameters of concrete with

sand唱gravel aggregates varied with the cylinder strengthf′c . T hese quan tities co rrespond to themaximum values ofk１ k３ found in each test.

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Fig.6.2　 Strain and stress distribution in the compressed concrete of a sectionas the bendingmoment is increased up to the flexural strength

F ig.6.3　 Compressive stress distribution in the compression zone o f a rectangular concrete section

F ig.6.4　 Portland cement association test specimen

Notes(1 ) A large number o f tests on rein fo rced concrete m embers have ind icated that th is

assumption is very nearly correct at all stages of loading up to flexural failure, provided good

·５４·Unit ６

bond exists between the concrete and steel.句中 have ind icated that… .中的 that引导宾语从句 ，p rov ided… the concrete and steel为条件状语从句 。 全句可译为 ：混凝土构件的大量试验表明 ：只要在混凝土和钢筋之间存在良好的粘结 ，此假定对弯曲破坏前的各个加载阶段几乎都是非常准确的 。

(2)W hen an increase in strength cou ld cause an un favo rab le cond ition (e.g., resu lting in abrittle shear failure rather than a ductile flexural failure in seismic design), the designer may take

the add itional strength due to strain harden ing in to account by referring to the actual stress唱strain curve for the steel.句首 w hen引导状语从句 ，by referring to…为方式状语 ，表示采用的方法或手段 。全句可译为 ：当强度增加会导致不利情况时（例如在抗震设计时会导致脆性剪切破坏而非延性弯曲破坏） ，设计者便可通过参考钢材的实际应力 -应变曲线来考虑由于应变硬化而引起的强度提高 。

New Words1. assump tion［待餐s礍mp礏待n］ n .假定 ，设想2. tensile［餐tensail］ a.可拉长的 ，拉力的 ，受拉的3. rein fo rce［仓ri礑in餐f礎礑s］ v .加强 ，增援 ，加劲 ，加筋4. bond［b礎nd］ n .粘结 ，结合 (物 )，联结5. slip ［slip］ n .滑移 ，滑倒 　 v .滑动 ，滑倒6. gauge［ged礒］ n .标准尺 ，规格 ，量表 　 v .测量7. strain［strein］ n .应变 ，紧张 　 v .拉紧 ， (使 )紧张 ，损伤8. linearity ［仓lini餐辈 riti］ n .线性 ，直线性9. inaccuracy ［in餐辈kjur待si］ n .错误10. p ro file［餐pr待ufail］ n .剖面 ，侧面 ，外形 ，轮廓11. stipu late［餐stipjuleit］ v .规定 ，保证12. specification［仓spesifi餐kei礏待n］ n .规格 ，说明书 ，规范13. comp ressive［k待m餐presiv］ a.有压缩力的 ，受压的14. uncon fined［餐礍nk待n餐faind］ a.无限制的 ，无约束的15. no tab le［餐n待ut待bl］ a.值得注意的 ，显著的 ，著名的16. brittle［餐britl］ a.易碎的 ，脆弱的 ，脆性的17. ductile［餐d礍ktail］ a.易延展的 ，柔软的 ，柔性的18. eccen trically ［ik餐sentrik待l］ adv .偏心地19. gravel［餐礔r 辈 v待l］ n .沙石 ，沙砾 ，沙砾层20. aggregate［餐辈礔ri礔eit］ n .集料 ，骨料 ，合计 　 a.合计的 ，集合的

Phrases and E xpressions1. B ernou lli's p rincip le　柏努利原理

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2. tensile strength　抗拉强度3. rein fo rced concrete　钢筋混凝土4. gauge length　标距5. in ternal lever arm 　内力臂6. effective dep th　有效高度7. cy linder strength　圆柱体强度8. flexural strength　抗弯强度9. strain harden ing　应变硬化10. seism ic design　抗震设计11. lever arm 　力臂12. stress b lock　应力块13. Po rtland C em ent A ssociation (PCA )　 波特兰水泥协会

E xercises1. T ranslate the fo llow ing paragraphs in to Chinese.Rein fo rced concrete can be considered to fail w hen the concrete cracks , creating defects

which can allow moisture to penetrate and corrode the reinforcement. This is a serviceability

failure in limit state design. Cracking is normally the result of an inadequate quantity of rebar,

o r rebar spaced at too great a d istance. The concrete then cracks either under excess load ing o rdue to in ternal effects such as early therm al shrinkage w hen it cures.

U ltim ate failure lead ing to co llap se can be caused by crush ing o f the concretem atrix,w henstresses exceed its strength ; by y ield ing o f the rebar; o r by bond failure betw een the concrete

and the rebar.

2. T ranslate the fo llow ing sen tences in to English .(1)混凝土受拉区出现裂缝就意味着混凝土与钢筋之间已经出现滑移 。(2)如果测量混凝土应变的标距包括数个裂缝 ，则柏努利原理可适用于平均拉应变 。(3)由于每个应变的测量误差和测量线位置的误差 ，计算结果可能会偏离线性假定 。(4)混凝土的应力 － 应变曲线也可由轴心受压圆柱体试件确定 ，而且可以发现它与本

文结果类似 。(5)中性轴下方混凝土中的拉应力很低 ，而且其内力臂也很小 。

Reading Material

Reinforced ConcreteRein fo rced concrete, also called ferroconcrete in som e coun tries , is concrete in w hich

reinforcement bars ("rebars") or fibers have been incorporated to strengthen a material that

·７４·Unit ６

would otherwise be brittle. In industrialized countries, nearly all concrete used in construction

is rein fo rced concrete.· History

The use o f rein fo rced concrete is a relatively recen t inven tion , usually attribu ted toJoseph唱Louis Lambot in 1848. Joseph M on ier, a F rench gardener, paten ted a design fo rreinforced garden tubs in1867, and later paten ted rein fo rced concrete beam s and posts fo rrailway and road guardrails.

Early rein fo rced concrete rem ained a paten ted rather than generic p roduct, w ith d ifferen tfirms developing competing systems. The German company Wayss & Freitag was formed in

1875, w ith A .G . W ay ss pub lish ing a book on rein fo rced concrete in 1887. Their m ajo rcompetitor in Europe was the firm of Francois Hennebique, set up in1892. H enneb iquecompleted over7,000 structures in rein fo rced concrete w ith in h is firm 's firs t ten y ears .

A rein fo rced concrete sy stem w as paten ted in the U n ited States by T haddeus H y att in1878. The first rein fo rced concrete bu ild ing constructed in the U n ited S tates w as the PacificCoast Borax Company's refinery in A lam eda, C alifo rn ia, bu ilt in 1893.

Them ajo r developm ents o f rein fo rced concrete have taken p lace since the y ear 1900; andfrom the late 20th cen tury , engineers have developed su fficien t con fidence in a new m ethod o frein fo rcing concrete, called p restressed concrete, to m ake rou tine use o f it .· Use in Construction

Concrete is rein fo rced to give it extra tensile strength ; w ithou t rein fo rcem en t, m anyconcrete buildings would not have been possible.

Rein fo rced concrete can encompass m any types o f structures and componen ts , includ ingslabs, walls, beams, columns, foundations, frames and more.

Rein fo rced concrete can be classified as p recast concrete and cast in唱 situ concrete.M uch o f the focus on rein fo rcing concrete is p laced on floo r sy stem s . D esign ing and

implementing the most efficient floor system is key to creating optimal building structures.

Small changes in the design of a floor system can have significant impact on material costs,

construction schedule, ultimate strength, operating costs, occupancy levels and end use of a

building.

· Materials

Concrete is a m ixture o f cem ent (usually Po rtland cem en t ) and stone aggregate. W henmixed with a small amount of water, the cement hydrates to form a microscopic opaque crystal

lattice structure encap su lating and lock ing the aggregate in to its rigid structure. T yp icalconcrete mixes have high resistance to compressive stresses［about 4,000 p si (27.5 M Pa )］ ;however, any appreciable tension (e.g. due to bending) will break the microscopic rigid lattice

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resulting in cracking and separation of the concrete. For this reason, typical non唱reinforced

concrete must be well supported to prevent the development of tension.

If a m aterial w ith h igh strength in tension , such as steel, is p laced in concrete, then thecomposite material, reinforced concrete, resists compression but also bending, and other direct

tensile actions. A reinforced concrete section where the concrete resists the compression and

steel resists the tension can be made into almost any shape and size for the construction

industry.

D epending on the type o f concretem ix and steel emp loy ed , rein fo rced concrete structurescan support 300 to 500 tim es their comb ined w eigh t and behave, acco rd ing to generalmechanics, as a single structural entity. Although concrete and steel would appear to have a

weight disadvantage, this support ratio is competitive with student balsa唱wood bridges.

· Key Characteristics

Three phy sical characteristics give rein fo rced concrete its special p roperties . F irst , thecoefficient of thermal expansion of concrete is similar to that of steel, eliminating internal

stresses due to differences in thermal expansion or contraction. Second, when the cement paste

w ith in the concrete hardens th is con fo rm s to the surface details o f the steel, perm itting anystress to be transmitted efficiently between the different materials. Usually steel bars are

roughened or corrugated to further improve the bond or cohesion between the concrete and

steel. Third, the alkaline chemical environment provided by calcium carbonate (lime) causes a

passivating film to form on the surface of the steel, making it much more resistant to corrosion

than it w ou ld be in neu tral o r acid ic cond itions .The rein fo rcing bars are generally su fficien tly w ell唱 bonded to the concrete to resist m ost

tension forces. However, where this is not the case, anchorage of the steel can be increased by

bend ing the rebar, fo r examp le in to a 90 degree bend o r 180 degree hook .In som e structuralm embers w here a sm all cross唱 section is desired , steel m ay be used to

carry some of the compressive load as well as tensile load. This occurs, for example, in

columns. In general, beams and slabs have reinforcing steel on all faces, whether or not they are

in tension , as th is help s to tie the concrete together and p reven ts crack ing from o ther causes ,such as the early thermal shrinkage which occurs as the concrete cures. In the case of

continuous beams where the tensile stress alternates between top and bottom of the member,

multiple runs (layers) of steel may be used or the steel may be bent into a zig唱zag shape within

the beam .The relative cross唱 sectional area o f steel requ ired fo r typ ical rein fo rced concrete is usually

qu ite sm all and varies from 1% fo rm ost beam s and slabs to 6% for som e co lumns .Rein forcingbars are no rm ally round in cross唱 section and vary in d iam eter. In the U nited S tates , rebarcomes in two grades of carbon content, Grade60 and G rade 40, w h ich typ ically sell fo r thesame price. Grade60 has a h igher carbon con ten t and , therefo re, a h igher tensile strength , bu t

·９４·Unit ６

its stiffness can make it difficult to bend and cut. Construction workers always prefer to use

Grade 40 rebar.G alvan ized , epoxy唱 coated , and stain less steel rebar are also availab le fo r use incorrosive env ironm ents.

Rein fo rced concrete structures som etim es have p rov isions such as ven tilated ho llow co resto con tro l their m o isture.

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Unit 7

Tex tAxially Loaded Short Columns

C reep and shrinkage o f concrete have a strong in fluence on the stresses in the steel and theconcrete o f an axially loaded rein fo rced concrete co lumn at the serv ice load , tend ing to increasethe longitud inal steel stress and to reduce the concrete stress . Fo r a co lumn hav ing a large

percentage of steel and a heavy initial load, which is later largely removed, it is even possible to

have tension in the concrete and comp ression in the steel. Therefo re it is extrem ely d ifficu lt toassess the safety o f rein fo rced concrete co lumns using elastic theo ry and allow ab le stresses .

O n the o ther hand , the u ltim ate load o f a co lumn does no t vary app reciab ly w ith thehistory of loading. When the load is increased, the steel will normally reach the yield strength

before the concrete reaches its full strength. However, at this stage the column has not reached

its u ltim ate load . The co lumn can carry further load because the steel sustains the y ield stresswhile the deformations and load increase until the concrete reaches its full strength. Fig.7.1illustrates th is behav io r.A lternatively , if the concrete app roaches its strength befo re the steel

yields, as it would when very high yield steel is used, the increased deformation of the concrete

w hen near its fu ll s trength allow s the steel to reach the y ield strength(1 ) . T herefo re, the u ltim ateload o f an axially loaded , rein fo rced concrete co lumn (perhap s better referred to as the y ield

load) is the sum of the yield strength of the steel plus the strength of the concrete. It has been

found (e.g., by R ichart and B row ns and H ognestad ) that the strength o f the concrete in anaxially loaded column is approximately0.85 f ′c , w here f ′c is the comp ressive strength o f acylinder. The strength is rather lower than that of a cylinder because of the difference in

specimen shape and size, and because the vertical casting of a column leads to sedimentation

and water gain in the top region of the column. Thus the ultimate load of an axially loaded

column may be written as

Po ＝ ０ ．８５ f′c（ Ag － As t ） ＋ f y As t (7 .1)w here A g is the gross area o f the cross section , A s t is the to tal area o f longitud inal steel in thesection, andf y is the y ield strength o f the steel.

F ig.7.1　 Axial load唱 strain curves for the steel and concrete o f an axially loaded reinforced concrete column　 　 Up to the loadP o , tied and sp iral co lumns behave alm ost iden tically , and the transversesteel adds very little to the strength of the column. Once the loadP o is reached , a tied co lumnw ith ties no t closely spaced imm ediately fails , accompanied by breakdow n o f the concrete andbuck ling o f the longitud inal steel bars betw een the ties , because the spacing betw een the ties isgenerally too large to p reven t general concrete failure and buck ling o f bars(2 ) .

In a sp iral co lumn , after load P o has been reached , the shell o f concrete ou tside the sp iralis cracked o r destroy ed . The load capacity is reduced because o f loss o f concrete area, but the

spacing of the spiral steel is usually small enough to prevent buckling of the longitudinal bars

between the spirals. Hence the longitudinal bars continue to carry load; large increased

deformation follows, and the core concrete (which is tending to increase in volume because of

internal disruption) bears against the spiral, causing the spiral to exert confining reaction on the

core. The resu lting rad ial comp ressive stress increases the load唱 carry ing capacity o f the co reconcrete, and in spite of the loss of the concrete shell, the ultimate load of a column with a

heavy spiral can increase to greater thanP o . T he enhancem en t in strength o f concrete due tothe confinement of a steel spiral was discussed in the previous section where equation B gives

the strength o f con fined concrete cy linders w hen the sp iral reaches the y ield strength . If theunconfined cylinder strengthf ′c in that equation is rep laced by the uncon fined strength o fconcrete in a column,0.85f ′c , the u ltim ate load o f a sp iral co lumn m ay be w ritten as

Pu ＝ ０ ．８５ f ′c ＋ ８ ．２ f y Aspds s A cc ＋ f y As t (7 .2)

w here f y is y ield strength o f the steel,d s is d iam eter o f the sp iral,A sp is area o f the sp iral bar,s is pitch of the spiral, andA cc is area o f concrete in the co lumn core.

N ow８ ．２ f y Asp

ds s A cc ＝ ８ ．２ f y Aspds s

π d２s４ － As t ＝ ２ ．０５ f y V s － ８ ．２ f y Asp As t

ds s (7 .3)

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w hereV s = A sp π d s /s , is vo lum e o f sp iral steel per un it length o f co lumn core,A s t is to tal areao f longitud inal steel in the section .

Therefo re, Eq .(7 .2) m ay be w ritten asPu ＝ ０ ．８５ f′c Acc ＋ ２ ．０５ f y V s ＋ f y Ast １ － ８ ．２ Asp

ds s (7 .4)　 　 If the steel is rep laced by an equ ivalen t vo lum e o f longitud inal steel,V s w ill equal the areao f that longitud inal steel. Therefo re Eq . (7 . 4 ) ind icates that the steel in the sp iral isapproximately twice as effective as the same volume of longitudinal steel in contributing to the

strength o f the co lumn . H ow ever, the h igh load唱 carry ing capacity o f co lumns hav ing heavyspirals is available only at very large deformations and after the shell concrete has spalled. If

the ultimate load carried after the spalling of the shell concrete when the spiral reaches yield is

to exceed the y ield load o f the co lumn befo re spalling,P u from Eq .(7 .4)must be greater than P o

from Eq .(7 .1). Th is requ ires satis faction o f the fo llow ing cond ition０ ．８５ f′c Acc ＋ ２ ．０５ f y V s ＋ f y ＋ As t １ － ８ ．２ Asp

ds s ＞ ０ ．８５ f′c （ Ag － As t ） ＋ f y As t

hence w e must also haveV s ＞ ０ ．４１５ f′c

f y （ Ag － Acc － As t ） ＋ ４ Asp As tds s

w hich m ay be w ritten asρs ＝ V s

Ac＞ ０ ．４１５ f′c

f yAgAc

－ １ ＋ ４ Asp As tds sA c

(7 .5)w here A c = A cc + A s t , the gross area o f the co lumn core .

Fo r sp iral co lumns, the AC I code requ iresρs to be no t less than the value given byρs ＝ ０ ．４５ f ′c

f yAgAc

－ １ (7 .6)w here A c = co re area m easured to the ou tside d iam eter o f the sp iral. C omparison o f Eq .(7 .5 )and Eq.(7.6) ind icates that the AC I requ irem ent w ill ensure that the u ltim ate load o f the co lumnafter spalling exceeds the load befo re spalling. The large ductility o f sp iral co lumns (F ig.7 .2) iso f considerab le in terest .W hereas the axially loaded tied co lumn w ith ties no t closely spacedshows a brittle failure, a spiral column has a large capacity for plastic deformation.

T ests have show n that closely spaced rectangu lar ties also enhance the strength andductility of the confined concrete, although not as effectively as circular spirals. This is because

rectangu lar ties w ill app ly on ly a con fin ing p ressure near the co rners o f the section , sincelateral pressure from the concrete will cause lateral bowing of the tie sides, whereas circular

spirals, because of their shape, are capable of applying a uniform confining pressure around the

circum ference(3 ) . T ests by Chan suggested that w hen considering strength enhancem en t, theefficiency of square ties may be50% o f that o f the sam e vo lum e o f circu lar sp irals . T ests bymany others have also indicated an enhancement of strength due to closely spaced rectangular

ties, but the results reported by Roy and Sozen indicated no gain in strength. It is likely that

·３５·Unit ７

the concrete strength gain from rectangular ties will be small in most cases. However, test

results have always shown that a significant improvement in the ductility of the concrete

resulted from the use of closely spaced rectangular ties.

F ig.7.2　 Comparison o f to tal load唱 strain curves of tied and sp iral columns

Notes(1) A lternatively , if the concrete app roaches its strength befo re the steel y ields , as it

would when very high yield steel is used, the increased deformation of the concrete when near

its fu ll s trength allow s the steel to reach the y ield strength .句中 as it w ou ld表示虚拟 ，说明这种情况很难出现 ；w hen near its fu ll strength为省略了的状语从句 ，补全时应为 ：w hen itis near its full strength。全句可译为 ：另一种情况是如果混凝土在钢筋屈服前就达到其 (抗压 )强度 ，如同采用强度极高的钢筋时那样 ，接近极限抗压强度的混凝土的进一步变形会使钢筋达到其屈服强度 。

(2) O nce the load P o is reached , a tied co lumn w ith ties no t closely spaced imm ediatelyfails, accompanied by breakdown of the concrete and buckling of the longitudinal steel bars

between the ties, because the spacing between the ties is generally too large to prevent general

concrete failure and buck ling o f bars .句中 accompanied by… betw een the ties ,为过去分词短语 ，做补充说明 ，全句可译为 ：一旦达到荷载 P o ，箍筋间距较大的箍筋柱便立即破坏 ，并伴随着混凝土压碎和箍筋间纵筋的压屈 ，这是因为箍筋间距一般都太大从而不能防止混凝土的总体破坏和钢筋的压屈 。

(3) Th is is because rectangu lar ties w ill app ly on ly a con fin ing p ressure near the co rnersof the section, since lateral pressure from the concrete will cause lateral bowing of the tie sides,

w hereas circu lar sp irals , because o f their shape, are capable o f app ly ing a un ifo rm con fin ingpressure around the circumference.句中 since… o f the tie sides ,修饰 This is because… o f thesection，whereas引导状语从句 ，从意义上讲与主句并列 ，全句可译为 ：这是因为 ，由于混凝

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土的侧向压力将使箍筋的各边向外弯曲 ，矩形箍筋只能对截面的角部施加约束压力 ；而由于其（特有的）形状 ，圆形螺旋筋能在截面周围施加均匀的约束压力 。

New Words1. creep ［kri礑p］ n .徐变 　 v i.徐变 ，蠕变2. shrinkage［餐礏ri nkid礒］ n .收缩3. allow ab le［待餐lau待bl］ a.允许的 ，正当的4. sustain［s待s餐tein］ v t.支撑 ,维持5. u ltim ate［餐礍ltimit］ a.最后的 ，最终的 ，根本的6. y ield［ji礑ld］ v i.屈服 ，屈从 　 v t.出产 ，生产7. app roxim ately ［待pr礎ksi餐m待tli］ ad .近似地 ，大约8. sed im entation［仓sedimen餐tei礏待n］ n .沉淀 ，沉降9. gross［gr待us］ a.总的 ，毛的10. transverse［餐t r 辈nzv待礑s］ a.横向的 ，横断的11. crack［kr 辈k］ n .裂缝 ，劈啪声 　 v .(使 )破裂 ，裂纹 ， (使 )爆裂12. equ ivalen t［i餐kwiv待l待nt］ a.相等的 ，相当的 ，同意义的13. spall［sp礎礑l］ n .碎片 　 v t.弄碎14. code［k待ud］ n .规范 ，代码 ，代号15. comparison［k待m餐p辈 risn］ n .比较 ，对照16. ductility ［d礍k餐tiliti］ n .延性 ，柔软性 ，顺从17. circum ference［s待餐k礍mf待r待ns］ n .圆周 ，周围18. enhancem ent［in餐h袋礑nsm待nt］ n .增进 ，增加19. breakdow n［餐breikdaun］ n .崩溃 ，衰弱

Phrases and E xpressions1. serv ice load　工作荷载2. steel bar　钢筋3.AC I (Am erican C oncrete Institu te)　美国混凝土学会4. y ield strength　屈服强度5. sp iral bar　螺旋筋6. tied co lumn　 箍筋柱

E xercises1. T ranslate the fo llow ing paragraph in to Ch inese.C o lumns are structural elem ents used p rim arily to suppo rt comp ressive loads. A sho rt

·５５·Unit ７

column is one in which the ultimate load at a given eccentricity is governed only by the

strength of the materials and the dimensions of the cross section. A slender column is one in

which the ultimate load is also influenced by slenderness, which produces additional bending

because of transverse deformations. Concrete columns are reinforced by longitudinal and

transverse steel. The transverse steel is generally in the form of ties or closely spaced spirals.

2. T ranslate the fo llow ing sen tences in to English .(1)混凝土徐变对工作荷载作用下的钢筋混凝土偏心受压柱的钢筋和混凝土应力影

响很大 。(2)随着荷载的增加 ，钢筋通常能在混凝土达到其抗压极限强度前达到抗压屈服

强度 。(3)螺旋筋的约束作用对混凝土抗压强度增加的影响将在下一章加以讨论 。(4)尽管不如螺旋筋有效 ，间距很密的箍筋也能提高约束混凝土的强度和延性 。(5)混凝土保护层剥落后 ，密布螺旋筋所产生的径向压应力仍能增加核心区混凝土的

承载能力 。

Reading Material

The Elastic Bending Moment Diagram of Concrete BeamsThe bend ing m om ents and the fo rces in the structure at the u ltim ate load , fo r the various

load combinations, may be calculated using linear elastic structure analysis. The sections are

designed to have ultimate capacities that at least equal the bending moments and forces

obtained from such an analysis. This is the method recommended by ACI and by most other

building codes. The ACI code allows any reasonable assumptions in the computation of the

relative flexural and torsional stiffness of the members, provided the assumptions are

consistent throughout the analysis.

It m igh t seem incongruous that although the sections are designed by the strength m ethod ,tak ing in to accoun t inelastic behav io r o f the concrete and steel, the bend ingm om ents and fo rceat the u ltim ate load are calcu lated assum ing linear elastic behav io r o f the m embers . H ow ever,this approach is valid because the distribution of the bending moments and forces so found

satisfies the conditions of static equilibrium and the boundary conditions. That is, the bending

m om ent d istribu tion is statically adm issib le. Such a design cou ld in fact be regarded as a validlower唱bound (limit唱design) solution.

A ssum ing linear elastic structural behav io r has the fo llow ing advan tage: it ensures thatonly a small amount of redistribution of bending moments will occur before the ultimate load is

reached , because the critical sections w ill tend to reach their u ltim ate capacities together.Therefore, the plastic rotation required at the critical sections will be small and the plastic

rotation capacity of sections need not be checked. It is evident that some moment

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redistribution will always be necessary, however. This is because once cracking and inelastic

strains commence, the flexural stiffness of the members will change, and unless the bending

moments calculated by linear elastic structural analysis are based on the final complex

distribution of flexural stiffness, some moment redistribution will be necessary before all the

critical sections can attain their flexural strength.

There are at least tw o m o re advan tages o f assum ing linear elastic behav io r o fm embers: oneis that it ensures that the steel and concrete stresses at the serv ice load are kep t as low as

possible, thus minimizing the widths of cracks in the concrete; and the other is that the design

m om ents and fo rces can be found using relatively sim p le and w ell唱 estab lished structural theo ry .C omm on ly , the flexural stiffness values used in the structural analy sis are based on the

gross concrete section: no allowance is made for concrete cracking, and the steel is ignored. It

may seem that this is a crude approximation because when members crack the flexural stiffness

change. Fo r examp le, fo r a rectangu lar section w ith a m odu lar ratio o f 10, the reduction inflexural rigidity from the gross section value on cracking may be30 to 60% fo r sections w ithρ＝ ρ′ ＝ 0.01, and 40% to 60% fo r sections w ith ρ = 0.01 and ρ′ = 0, depend ing on the steelpositions in the section. However, it must be remembered that the distribution of bending

moments depends on the ratios of the flexural stiffness of the members. Sometimes after

cracking of the members, the ratios of the flexural唱stiffness are still approximately as initially

assumed, because similar changes in the flexural rigidity may occur at all sections; then

relatively little moment redistribution is necessary at high loads to develop the assumed

bending moment pattern. However, the change in the ratios of the flexural stiffness resulting

from cracking may be significant in some cases. In continuous T beams, for example, cracking

causes a greater reduction in the flexural rigidity of the negative moment regions than the

positive moment regions; after cracking, therefore, the ratio of the maximum negative to

positive moments will be lower than the ratio obtained assuming a uniform flexural rigidity.

Also, in frames the changes of flexural rigidity of the columns may not be as great as for beams,

because co lumns are generally m ore heav ily rein fo rced than beam s and they no rm ally carryaxial compressive loads. Hence for columns the change in flexural rigidity from the gross

section value to the cracked section value will not be so great. In fact, in many frames the

beams will be cracked but the columns will remain uncracked in the service load range. The

reduced flexural rigidity, of cracked beams may lead to a bending moment to the columns larger

than that calcu lated on the basis o f gross section stiffness: N ear u ltim ate load , the flexuralrigidity of the columns will reduce, and the moment will be redistributed back to the beams. To

avo id sign ifican t m om ent red istribu tion , it m ay be better to base the m om ent o f inertia o f thebeams on an approximate transformed cracked section value (e.g.,0.5I g ) and the m om en t o finertia of the columns on the gross section valueI g . O kamura et al recomm end use o f thetransformed cracked section for the beam and the transformed uncracked section for the

column, with modified (increased) modular ratios to reflect inelastic behavior. Probably the

·７５·Unit ７

greatest variations in flexural rigidity from gross section values occurs in frames in which both

the to rsional and the flexural stiffness o f m embers are considered , because crack ing resu lts in amuch greater reduction in the to rsional stiffness than in the flexural stiffness . Fo r examp le,cracking may reduce the torsional stiffness of a member by more than90% . Therefo re, veryoften the torsion Stiffness may be ignored.

The fo rego ing d iscussion again emphasizes that un less the final comp lex d istribu tion o fstiffness is used in design, some moment redistribution will always be necessary, the extent of

the red istribu tion depend ing on the designer's assump tions abou t the flexural stiffness .H encealthough linear elastic structural analysis gives a convenient approach for determining the

distribution of moments and forces in strength design, it should be kept in mind that the critical

sections w ill requ ire som e ductility to attain the design u ltim ate load . T herefo re, reasonab lyrealistic approximations for the stiffness of member should be used.

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Unit 8

Tex tThe Nature of Soils

T o the civ il engineer, so il is any uncem ented o r w eak ly cem en ted accumulation o f m ineralparticles fo rm ed by the w eathering o f rocks, the vo id space betw een the particles con tain ingwater and/or air(1 ) .W eak cem entation can be due to carbonates o r oxides p recip itated betw eenthe particles or due to organic matter. If the products of weathering remain at their original

location they constitute a residual soil. If the products are transported and deposited in a

different location they constitute a transported soil, the agents of transportation being gravity,

w ind , w ater and glaciers . D uring transpo rtation the size and shape o f particles can undergochange and the particles can be sorted into size ranges.

· Physical and Chemical Processes

The destructive p rocess in the fo rm ation o f so il from rock m ay be either phy sical o rchemical. The physical process may be erosion by the action of wind, water or glaciers, or

disintegration caused by alternate freezing and thawing in cracks in the rock. The resultant soil

particles retain the sam e composition as that o f the paren t rock . Particles o f th is ty pe aredescribed as being of'bu lky ' fo rm and their shape can be ind icated by term s such as angu lar,rounded, flat and elongated. The particles occur in a wide range of sizes, from boulders down to

the fine rock flour fo rm ed by the grind ing action o f glaciers. The structural arrangem ent o fbulky particles (Fig.8.1) is described as single grain , each particle being in d irect con tact w ithadjoining particles without there being any bond between them. The state of the particles can

be described as dense, medium dense or loose, depending on how they are packed together.

The chem ical p rocess resu lts in changes in them ineral fo rm o f the paren t rock due to theaction o f w ater (especially if it con tains traces o f acid o r alkali), oxy gen and carbon d ioxide.Chemical weathering results in the formation of groups of crystalline particles of colloidal size

(＜ 0.002mm ) know n as clay m inerals . The clay m ineral kao lin ite, fo r examp le, is fo rm ed by thebreakdow n o f feldspar by the action o f w ater and carbon d ioxide.M ost clay m ineral particlesare of 'p late唱 like' fo rm hav ing a h igh specific surface (i.e. a h igh surface area to m ass ratio ) w iththe resu lt that their structure is in fluenced sign ifican tly by surface fo rces(2 ) . Long 'need le唱

shaped' particles can also occur bu t are comparatively rare.

· Clay Minerals

The basic structural un its o f m ost clay m inerals are a silicon oxy gen tetrahedron and analuminium唱hydroxyl octahedron, as illustrated in Fig.8.2 (a ). T here are valency im balances inboth units, resulting in net negative charges. The basic units, therefore, do not exist in isolation

but combine to fo rm sheet structures . The tetrahedral un its combine by the sharing o f oxy genions to form a silica sheet. The octahedral units combine through shared hydroxyl ions to form

a gibbsite sheet. The silica sheet retains a net negative charge bu t the gibbsite sheet iselectrically neutral. Silicon and aluminium may be partially replaced by other elements, this

being known as isomorphous substitution, resulting in further charge imbalance(3 ) .T he sheetstructures are represented symbolically in Fig.8.2 (b ). Lay er structures then fo rm by thebonding of a silica sheet with either one or two gibbsite sheets. Clay mineral particles consist

of stacks of these layers, with different forms of bonding between the layers. The structures of

the p rincipal clay m inerals are rep resen ted in F ig.8 .3.

F ig.8.1　 Single grain structure F ig.8.2　 C lay m inerals: basic units

F ig.8.3　 Structures of principal clay m ineralK ao lin ite consists o f a structure based on a single sheet o f silica combined w ith a single

sheet of gibbsite. There is very limited isomorphous substitution. The combined silica唱gibbsite

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sheets are held together relatively strongly by hydrogen bond ing. A kao lin ite particle m ayconsist of over100 stacks. Illite has a basic structure consisting o f a sheet o f gibbsite betw eenand combined w ith tw o sheets o f silica. In the silica sheet there is partial substitu tion o f siliconby alum in ium . The comb ined sheets are linked together by relatively w eak bond ing due to non唱exchangeab le po tassium ions held betw een them .M ontm orillon ite has the sam e basic structureas illite. In the gibbsite sheet there is partial substitu tion o f alum in ium by m agnesium and iron ,and in the silica sheet there is again partial substitu tion o f silicon by alum in ium . The spacebetween the combined sheets is occupied by water molecules and exchangeable cations other

than potassium, resulting in a very weak bond(4 ) . C onsiderab le sw elling o f m on tm orillon ite canoccur due to add itional w ater being adso rbed betw een the combined sheets .· Structure of Clay Minerals

The surfaces o f clay m ineral particles carry residual negative charges,m ain ly as a resu lt o fthe isom orphous substitu tion o f silicon o r alum in ium by ions o f low er valency bu t also due tod isassociation o f hydroxy l ions. U nsatis fied charges due to 'broken bonds ' at the edges o fparticles also occur. The negative charges result in cations present in the water in the void

space being attracted to the particles. The cations are not held strongly and, if the nature of the

w ater changes , can be rep laced by o ther cations, a phenom enon referred to as base exchange.C ations are attracted to a clay m ineral particle because o f the negatively charged surface

but at the same time they tend to move away from each other because of their thermal energy.

The net effect is that the cations fo rm a dispersed lay er ad jacen t to the particle, the cationconcentration decreasing with increasing distance from the surface until the concentration

becomes equal to that in the general mass of wafer in the void space of the soil as a whole. The

term doub le lay er describes the negatively charged particle surface and the d ispersed lay er o fcations. For a given particle the thickness of the cation layer depends mainly on the valency

and concentration of the cations: an increase in valency (due to cation exchange) or an increase

in concen tration w ill resu lt in a decrease in lay er th ickness. T emperature also affects cationlayer thickness, an increase in temperature resulting in a decrease in layer thickness.

Lay ers o f w ater m o lecu les are held around a clay m ineral particle by hydrogen bond ingand (because water molecules are dipolar) by attraction to the negatively charged surfaces. In

addition the exchangeable cations attract water (i.e. they become hydrated). The particle is thus

surrounded by a lay er o f abso rbed w ater. The w ater nearest to the particle is strongly held andappears to have a h igh v iscosity , bu t the v iscosity decreases w ith increasing d istance from theparticle surface to that o f 'free'w ater at the boundary o f the adso rbed lay er. A dso rbed w atermolecules can move relatively freely parallel to the particle surface but movement

perpendicular to the surface is restricted.

Forces o f repu lsion and attraction act betw een ad jacen t clay m ineral particles . Repu lsionoccurs between the like charges of the double layers, the force of repulsion depending on the

·１６·Unit ８

characteristics of the layers. An increase in cation valency or concentration will result in a

decrease in repulsive force and vice versa. Attraction between particles is due to short唱range

van der Waals forces (electrical forces of attraction between neutral molecules), which are

independent of the double唱layer characteristics, that decrease rapidly with increasing distance

between particles. The net interparticle forces influence the structural form of clay mineral

particles on deposition. If there is net repulsion the particles tend to assume a face唱to唱face

orientation, this being referred to as a dispersed structure. On the other hand, if there is net

attraction the orientation of the particles tends to be edge唱to唱face or edge唱to唱edge, this being

referred to as a flocculated structure(5 ) . T hese structures , invo lv ing in teraction betw een singleclay mineral particles, are illustrated in Fig.8.4(a) and F ig.8 .4(b ).

In natural clay s ,w h ich no rm ally con tain a sign ifican t p ropo rtion o f larger, bu lky particles ,the structural arrangem ent can be extrem ely comp lex. In teraction betw een single clay m ineral

particles is rare, the tendency being for the formation of elementary aggregations of particles

(also referred to as domains ) with a face唱to唱face orientation. In turn these elementary

aggregations combine to form larger assemblages, the structure of which is influenced by the

depositional environment. Two possible forms of particle assemblage, known as the bookhouse

and turbostratic structures , are illustrated in F ig.8 .4 (c) and F ig.8 .4 (d ). A ssemblages can alsooccur in the form of connectors or a matrix between larger particles. An example of the

structure of natural clay, in diagrammatical form, is shown in Fig.8.4(e).

F ig 8.4　 C lay structures

Notes(1) T o the civ il engineer, so il is any uncem ented o r w eak ly cem ented accumulation o f

mineral particles formed by the weathering of rocks, the void space between the particles

containing water and/or air.全句可译为 ：对于土木工程师来说 ，土是未胶结或者弱胶结的矿物颗粒的堆积物 ，（这些矿物颗粒）是岩石的风化产物 ，颗粒之间的孔隙含有水和（或）空气 。

(2)M ost clay m ineral particles are o f 'p late唱 like' fo rm hav ing a h igh specific surface (i.e. a

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high surface area to m ass ratio ) w ith the resu lt that their structure is in fluenced sign ifican tly bysurface fo rces .句中 that引导的从句作同位语从句 。 全句可译为 ：大多数粘土矿物颗粒都是片状的 ，而且比表面积很大（即表面积与质量的比值较大） ，这使得作用于颗粒表面上的力会显著影响它们的结构 。

(3) S ilicon and alum in ium m ay be partially rep laced by o ther elem ents , th is being know nas isomorphous substitution, resulting in further charge imbalance.句中 th is being know n asisomorphous substitution作为插入语 ，修饰前面的句子 。 全句可译为 ：硅和铝可以被其他元素部分取代 ，即同晶形取代 ，这会进一步导致电荷的不平衡 。

(4 ) The space betw een the combined sheets is occup ied by w ater m o lecu les andexchangeable cations other than potassium, resulting in a very weak bond.全句可译为 ：相互联结的晶片之间的间隙由水分子和可交换的阳离子所占据 ，而不是钾离子 ，因此联结很弱 。

(5) O n the o ther hand , if there is net attraction the o rien tation o f the particles tends to beedge唱 to唱 face o r edge唱 to唱 edge, th is being referred to as a floccu lated structure.全句可译为 ：另一方面 ，如果存在净引力 ，那么颗粒的定位倾向于面 —边接触或者边 —边接触 ，这就是所谓的絮状结构 。

New Words1. w eathering［餐we礖待ri礗］ n .风化2. carbonate［餐k袋礑b待neit］ n .碳酸盐3. p recip itate［pri餐sipiteit］ n .沉淀物 　 v t.使 … … 陷入 ，使 … …沉淀4. glacier［餐礔l辈 sj待 ，餐glei礏待］ n .冰河 ，冰川5. composition［仓k礎mp待餐zi礏待n］ n .成分6. bu lky［餐b礍lki］ a.大块的7. elongated［餐i礑l礎礗礔eitid］ a.细长的 ，伸长的8. d isin tegration［dis仓inti餐礔rei礏待n］ n .瓦解 ，衰变9. cry stalline［餐krist待lain］ a.水晶的 ，晶体的10. co llo idal［k待餐l礎idl］ a.胶状的 ，胶质的11. grind［礔raind］ v t.磨（碾）碎 ，磨光 ，磨成粉12. kao lin ite［餐kei待linait］ n .高岭石13. feldspar［餐feldsp袋礑］ n .长石14. tetrahedron［餐tetr待餐hedr待n］ n .四面体15. hydroxy l［hai餐dr礎ksil］ n .羟基 ，氢氧根16. octahedron［仓礎kt待餐hedr待n］ n .八面体17. valency［餐veil待nsi］ n .原子价 ，化合价18. ion［餐ai待n］ n .离子19. gibbsite［餐礔ibzait］ n .三水铝石 ，铝土矿 ，水铝氧20. isom orphous［餐ais待u餐m礎礑f待s］ a.同形的

·３６·Unit ８

21. po tassium［p待礑t 辈 sj待m］ n .钾22. illite［餐ilait］ n .伊利石23.m ontm o rillon ite［仓m礎nt待m待餐ril待餐nait］ n .蒙脱石24.m agnesium［m 辈礔餐ni礑zj待m］ n .镁25. d isassociation［餐dis待仓s待usi餐ei礏待n］ n .分离 ，分裂26. cation［餐k辈 tai待n］ n .阳离子27. d ispersed［dis餐p待礑st］ a.分散的28.m o lecu le［餐m礎likju礑l］ n .分子29. concen tration［仓k礎s待n餐t rei礏待n］ n .集中 ，浓度30. d ipo lar［dai餐p待ul待］ a.两极性的 ，偶极的31. v iscosity［vis餐k礎siti］ n .粘度 ，黏性32. floccu late［餐fl礎kjuleit］ v t.结絮33. assemblage［待餐semblid礒］ n .集合 ，聚集

Phrases and E xpressions1. residual so il　残积土2. transpo rted so il　运集土3. carbon d ioxide　二氧化碳4. chem ical w eathering　化学风化5. specific surface　比表面积6. silica sheet　硅 － 氧晶片7. gibbsite sheet　铝 －氢氧晶片8. isom orphous substitu tion　同晶形取代9. hydrogen bond ing　氢键10. base exchange　碱基交换 ，阳离子交换11. fo rces o f repu lsion　排斥力12. van derW aals fo rces　范德华力13. v ice versa　反之亦然14. like charges　同极性电荷15. d ispersed structure　分散型结构16. floccu lated structure　絮状结构17. paren t rock　母岩18. silicon oxygen tetrahedron　硅 － 氧四面体

E xercises1. T ranslate the fo llow ing paragraph in to Ch inese.

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In general, clay m inerals are alum ino唱 silicates m ade by a comb ination o f silica andaluminium oxide units with metal ions substituted within the crystal. A schematic diagram of a

silica un it is show n in F ig.8 .1 (a ). Each silica un it consists o f a tetrahedron w ith four oxy genatoms, O, located at the vertices of the tetrahedron equidistant from each other. A silicon atom,

Si, is located inside the tetrahedron equ id istan t from the oxy gen atom s . These un its combine tofo rm a silica sheet as show n in F ig.8 .1 (b ). The arrangem en t cou ld happen in variety o f w ay s .

Fig. 8.1 (b ) show s an arrangem en t in a hexagonal pattern in w h ich each basal oxy gen atom isshared with the adjacent unit. This sharing results a negative charge in the basic unit which can

be increased to zero if , fo r examp le, alum in ium rep laces silicon . F ig.8 .1(c) show s the sho rt handsymbo l generally used fo r silica. F ig.8 .2(a) show s a un it o f alum ina (alum in ium oxide) w here sixhydroxy l ions surround one alum in ium atom ,A l, in an octahedral arrangem en t.

2 . T ranslate the fo llow ing sen tences in to English .(1)如果风化产物留在原地 ，它们就构成残积土 。(2)物理过程包括风 ，水以及冰川的侵蚀 ，或者岩缝中水的冻融交替而引起的岩石

瓦解 。(3)四面体单元通过共用氧离子而联合在一起 ，形成硅氧晶片 。(4)负电荷导致孔隙水中存在的阳离子被吸附到颗粒上 。(5)阳离子化合价或浓度的增加会导致斥力的减小 ，反之亦然 。

Reading Material

Ultimate Bearing CapacityThe u ltim ate bearing capacity (q f ) is defined as the p ressure w hich w ou ld cause shear

failure of the supporting soil immediately below and adjacent to a foundation.

· Failure Modes

F ig.8.5　 M odes of failure

·５６·Unit ８

Three d istinct m odes o f failure have been iden tified and these are illustrated in F ig.8 .5 :they will be described with reference to a strip footing. In the case of general shear failure,

continuous failure surfaces develop between the edges of the footing and the ground surface as

show n in F ig.8 .5 . A s the p ressure is increased tow ards the value q f the state o f p lasticequilibrium is reached initially in the soil around the edges of the footing, then gradually

spreads downwards and outwards. Ultimately the state of plastic equilibrium is fully

developed throughout the soil above the failure surfaces. Heaving of the ground surface occurs

on bo th sides o f the foo ting although the final slip m ovem ent w ou ld occur on ly on one side,accompanied by tilting of the footing. This mode of failure is typical of soils of low

compressibility (i.e. dense or stiff soils) and the pressure唱settlement curve is of the general

form shown in Fig.8.5, the u ltim ate bearing capacity being w ell defined . In the m ode o f localshear failure there is significant compression of the soil under the footing and only partial

development of the state of plastic equilibrium. The failure surfaces, therefore, do not reach the

ground surface and on ly sligh t heav ing occurs . T ilting o f the foundation w ou ld no t be expected .Local shear failure is associated w ith so ils o f h igh comp ressib ility and , as ind icated in F ig.8 .5 ,is characterized by the occurrence of relatively large settlements (which would be unacceptable

in p ractice) and the fact that the u ltim ate bearing capacity is no t clearly defined . Punch ing shearfailure occurs w hen there is relatively h igh comp ression o f the so il under the foo ting,

accompanied by shearing in the vertical direction around the edges of the footing. There is no

heaving of the ground surface away from the edges and no tilting of the footing. Relatively large

settlem ents are also a characteristic o f th is m ode and again the u ltim ate bearing capacity is no tw ell defined . Punch ing shear failure w ill also occur in a so il o f low comp ressib ility if thefoundation is located at considerable depth. In general the mode of failure depends on the

compressibility of the soil and the depth of the foundation relative to its breadth.

· Ultimate Bearing Capacity

The bearing capacity p rob lem can be considered in term s o f p lasticity theo ry . The low erand upper bound theorems can be applied to give solutions for the ultimate bearing capacity of

a so il. In certain cases , exact so lu tions can be ob tained co rrespond ing to the equality o f thelower and upper bound solutions. However, such solutions are based on the assumption that

the soil can be represented by a perfectly plastic stress唱train relationship. This approximation

is on ly realistic fo r so ils o f low comp ressib ility , i.e. so ils co rrespond ing to the general shearmode of failure. However, for the other modes, settlement and not shear failure is normally the

lim iting criterion .A su itab le failurem echan ism fo r a strip foo ting is show n in F ig.8 .6 . The foo ting, o f w id th

B and infinite length, carries a uniform pressureq0 on the surface o f a m ass o f hom ogeneous ,isotropic soil. The shear strength parameters for the soil are denoted by the general symbolscand φ. As a simplifying assumption the unit weight of the soil is neglected (i.e.γ= 0).W hen the

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p ressure becom es equal to the u ltim ate hearing capacity q f the foo ting w ill have been pusheddownwards into the soil mass, producing a state of plastic equilibrium, in the form of an active

Rankine zone, below the foo ting, the angles ABC and BAC being 45° + φ/ 2. The dow nw ardmovement of the wedge ABC forces the adjoining soil sideways, producing outward lateral

forces on both sides of the wedge. Passive Rankine zones ADE and BGF therefore develop on

bo th sides o f the w edgeABC , the angles DEA and GFB being 45° - φ/ 2.T he transition betw eenthe dow nw ard m ovem ent o f the w edge ABC and the lateralm ovem en t o f the w edges ADE andBGF takes p lace through zones o f rad ial shear (also know n as slip fans ) ACD and BCG , thesurfaces CD and CG being logarithmic spirals (or circular arcs ifφ = 0) to w hich BC and ED , o rAC and FG , are tangen tial.A state o f p lastic equ ilibrium thus exists above the surface EDCGF ,the rem ainder o f the so ilm ass being in a state o f elastic equ ilibrium .

The fo llow ing exact so lu tion can be ob tained , using p lasticity theo ry , fo r the u ltim atebearing capacity of a strip footing on the surface of a weightless soil, based on the mechanism

described above. Fo r the undrained cond ition (φ u= 0) in w hich the shear strength is given bycu :

q f ＝ （２ ＋ π） ＝ cu ＝ ５ ．１４ cu (8 .1)The derivation o f th is value has been given by A tk inson and Parry .

Fo r the general case in w hich the shear strength param eters are c and φ, it is necessary to

consider a surcharge p ressure q0 acting on the so il surface as show n in F ig.8.6 ; o therw ise if c=0 the bearing capacity o f a so il fo r w h ich the un it w eigh t is neglected w ou ld he zero . T hesolution for this case, attributed to Prandtl and Reissner, is

q f ＝ c cot φ［exp（πtan φ） tan２ （４５° ＋ φ／２） － １］＋ q０ ［exp（πtan φ）tan２ （４５° ＋ φ／２） － １］ (8 .2)

　 　 H ow ever, an add itional term must be added to Eq .8.2 to take in to accoun t the componen to f bearing capacity due to the self唱w eigh t o f the so il. T h is componen t can only be determ inedapp roxim ately , by num erical o r graph icalm eans , and is sensitive to the value assum ed fo r theangles ABC and BAC in Fig.8.6 .

F ig.8.6　 Failure under a strip foo ting

·７６·Unit ８