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Load Reduction Factor Ǿ
ACI Code Section 9.3 specifies the following values to be used:
Tension controlled section Ǿ = 0.90
Compression controlled section
With Spiral Reinforcement Ǿ = 0.75
Other Reinforcement members Ǿ = 0.65
Plain Concrete Ǿ = 0.60
Shear and Torsion Ǿ = 0.75
Bearing on Concrete Ǿ = 0.65
Strut and tie models Ǿ = 0.75
WSD
휌 =
푛 =
푘 = 2휌푛 + (휌푛) − 휌푛
푗 = 1 −
푓 = 0.45푓
푓 = 0.4푓
Resisting moment of concrete
푀 = 푓 푗푘푏푑
Resisting moment of steel
푀 = 퐴 푓 푗푑
휌 =
휌 = 0.85훽 × = 0.85 × 0.85 × × .. .
= 0.013
휌 = 0.75휌
휌 < 휌
So the beam will fail by yielding
푎 = .
푀 표푟푀 = ∅퐴 푓 푑 −
Design steps of USD Beam
휌 = 0.85훽 × 휖 = 0.003,휖 = 0.005
푑 = =∅ .
Minimum 퐴 =
퐴 =∅
∅ = 0.90
푎 = .
General solution of
푎푥 + 푏푥 + 푐 = 0
푥 = ±√
푃 ( ) = 0.85∅ 0.85푓 퐴 − 퐴 + 퐴 푓
Axial capacity of tied column
푃 ( ) = 0.85∅ 0.85푓 퐴 − 퐴 + 퐴 푓 ∅ = 0.75푓표푟푡푖푒푑푐표푙푢푚푛
Axial capacity of spiral column
푃 ( ) = 0.80∅ 0.85푓 퐴 − 퐴 + 퐴 푓 ∅ = 0.65푓표푟푠푝푖푟푎푙푐표푙푢푚푛
Design a footing of column by USD method considering that the length of the footing is 1.5 times of width of the footing.
Given
퐷퐿 = 200푘
퐿퐿 = 160푘
푞 = 5푘푠푓푎푡5 푑푒푝푡ℎ
푓 = 3푘푠푖 and 푓 = 60푘푠푖
Column size = 16푖푛푐ℎ푠푞푢푎푟푒
Solution
푃 = (200 × 1.2 + 160 × 1.6) = 496푘푖푝
Assume self weight 3%
푃 = (200 + 160) × 1.03 = 370.8푘푖푝
퐴 = . = 74.16푓푡
Now
L = 1.5B
1.5B = 74.16
B = 7.03 ft L = 10.55 ft
q =.
= 6.69k/ft
Assume t = 23” d = 23 – 3 =20”
Punching Shear
V = (DL× 1.2+ LL× 1.6)–(a+ d) × q = 496 − ( ) ×6.69 = 442.3k
Resisting Shear
푉 = 4∅ 푓 푏 푑 = 4 × 0.75√3000 × × × = 473.23푘푖푝 > 442.3푘푖푝
Wide beam shear
푉 = . × 1 × 6.69 = 19.68푘푖푝
푉 = 2∅ 푓 푏 푑 = 2 × 0.75√3000 × × = 19.72푘푖푝 > 19.68푘푖푝
Moment calculation
푀 = = . × .
= 71.04푘푖푝 − 푓푡/푓푡
푀 = = . × .
= 27.14푘푖푝 − 푓푡/푓푡
휌 = 0.85훽 × = 0.85 × 0.85 × × .. .
= 0.0135
푑 = =∅ .
= . ×
. × . × × . × . × = 10.77" <
20"
Minimum 퐴 = = × × = 0.8푖푛
퐴 =∅
= . ×. × ×
= 0.81푖푛
푎 = .
= . ×. × ×
= 1.59푖푛푐ℎ
Provide ∅[email protected]"푐/푐.
퐴 =∅
= . ×
. × × . = 0.306푖푛
푎 = .
= . ×. × ×
= 0.6푖푛푐ℎ
Provide ∅[email protected]"푐/푐.
Pre-stressed Concrete:
Concrete in which there have been introduced internal stresses of such magnitude and distribution that the stresses resulting from given external loadings are counteracted to a desired degree. In reinforced concrete members the pre-stress is commonly introduced by tensioning the steel reinforcement.
Losses of pre-stressing
Losses due to
Elastic shortening Creep of concrete Shrinkage of concrete Steel relaxation Anchorage slip Frictional loss Bending of member
1. Classify soil Based on grain size.
Classification System or
Name of the organization
Particle size (mm)
Gravel Sand Silt Clay
Unified 75 – 4.75 4.75 – 0.075 Fines (silts and clays) < 0.075
AASHTO 75 – 2 2 – 0.05 0.05 – 0.002 < 0.002
MIT > 2 2 – 0.06 0.06 – 0.002 < 0.002
ASTM > 4.75 4.75 – 0.075 0.075 – 0.002 < 0.002
Permeability
푄 = 푘푖퐴 푘 = 퐶퐷
퐺퐼 = (퐹 − 35)[0.2 + 0.005(퐿퐿 − 40) + 0.01(퐹 − 15)(푃퐼 − 10)]
Uniformity Coefficient
퐶 =
Coefficient of Curvature
C = .
0
10%
20%
40%
30%
50%
60%
% F
iner
by
Mas
s
70%
80%
90%
100%
Grain Size, D (mm)
10 1
10D
60D
30D
0.1
The moisture contents of a soil at the points where it passes from one stage to the next are called consistency limits or Atterberg limits
PI = LL – PL.
퐿퐼 =
푆 = 퐶 푙표푔 ∆
Where,
푆 = 퐶표푛푠표푙푖푡푎푡푖표푛푆푒푡푡푙푒푚푒푛푡
퐶 = 퐶표푚푝푟푒푠푠푖표푛퐼푛푑푒푥
푒 = 푁푎푡푢푟푎푙푉표푖푑푅푎푡푖표표푓푆표푖푙푆푎푚푝푙푒
퐻 = 푇ℎ푖푐푘푛푒푠푠표푓푆표푖푙퐿푎푦푒푟
휎 = 퐼푛푖푡푖푎푙퐸푓푓푒푐푡푖푣푒푆푡푟푒푠푠
∆휎 = 퐶ℎ푎푛푔푒푖푛퐸푓푓푒푐푡푖푣푒푆푡푟푒푠푠
Compaction Consolidation
It is a dynamic Process It is a static Process
Volume reduction by removing of air
voids from soil grains
Volume reduction by removing of
water from soil grains
It is almost instantaneous
phenomenon
It is time dependent phenomenon
Soil is Unsaturated Soil is always saturated
Specified Compaction techniques are
used in this process.
Consolidation occurs on account of a
load placed on the soil
Perc
ent P
assi
ng
40
30
20
10
0
100
90
80
70
60
50
0.061 0.6 0.2 0.10 0.02 0.01 0.005 0.002
Well GradedUniform Graded
Gap Graded
Particle Size in mm (log Scale)
Open Graded
Dense Graded
Void ratio: Void ratio (e) is defined as the ratio of the volume of voids to the volume of solids. Mathematically
푒 =푉푉
Porosity: Porosity (n) is defined as the ratio of the volume of voids to the total volume. Mathematically
푛 =푉푉
The relationship between void ratio and porosity
e = = = =
n = Degree of saturation Degree of saturation (S) is defined as the ratio of the volume of water to the volume of voids.
푆 =푉푉
The degree of saturation is commonly expressed as a percentage.
Moisture Content Moisture content (w) is also referred to as water content and is defined as the ratio of the weight of water to the weight of solids in a given volume of soil. Mathematically
푤 =푊푊 × 100
Unit weight Unit weight (γ) is the weight of soil per unit volume.
훾 = 푊푉
The unit weight can also be expressed in terms of weight of soil solids, moisture content, and total volume.
훾 = 푊푉 =
푊 + 푊푉 =
푊 1 + 푊푊
푉 = 푊 (1 + 푤)
푉
Density Index or Relative Density The term relative density is commonly used to indicate the in situ denseness or looseness of granular soil. The ratio between the minimum density to the maximum density of granular soil is defined as relative density.
퐷 = 푒 − 푒
푒 − 푒
Where 퐷 = 푅푒푙푎푡푖푣푒푑푒푛푠푖푡푦, 푢푠푢푎푙푙푦푔푖푣푒푛푎푠푎푝푒푟푐푒푛푡푎푔푒 푒 = 퐼푛푠푖푡푢푣표푖푑푟푎푡푖표표푓푡ℎ푒푠표푖푙 푒 = 푉표푖푑푟푎푡푖표표푓푡ℎ푒푠표푖푙푖푛푡ℎ푒푙표표푠푒푠푡푐표푛푑푖푡푖표푛 푒 = 푉표푖푑푟푎푡푖표표푓푡ℎ푒푠표푖푙푖푛푡ℎ푒푑푒푛푠푒푠푡푐표푛푑푖푡푖표푛
퐿표푛푔표푟푐표푛푡푖푛푢표푢푠퐹표표푡푖푛푔 = 푞 = 푐푁 + 훾퐷푁 + 퐵푁
푆푞푢푎푟푒퐹표표푡푖푛푔 = 푞 = 1.3푐푁 + 훾퐷푁 + 0.4훾퐵푁
퐶푖푟푐푢푙푎푟퐹표표푡푖푛푔 = 푞 = 1.3푐푁 + 훾퐷푁 + 0.3훾퐵푁
Where
q = Ultimatebearingcapacity
N ,N , N = Bearingcapacityfactordependsonangleoffriction∅
푐 = 퐶표ℎ푒푠ℎ푖표푛표푓푠표푖푙
푞 = 훾퐷
퐷 = 퐷푒푝푡ℎ표푓푓표푢푛푑푎푡푖표푛
훾 = 푈푛푖푡푤푒푖푔ℎ푡표푓푠표푖푙
N ,N , N iscalledTerzaghibearingcapacityfactor.
N = Cohesionfactor
N = Surchargefactor
N = Unitweightfactor
Laboratory Tests of Soil
Properties Test
Grain size distribution Sieve analysis and hydrometer test Consistency Liquid limit
Plastic limit Plasticity index
Compressibility Consolidation Compaction Characteristics Standard proctor, Modified proctor Unit Weight Specific Gravity Shear Strength
1. Cohesive Soils 2. Non-cohesive soils 3. General
Corresponding Tests: 1. Unconfined Compression test 2. Direct Shear test 3. Tri-axial test
Field Tests of Soil
Properties Test Compaction control Moisture – Density relation
In place density Shear Strength – (Soft Clay) Vane shear test Relative Density – (Granular Soil) Penetration test Field density Core Cutting
Sand replacement Permeability Pumping test Soil Sampling and resistance of the soil to penetration of the sampler
Standard Penetration test Split Barrel Sampling
Bearing Capacity Pavement Footing
Corresponding Tests CBR, Plate Beating test Plate Bearing test
Piles Vertical Piles Batter Piles
Corresponding Tests
Load Test Lateral Load Test
2. Example
Determine the net ultimate bearing capacity of a mat foundation measuring 15m×
10푚on saturated clay with 푐 = 95푘푁/푚 ,∅ = 0,푎푛푑퐷 = 2푚.
Solution:
푞 ( ) = 5.14푐 1 +0.195퐵
퐿 1 + 0.4퐷퐵
푞 ( ) = 5.14 × 95 × 1 +0.195 × 10
15 1 + 0.42
10 = 595.9푘푁/푚
The mat has dimension of 30푚 × 40푚. The live load and dead load on the mat are
20MN. The mat is placed over a layer of sot clay. The unit weight of het clay is . .Find the 퐷 for a fully compensated foundation.
Solution:
퐷 =푄퐴훾 =
200 × 10(30 × 40)(18.75) = 8.89푚
Chemical oxygen demand (COD) Chemical oxygen demand (COD) is a measure of the quantities of such materials present in the water. COD, however, as measured in a COD test, also includes the demand of biologically degradable materials because more compounds can be oxidized chemically than biologically. Hence, the COD is larger than the BOD.
The amount of oxygen required by micro-organisms to oxidize organic wastes aerobically is called biochemical Oxygen demand (BOD).
Why COD is greater than BOD?
Because BOD contains only biodegradable but whereas COD includes both biodegradable and non biodegradable that is the reason why cod is larger than BOD.
1. Example:
At 25℃, hydrogen ion concentration of a solution is 0.001M. Determine the 푃 of the solution.
Answer:
Given, [퐻 ] = 0.001푀 = 10 푀
We know,
푃 = − log[퐻 ]
= − log 10
= 3.00
2. Factors influencing water use:
• Size of city • Climate and location • Industrial development • Habits and living standards • Parks and gardens • Water quality • Water pressure • Cost of water
3. Essential elements of water supply
Source of supply Collection system Treatment plant Distribution system
4. The most common water treatment methods are
Plain sedimentation Sedimentation with coagulation Filtration Disinfection
Sewer A sewer is a conduit through which wastewater, storm water, or other wastes flow. Sewerage is a system of sewers. The system may comprise sanitary sewers, storm sewers, or a combination of both. Usually, it includes all the sewers between the ends of building-drainage systems and sewage treatment plants or other points of disposal.
Sanitary or separate sewer o Sanitary sewage o Industrial sewage
Storm sewer Combined sewer
5. Name deferent types of test for environmental engineering
Determination of Iron Concentration of Water Determination of Sulfur from a Soluble Sulfate Solution Determination of 푃 of water Determination of Total Dissolved Solid (TDS)
Determination of Alkalinity of Water
Determination of Ammonia in an Ammonium Salt Determination of Chlorine Concentration of Water Determination of Arsenic Determination of Hardness of Water Determination of Dissolved Oxygen Determination of Biochemical oxygen demand (BOD)
Determination of Chemical oxygen Demand (COD) Determination of Turbidity of Water
Correction for pull
퐶 = (푃 − 푃 )퐿
퐴퐸 Where,
푃 = 푃푢푙푙푎푝푝푙푖푒푑푑푢푟푖푛푔푚푒푎푠푢푟푒푚푒푛푡
푃 = 푃푢푙푙푎푡푤ℎ푖푐ℎ푡푎푝푒푖푠푠푡푎푛푑푎푟푑푖푠푒푑
퐴 = 퐶푟표푠푠 − 푠푒푐푡푖표푛푎푙푎푟푒푎표푓푡ℎ푒푡푎푝푒
퐸 = 푀표푑푢푙푢푠표푓푒푙푎푠푡푖푐푖푡푦표푓푡ℎ푒푡푎푝푒푚푎푡푒푟푖푎푙푠
Correction for sag
퐶 = 푤 푙24푃
Where 푤 = 푊푒푖푔ℎ푡표푓푡ℎ푒푡푎푝푒
퐿 = 퐿푒푛푔푡ℎ표푓푡ℎ푒푡푎푝푒
푃 = 푃푢푙푙푎푝푝푙푖푒푑
Correction for slope or vertical alignment
퐶 = ℎ2푙
If slopes are given in terms of vertical angels
퐶 = 2푙푠푖푛휃2
Where, ℎ = 퐷푖푓푓푒푟푒푛푐푒푖푛ℎ푒푖푔ℎ푡푏푒푡푤푒푒푛푡ℎ푒푒푛푑푠표푓푡ℎ푒푠푙표푝푒
푙 = 퐿푒푛푔푡ℎ표푓ℎ푡푒푠푙표푝푒
휃 = 퐴푛푔푙푒표푓푡ℎ푒푠푙표푝푒
Es or G =
= ( )
Cement Compound Weight
Percentage Abbreviation
Chemical Formula
Tri calcium silicate 50 % C3S Ca3SiO5 or 3CaO.SiO2
Di calcium silicate 25 % C2S Ca2SiO4 or 2CaO.SiO2
Tri calcium aluminate 10 % C3A Ca3Al2O6 or 3CaO .Al2O3
Tetra calcium aluminoferrite
10 % C4AF Ca4Al2Fe2O10 or
4CaO.Al2O3.Fe2O3
Gypsum or Calcium Sulphate
5 %
CaSO4.2H2O
1. Write the standard of strength testing of cement according to ASTM C 109.
American Society for Testing Materials Standard (ASTM C-109) 3 -days 1740 psi (12.0 MPa) 7 -days 2760 psi (19.0 MPa) 28 -days 4060 psi (28.0 MPa)
2. Write allowable slumps for various constructions
Type of Construction
Slumps mm Inch
RCC Foundation walls & Footings 25 – 75 1 – 3 Plain Footings, caissons & substructure walls 25 – 75 1 – 3 Slabs, beams & reinforced walls 25 – 100 1 – 4 Building columns 25 – 100 1 – 4 Pavements 25 – 75 1 – 3 Heavy mass constructions 25 - 50 1 – 2
Sand is commonly divided into five sub-categories based on size:
a) Very fine sand (1/16 - 1/8 mm) b) Fine sand (1/8 mm - 1/4 mm) c) Medium sand (1/4 mm - 1/2 mm) d) Coarse sand (1/2 mm - I mm), and e) Very coarse sand (I mm. - 2 mm).
3. Example
The fineness modulus of two different types of sand is 2.84, and 2.24 respectively. The fineness modulus of their mixture is 2.54. Find the mixing ratio. Assume 퐹 = 2.84,퐹 = 2.24 푅 = = . .
. .= 1
R: 1 = 1:1
Cul-de-secLocal Street
Collector Street
Major Arterial
Expressway
Freeway
No throughtraffic
No throughtraffic
Unr
estri
cted
acce
ss
Increasing proportion of thoughtraffic; increasing speed
Incr
easi
ng u
se o
f stre
etfo
r acc
ess p
urpo
ses;
park
ing,
load
ing,
etc
.
Dec
reas
ing
degr
ee o
fac
cess
con
trol
Compleate access control
Road Way10 m
Slope (2:1)3 m
Berm10 m
Borrow pit10 m
Slope (2:1)3 m
Berm10 m
Borrow pit10 m
Road MarginRoad Margin
Right of Way
2:12:1
1 m
1 m 1 m
Section of National Highway
1. What are the lab testing of Aggregates of roadway.
Ans o Los Angeles Abrasion test o Aggregate Impact value o Aggregate Crushing Value o Soundness Test o Gradation test o Unit weight and Void test o Flakiness Index o Elongation Index o Angularity Number
2. What are the laboratory test for bituminous materials
Ans o Specific Gravity of Semi-Solid Bituminous Materials o Loss on Heating test o Penetration test o Softening Point test o Solubility test o Ductility test o Flash And Fire Points test o Spot test o Specific Gravity test o Distillation test