Welded Continuous Frames and Their Components

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Welded

Continuous

Frames and

Their

Components

irI l E V.L·lIJUL i I

1

IOlf

OF

P ~ L ~ l S T I C , l N ~ ~ J ~ Y S I : 3

L· S

~ ~ F P r - J I F ~ I )

TO

STRUC :PUR.d.T I

DESIG·N

by

For o ~ n i t t e e

D i s t r i b u t i o n

Only)

I ~ r l l i s

WOTlk

has been cal )l 1ied out as

a

p a l

t

o f

an

in v e stlg a tio 1 1

Sl 11S red

j

oint ly

by tIle

Welc1ing

}{e seE1Ilch

CounoiJ4 and. th e I)epartlue11t

the

l ~ u v y vifi th :C1..mcls f U l n i s l l e d

by

th e

f

oJ.lovvlI1g:

lirne r i can I l lS tu

to of

be e1 Cons

t l ~ U . C t i on

iiffie1

1

i can

I r ~ o l l

al1 1 ,Steel Ins t i tu te



9 8 52

205 14

T LE OF CONTENTS

Page

Introduction • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

r

The

Uncertainty of Material Properties in

the

Inelastic

Range

• • • • • • • • • • • • • • • • • • • • • • •

6

Theories

of

In i t ia l Inelastic Yield ••••••••• 7

Deflection

as

a

Limitat ion

in

Design

••••••••

8

5

Resistance to Moment

in the

Plastic Range

•

•

•

11

a

b

c

d

e

f

g

h

Cross sectional

Shape and

the

Stress

Strain

Di agram

• • • • • • • • • • • • • • • • • • • • • •• • • •

Effec t of Shear

• • • • • • • • • • • • • • • • • • • • • • • • • •

Effect of Axial

Load

• • • • • • • • • • • • • • • • • • • • •

Effect of Local Flange Buckling • • • • • • • • • •

Effect

of

Residual

Stress

• • • • • • • • • • • • • • • •

Effect of

Latera l Buckling • • • • • • • • • • • • • • •

Shape of r o s s ~ s e t i o n and Longitudinal

Distr ibution of Mate rial

• • • • • • • • • • • • • • • • •

Effect

of Encasement •••••••••••••••••••••

11

12

13

14

15

16

17

18

6

7

8

The

Design

of

Deta i l s

• • • • • • • • • • • • • • • • • • • • • • •

Shear as a Primary Uesign Criter ion

0

The

Limitation

of Failure by Fatigue

••••••••

Sha.kedown

• • • • • • • • • • • • • • •

• • • • • • • • • • • • • • • • • • •

19

21

24

26



9/18/52

205.14

P r o g r e

s s

r ~ e p b r ~ t IJ

0 •

Welded Continuous

Frames

and

Their

Components

AI\f

E V A L U A ~ [ 1 I O N

OF

PLi \srrr

A1J.l\IJ:{;SI1S

AS

i i P P L I I ~ r

TO

ST.R(JC1URAL

DEl3IGN

Bruce G. Johnston*

C

F

\

J. .

an g

Lynn

S. Beedle***

Introd Clc t ion

Th is

a r t i c l e

p r e s e n t s

a

resume

o f

l imi

t a t ions

as

wel l

as

t r e D ~ ( l s

in th e app l ica t lon of\

p l as t i c ana lys is

as

appl ied

to

s t r l l c t t l r a l

d e s i g n .

Many

of

the

items dis cus s ed

are

being stu d ied

in r e s e a r c t

pro jec t s

now in p r o g l ~ e s s a t Lehi.gh Univ81 sity

a n d

e l s e w h e r ~ e . rI11e

resu l t s o f t h es e

inves t iga t ions

may p ro v i d e a t l ~ t some

of

t h e

answers

needed

to broaden

the Scope of a p p l i c a t i o n of plas t ic

an-

alysis in

s t ruc tura l

des ign.

11118 p a p e r ~ does n o t p u r p o r t to

1,)6 a

s U l ~ T e y

01

in f

l

oJ:l a

t:1.on on

tl1.6

pla s t i c bells.vior o f s tX llC G1.1res. Refel en.ce v lill

be macle

pr i

m a r i l y

to

vV ork

c a I ~ l ) i e d

on

t

t11e F ri tz E11E;in.BerJ.ng r - l a b o r a t o r ~ y of

l

Lehigh

U n iv ersity as d e s c r i b e d

in pr ogr e ss

r e p o r t s publis hed o r



9/18/52

2- 205.14

01' fl )ame s tl UC

t1..lre.

11 Cl18Ck on the v a l i d l ty of tI1CJ aSSUlllptions

t h a t are usually made in continuous

welded

frame analysis

as

a p p l i e d to conventional or s o c a l l e d U e l a s t i c

H

desJ.gn tl d e s i r e d

al1.d a

C

oTIlple t e study of tIle el8.3

t i c

arld

p l a s t i c

be11a\ri

01')

of

C

o r l -

tinll.OUS f r

1

am8s and. t h e i r comp011ents was ElIsa contemI)latec l so

t l l t

the

c U l ~ I ~ e l t

i11tere

s

t;

n

the pas

S

J

btl:i.

ty

t l

t

~ ~ t n [ ~

1 8

serve

I)I.as

t i c s

t r e r l [ ~ t h

i n the des

igl l

of s

t ru e t u re

s m i g ~ h t

p x ~ o p e

J:,ly

be

eva].tlql,

ated by actual t e s t s .

Tile

plclSt1c

01

1

d u c t i l e b e h ~ : : t v i o r

of

s t e e l

11sed i n stl iucturaJ.

members

and

frames

i s important

both

to e l a s t i c and p l a s t i c d e s i g ~

pr ocodl...lres.

111 t118 CLlse

1: 1

ela.sti,c desig;11, tl1.8

j 11ception

of plas

3

t i c i t y (on th.e

lJasls of

s t r e s s CEtlcll l ,at i i .J11S t hat

n e F ~ J ~ e c t l o c a l £:tn.d

res idual s t r e s s

concentrat ions)

i s the e s s e n t i a l design

c r i t e r i o n ~

vvhel' 'eas

i l 1 the cq.se of

p l a s t i c ciestgn

t11G 1 1 1 a ? ~ i l n l l t n oapaci ty load.

oil

the

str1.1cttlre

i s

t he l )r ir lC ip al

desig11

c ri te l l io n. I Je fle ct;io n

C011

s i d e r ~ t i o n s

ma y

a l s o

be

of Importo.11ce

i n

eithel l e l a s t i c p 1 a s t i c



9/18/52

205.14

3 . To determine Pl lOC8(l l l reS of

a n a ly s i s t h at

w i l l

enable

one to calculate the collapse

londs

of

welded c o n t i l 1 l l O U S

f l ~ a m e s

and

to ver- ify the

analysis by sui table

t e s t s .

4.

To determine

procedures

of analysis

th at w ill

enable one to o a l c t l l a

te tb,e e18.8

t i c a d

per -

manent

defol llnations

i n

welded

contlnl10Us

f l ames

in the r a n g ~ intermediate

between

e l a s t i c

l irai

t arlcl col lapse l o a d .

5. To explore l imita t ions

in

the

application

of

p l a s t i c

range

design over and

above

d e f o ~ a

t ion l i m i t a t i o n s

namely,

fat igue,

local

bucklir.tg l a t e r a l buckling, e t c .

6.

To develop p r a c t i c a l design

procedures

fo r

the u t i l i z a t i o n of reserve

p l a s t i c

strength

i trle d 7E: ign continuous w e l d ~ e d frames.

Methods f o r

calculating the u ltimate s tr eng th of continuous



9/18/52

4-

205.14

seem

to have

been

d i r ~ e c tecl

towar d

removlng

some of

the

skept ic i sm

regarding the then new ideas of continuous beam and frame design.

Sett lement

of SlJ.ppOr)t may

cause

changes 2

the s t ress

d.istributJ.on

of

l

such s t r u c t l 1 x ~ e s

in

the e las t i c rQnge lJut 1VIo.ier-Lelbnitzl showed

thEtt

the ul t imate cn.pacity was

not affected by

sucl1

s e t t ] ~ 0 1 n e n t 8

In so doi11g he corl )oborated t Il e proced.UI es p r ~ e v i o u s l y develolJed.

by

others

fo r

the

calcula t ion

of

maximum

load

capaci ty .

However,

l i t t J e attem pt to actual ly eXl)loit

the

use

of

tlle u ltim ate lo ad

as a cri ter ion of

design

appears to 118 Ve been nude a t t ha t tirne.

The ef for t s of Van den Broek (3 ) in this country and J .F. Baker

(4)

and his associates in Great Britain

to

actually

ut i l ize

the

plast:l.c

reserve

s t rength

as

a design c r l ter ion al }8 well

known

and

will not be reviewed herein. A review of

recent

progress in

theol Y

of

·p las t ic

strllctul- Ctl

anaJ..ysis has been given by Symonds

cl nd l Jeal 5 .

Progress

toward the

ut i l iza t ion

of the

plas t ic

reserve

strength

in

s tee l structures as a design cr i te r ion can

best

be

made by a



-5

... 205.14

shear , and

bearing

in

the design of pins, r i v e t s and l o c a l points

of

C011taot t h a t

cause the y i e l d poirl t to be e.xceedecl

i n l o c a l

regions

of

most s t e e l

s t r u c t u r e s . In some cases th is

i s

due

to

neglect of stress concentrations

and in

other instances

of

high

s t r e s s Wl1.811

S U l ) I ~ o u n d e d

lJy I,ow stl )essed

mClteriQl. 11 110

maxim.urn

s t r e s s e s calculated by simple d e s i g n formulas are not the

true

m o xillll1m

s t r e s s e s .

CPhe

Inttel

o . l ~ e

not

c a l c u l a t e d .

and

p l a s t i c

t lction i s

depended upon

to

i n s u r e tIle s a f e t y

of

tl18

s t r t l c t u r e s

sInce

exper ience

ht.lS shown

t h a t

aV81 uge 01 nominal s t r e s s e s forlT

a

s a t i s f a c t o r y basis

fo r

design.

Under

appropriate c o n d i t i o n s ~

even the

average s t r e s s e s

nre near the

yield s tr e ss l e ve l. Such

local ized i n e l a s t i c behavior usually

does

not endanger a

structure

and

furthermore

most of these same

s t r u c t u r a l

members

have already

e x p e I ~ : t e n c

e

d g:P8 f:J. tel ) ~ r i e I d wl1 il e bei11g s t l ~ n . i g h te118 d

111

the

ml11.9

f o ~ r i c t e d i n

a

shop, 01 ) f o r c e d In.to

p o s i t i o l l

dlll )ing erect ion.

I t

actual ly

i s

during

these th re e ope ra ti on s

that

the

d u c t i l i t y

of s t e e l beyond the y i e l d point is cnl led upon to the greatest



9/18/52 205.14

In

the

ea r l i e s t

dctys of

the a l ~ t

tllo n e 1 1 g i n e e l ~

i n t u l t i ve l y

de-

signed s t J ~ u c t u l e s

thE: .t, as

l l

res1..11t of l lis

expel1ience and

fee l ing

for s tructura l

behavior, had

the

required

strength and durabi l i ty

l\

tha t was

needed.

Although theoret ical analysis is now a par t

of

a l l

des ign

p r o c e d u ~ 1 0 , expeJ}ience i s

probably

s t iJ l 0110 o,f t118

majol l factol )s in spec i f i ca t j on vvritirlg. Speci..:ficatiorlS 0.1 8 p]?i-

ma ri1 JT the

cod i f ica t ion

of

goocl

prac

t l c e

As

the

8 n [ ~ j . , 1 1 e e l ' )

leal ned

analyt ical methods

of elast ic s tress analysis

and coupled these

with

laboratory

t e s t resul ts on the strength of

materials

and

s t l ~ 1 1 c t u r Q ] melnber s hIs at tent ion was more

an.cl

11l0r}O

C1J:EtWl 1

to tIle

individual member ra the r than the whole st ructure .

Now

the

t rend

in

analysis and

in the laboratoDy

is buck to a

oonsiderat ion of

the C

omple te s

tI) l lC

tl11 8 ra

the r

than the i l 1 . d l , V i d u \ ' J . J ~ s 'blotlO

t

1.1 I )0.1

o m p o n n t ~

P l ~ I S

t ic

an.nlysis In

des ign

a.s

( ~ ~ ~ p l i e r d to tiOl l

bl1ildi.ng

f rames

was

foresh£tdowed by

the

appl

1

oximn.te

_ s o c ~ ~ J .

le( l

l I o 1 o . s t ~ c

mot110ds

of

anEllysis

t l 1 . ~ ; t crane in to 1J.SO ear ly

In tq.E?

cer.ltuJlY

J

or

tl1e

pur -



l a t i 011Ship 1s tIle lOVl/el'J y i e l d l e v e l of s t rue

t u r s t e e l .

Tllis i s

i l l u s t r a t e d

by t11e

p l a s

ti .c ' bendil1g bol1l1vlor

of

tlle

wide f l a n g e

s t r u c t u r a l

shape.

small

portion

of the typical s t r e s s - s t r a i n diagram for s t r u c t u r a l

s t e e l

in

the i n t

t i a l

pleas t i c

ral1ge up to

the

bo{gin1 1ing of g 8 1 1 8 I a l

stral.11

hal'1(lerlirlg. F i b .

2-b

may

serv'e

as

an

i n c l i c a t i o n

of

t l l ~

. f a c t ~

t h a t the pIns t i c b8 ldlng r e s i s

~ t a r l c e

] r a l ~ g e l y

may be retll:i.

zecl wi th -

o u t ~ US:Ll1g 111uch

of

the J ~ O V 1 1 F J : r l :y'ield range that: i s avaiJMable.

'me

lower

y i e l d level

i s

of obvious

importance

in p l a s t i c analyses and

may be

defined as

t h a t level or s t r e s s ju st s uf fic ie nt to

develop

successive new zones of p la s t i c s l ip in the port ions of a t e s t

specimen t h a t remains in the e l a s t i c

s t ~ t

Fig. taken from

may e x i s t in a p a r t ic u la r s t e e l a t a p a r t i c u l a r cross sect ion

of

n

wide-fla.llg;e

s11ape.

Iieepirlg

i n

mind

the

ftlC

t cha.

t

1111.11

tea

t s

i n

gelleraJ

a r ~ e l-lUll

t a 1 8.te s t l ~

2in ~ t ; h a t gives a

r e l a t i v e l y

rligll



9/18/52

-8

205.14

to d e t e r ~ n l i l e ·the

condi t ions fo r

e x p e r ~ i m e n t a l law for.,j.,ni tial

yielding

of

s tae l

or

othor

metals

in

a

s ta te

of

combined

s t ress .

Sucl1.

laws, hO N8ve

r tl e not; ge1:1el ally requi re d .for ti11e

px- edic

t l on

of

t ~ h e

i l l e 18.8

t ic be

h:1

v i 1 of

bo o.nls,

col

urnns, [ lnd te11S

1

011 lnembe rs ,

Such

s t ruc tura l

members are governed

primarily by u n l a x i ~ l s t ress .

In

other words, the

load carrying

par t of the s tress system is

one in which two

of the three

principal s t resses

arc

zero or

near ly

The duc t i l e

behavior

of

mater ia l

suell fL UJliuJtlal

s tress system

may be

based

on the

propert ies determined

by

the

simple

tensl011 or

oOlnpression

t e s t .

4.

Deflect ion

us

a Limitation

in

Design

.....

:r c _

...........

One of

the principal advantages of plas t ic

analysis

is

the

s impl ic i

ty by

w11ich

nlCtximum load cap- .lcl ty may be

deteJ:mined as

compared with procedures

of

indeterminate e las t ic frame

analysis .

I f def)lections

must be

ca.J,.cl11at8cl,

IntlCh

t h i s

adVElntage

i s l o s t

and

t must be recognized tha t

deflections

do

frequently

control

des ign whether i t be based on

e l a s t i c

ti

or Itplo.stic

anfl.lyses.



9/18/52

205.14

s ign proceclures.

In

elas t ic

design,

def lect ions

can

be computed

with

a

reason-

able

d_egree

of ce r ta in ty

in tile

e l a s t i c

working

loacl

ral1ge. In

the plas t i c design pr·ocedl1re

such

c erta in ty i s no t always poss ib le ,

F

1

igure

4 ,

taken from another Lehigh repor t

13 ,

COrl1r)ares t118

theore t ica l . and t e s t re su lts 1

1

a simply

supIJorterl

14

VVI 7

30

bealu

with cant i lever sections

e x t ~ n d i n g

beyond each support loaded

so

as to

simulate

a continuous beam between supports . In such

case

the theoret ical

curve for

load vs. deflect ion

S110WS

three s t ra igh t

l ine seglnents.

The rst bel1d in

tIle

t h eo re t i c a l

l lrVe

s t a r t s

when

the

y ie ld

moment

1s

reaehed at

the

supports

and

the

second

bend occurs when y ie ld mOluents a r ~ e

pflssed

a t the c e n t e l ~ of

wbhe

beam

span.

Tes t r e su l t s in the p r t i c u ~ r c se

illl,18

tl la ted f a l l

fax· ShOl t

of the t h eo re t i c a l l y

COmI)llte

r

l 11alues.

The i n i t l a l diver..

genae from

the theol letical

ValtleS

in the

elas t ic l ~ n g e i s pT

1

imar i ly

due to

res idual

s tress

and

the lowered

s trength

in the plas t ic

range i s

due to loca l

and

la te ra l

plas t ic

buckling of beam f langes.



9/18/52 -10 ..

205.14

up

of

8 B 13 members, of

greater

suscept ib i l i ty to loca l buckling,

did

not

quite

develop i t s

fu l l

plas t ic

strongth

nor

did

i t

sus tain

the plas t ic strength that was developed. Fig. 6 shows a photo

graph

of

Frame No. 1 in i t s f inal

deflected

posit ion.

I f many dupli c a te s trt,lCture s we re lnade to the s arne de s ign anrl

actually tes ted to fa i lu re ,

one

should expect a

considerable

s c a t t e r due only to v r ~ i t i o n in yielrl

po in t

(Fig . 3 ) . The f c t o l ~

of safety adopted in plas t ic

design

must

recognize

th is uncertainty

in m;ct:x:im lln l o ad . At { l11oWLlbJ_6 loads in p l a s t i c des ign u n c e r t ~ i n -

t i e s as to

def lec

t i on mus t {lIs a be t o l e ra t e d, becaus e of

tJ:18

e.f,flec t

01

r es idua l

s t r e s s .

T 6

impol ltance

of

d ef le ct io n in

p la s t i c

de

sign

is

one of the factors

discussed

in Progress

Report

No. 3 of

the Lehigh ser ies (8) .

In a discuss ion o.f

def lec t ion

t i s of i n t e r e s t to

I1efer to

t 8

AlSO specif ioat ion

for buildings

(9) ,

Section

17 of which

reads,

th e depth of bcan1s d g : t l ~ l e ] ~ s f loor s sha. l l

prete t i cnb le be

110t l ess

than 1/24

of tIle span, Ul d

1 V l l o l ~ e

s r ~ b j e c t

to S110cks



9/J.8/52

-11

..

205.14

probable

tho.

t

i.n many cases n s tl'1UO ·b lre des ign y pla s t ic pro

cedures

might

actually meet

this speci f icat ion because of the r e ~

duction

in deflection

produced y

continuity

even

when

plas t ic

design i s cons idered .

This

f a c t

has been discussed in

Lehigh

Pro

gress

Report

No.3

8).

In summary,

the

following

may be said

regarding

doflect ions:

1 .

In cases

where

experience,

as

ref lected

in

exis t ing speci f icat ions

hus shown a

l imi ta-

t ion of deflection to

be desirable , it will

be ne cessary to

consider

deflect ion in

the

applicat ion of

plas t ic

design.

2. In cases of

plas t ic

design wherein the

working loads are c on sid era bly

grea te r than

those

fo r

e las t ic design,

an

unavoidable

degree of

i nde f in i t eness in f ina l deflect ion

8

t

wo;rking

load

111US

t

be

t o l e r ~ l

t ed .

5. Resistance to n1o nent in. the Plast ic ~ a n g e

_

...

...

...

_



9/18/52

2 ~

205.14

I f a s t rue tura l s t e e l beam i s under pure bendi11g mom8nt, i t wi l l

stal' )t to

yie ld wb erl

tb.e f ibe rs

fur thes t f l

1

0m

the neutr t t l axis

r each

tl1 8

y ie ld p oin t.

F ig .

1)

Afte r

in i

t i a l

yie ld

tl1e

l )elation

betvleen

load D.ne). def l ec t ion

of

the b e ~ J m wil.l

be

nOl1.-1ineD.l l b11t

the beam wi l l

1 6Sist

i lCreQsing moment npproaclJ.ing

the

hinge

mornent

CtS

y ie ld ing penetl')D tes to l\Tard

tIle D.6utr 8.1

aJ<:ls of the

beam

ra t lo of t b ~ e hinge monlent to

the

moment

a t

i n i t i a l ~ v i e l d i s

SOlne

time s

t e r ~ m G d

the

U

shn.pe-fnc

tor of the beam it 1Nide

f lange

VvF) stl-'1J.cttlral sect iol l usual ly

has a

shQpe-f 'actor betvveen 1 1

and 1.20.

More

compact sect ions have la rger shape-factors; fo r

example, Q r e : c t a n g u ] ~ ~ J r

bOa TIl 11[18

a SllQpe-1')[lctor

of 1 .50 . Standt1rd

I-beam

shapes

vvi

th

110Qvy

vveb

t ~ l n d

slnctll

flt1nges

viII

ha.ve

greo.

te r

shape- fac tors

bhan vifide .flEtrlge

sect ions wlth th in webs.

In

addition to

the ef fec t

of

cross-soctional shape, there

may

be

secondary effec ts

insofar as s h ~ p e

affects

th e tendency toward

local

buckling,

l a t e ra l

buckling,

fai lure by shear , e tc . , as wil l

be discussed horeln[ l f t er

Tlle

C,9.1Cl11at:ton o.f

the

moment

-angle

curve from a given stre,$s str.:l in dlagl 43..m

1 lor

a wide f lan ge s ec tio n



9/18/52

205.14

problem

is a complicated one since the

dis t r ibu t ion of shear

st ress

depends

on

the support

detai ls

and

the

way

the load

is

brought in to the beam a t the

support.

I f

the

moment

f a l l o f f

r)apidly away f l ~ o m

the

SUPPo11t, in i

t i a l

yield ing due to moment may

be

so

local ized

that

s t ra in hardening

wil l commence before any

appreciable rota t ion

develops. In

such

a

case, the

moment

de

veloped a t

the support may

be

considerably greater than

the

hinge-moment predicted y simple plas t ic theory. In o th er c as es ,

vJhere

the

moment

gradient

i s no t

grea t , shear ma JT

reduce the

hlnge

moment sorIlewhat. Tl1e problem

of

shear

in

i t s

e f fec t

on

hinge-moment

has

been

studied

y

Horne

(12)

fo r

the

case

of

the

rectangular beam sect ion and s im lar

considerat ion of the

I-beam

sec t:i.on

are

now in pl logress

a t

Cambr:tclge a t Lehigh Univers i ty .

5 Ei fect

of ~ C i a l Load

The

ef i ec t

of

axia l

load

on

moment capaci ty fo r val )ious comb

ina t ions

of

erld moment and r e s t r a i n t are

repor ted

in Lehigh

l)rog

resa Report No.6

(13) .

In general , the

ef fec t

of axia l

load

i s



9/18/52

-1 4 -

205,14

column

w h r ~ s

th e

t e s t resul ts Qre .for

an

8 NF coll:unn w ith l / r

o f ll

t may be

seen from

the

t e s t l

e su lts th at i n i t i a l y ie ld

and

column

c o l l a p s e may OCCllr a· t londs

l ess

e v e n than th o se ca l

Cl11a

ted

fo r

in l

t i a l y ie ld th e s e c a n t f o r ~ m u l rrl tes·t re -

sul ts

are

n o t t y p i c a l of those t h a t

may

be expected from

o t h e r

c om bi na ti on s o f

a pp lie d lo ad ,

moment

and

s l e n d e r n e s s

ra t io

b u t

i l lus t ra te

what may

occur

under c e r t a i n c r i t i ca l co n d itio n s

c o ~ p l e d

w i t h

r e s i d u a l s tress an d

l o c a l

plast ic

buckling.

In o r d i n a r y pOl ltal f r ~ m e

columns th e

ra t io o f axia l to c r i t i c a l

load i s

u s u a l l y sma ll

so

t h a t any reduction

i n hinge moment may

be

ignor e d as

is done

in most s t u d i e s

o f c o l l a p s e

s t r e n g t h . How-

e v e r , in th e

case

o f t i e r b u ild in g s t r u c t u r e s , the res is t ing

moment of

th e

colum ns in

tllG

lower

flo o r)s

would

be

r e d u c e d

a x i a l lo ad and any e v a l u a t i o n

of c o l l a p s e

s tr e ng th in such a

case

should inc lude

c o n s i d e r a t i o n

o f

th is

e f fec t .

5D. E f t e c t of L oc al F lange Buckling

_ _

- - . - -



9/18/52

-15

2C)5.14

bea.n s • In s UC11 a

case

for

l

exrtrnp].e, 1008.1 buckJ .ing rlid

oee

u

in

the

re la t ; lve ly

bb,in

fla11ge

of

a

14

~ l F

30

simulEl

ted

con.tinuOlls

beam (14) .

Tl18

e f fec t was to l o w e J ~

the

rIlo ximum

res i s t ing

nloment

n t

the

support below the theox-eticaJ

hinge-molnent 3 l1d to produce

a

progressive

lowering

as

rotat ion proceeded. S im ilarly , in the

porta l

frame

connection

tests

reported

in Progress Report No.4

PS.rt 3 (15) the

fo l lowing i s

quoted l ~ o m

the

concluslons:

ilVVtlile

some of the bui l t up knee s

hL\Ve f[ t i r 11otation c t tpac i t i es rnost

of

them collQpse very

rapidly

a f te r

f i r s t loca l buckling. This in-

elud es tho se t h ~ l t a r e

welJ.

supporte.d l Q t e l ~ [ y Rotation cO pa-

c i ty

i s

dependent

on

an

abi11

y

of

tIle

knee

to

res i s

t

the

tend

sney

to

loca l

buckling. Thick flanges and

effect ive la te ra l

support r l l ~ e mos t helpf L1.1 . . Ii ig.

8,

from Progre s s

RepoJ:t 1\1

o. 4

Part 1, i l lus t ra tes

typical

local

buckling

adjacent

to

a connect

ion. I t may be added

tha t

th ick webs also tend to t ~ p r t f langes

agains t loca l

buckling and

improve the s i tua t ion in th is aspect



9/18/52

16-

to occur i f

the

elements are

of

intermediate

slenderness between

the

e la s t i c

buclcling

(very

s ] ~ e n d e r

rr.:lnge

ancl

the

very

shor t U d

COll1-l ClC t Inember tllQ t wi l l develop f u l l plas t ic y l e J ~ d s t rength even.

in the

presence

of

res idual s t ress

The

pr incipal

sources of res idual s tress are:

Uneven cooling of rol led

s tructura l sections

:lmmed.iate ly

af te r

roll ing )

2. Cold s tra ightening, punching, shearing, or

bending of sect ions .

3

VVeldil1g.

The

e f fec t s

of

cool ing

l ?rld

cold

l)ending

residl1.al

str-ess

htlVe

been

disc1.1SSed a t

some

lengtb.

t

T.Jehigh

P l ~ o g r e s s Report

5

(14) .

Effec ts of

iJ\181ding

residl1Ctl

str '0sses have bee11

110ted

In Pl'1ogress

Report

4 (15) wherein res idual s tress is considered to have

been

the cause of local.

pJ.nst ic

bucJ:r.l ing f [ l i l . 1 1 ~ e in

the hflunc11ed knees

along the

innexl compl' )8ssion f1lo.nge. t l l is

locat io11 the

inner)



9/18/52

-17

205.14

agains t in usual s t ructural design

proper

proportions

or

1 0 w e l ~ i n g

the D.l1owable s t re ss as in the case of oomp118ssion

m 8 1 n b ~ r s . ObviollSly in p ] ~ ~ l s t i c

design,

p J ~ o p o r t i o n s o a s t r ~ u c t -

Ul-le ml1st

be

sl..lch as to

el imin te

e l s t i c bl lckl lng o:£ any

type,

in-

eluding e l s t ic l te r l

buckling

Cons ider ing only

pl s t ic be

hav:tor,

l oc l

an.d/or

later1al

bl lckl ing

ma.y

lower

tb.e

effec t ive

hinge

moment

in

a continuous beam

or

frame member

and

may reduce

the moment value during continued ro t tio n in the pl s t ic range,

thtts preven t ing

tIle

re l i za

t ion

of the

fl111 pILls t ic

s

t r ~ e n g

t of

Many

tes ts of

frames

in the pl s t ic range, often on

small

models, have involved sol id rectangular bur sections bent in the

weak

plane (3

,

4). In such

a

case

loca l and/or

l te r l buckling

i s not

a

IJroblem.

Tests Brt. {8l ancl h is

associcLtes

lso

Inolude

smal l

model

fl l[tmeS

using

vide

.flt111ge

sect ions

bll t

the

e x t J ~ a p o l , ~ -

tiOll oil these

resu l t s to f1.11.1

si.ze stru.cttl1 lal members ul1.d frnmGs



9 /

1 8 / 5 2

-18-

2 0 5 .

]. 4

when n

round

tube

is

b e n t to a

sharp

ang le. In g en eral

the

con

t r ibut ion of bending

to

r e s i s t a n c e

to l a te ra l

lo ad w i l l

decrease

after

a ce r ta in

l ~ m o u n t o f

pJ.a.s

t ic

deforrrl

tio11

[tnd

fUl ther

J:8sista.nce

to

l o . t e l ~ [ l l lOD

d

wi l l l a rge ly depencl

on

th e

concl:t.tions

tl1at obtD.irl a t

th e EJUpports.

I f

th e

bearn i s n 1 e m l J e l ~ o f n

con

tinuous s t r u c t u r e

w ith

the s l ~ p o r t s o ~ s t r i n e d a g a i n s t

l a te ra l

moveUlent

c

o..torlLtry

D.ction nl8 Y d e v e l o p w h i c h l a t e l ~ 3 . 1 components

o f t118

d i l ~ e c t

t ens i l e f o r ~ c e

i n d u c e d

by

lal lge

clef,J

ec t ions may o f l f e r

th e prilnrJ.l Y

re

s i s t fl nce to In tel rll load . S1..lch letrge clef le c t l 0118

could

n o t

be

t o l e r a t e d

as a b asis fo r u su al des ign b u t might be

coxlsiclel )ed

in c o n n e c tI o n

w i t h res:tstc.rlce to l)omb blQst l [ l d s

A ll

of the

se fae t O l l S a re complicD

tJn g

Inflll.erlCes

iJ\Jhen plas t j ~ c

a n a l y s i s of

a

s t r u c t u r e

is

co n sid ered .

I t is

probable

t t an y

in i t i a l c o n s i d o r a t i o n of

plas t ic

de sign p r i m a r i l y should

make

use

o f

s JTlTIlnetricfll

sect ions c0111binecl vvith 1.oo.clln.g 111

e i t h r ~ pr in

c i p a l

p la n e. P la te

g i r d e r s with v aria ble le ng th cover p l a t e s

pr ob

ably woulcl

not

be

d e s l g n e d ctccol 1ding to plas t ic

t1180ry

s t n ce th e



9/18/.52

-19

205:;14

have

a

considerable

effec t

on

the

plas t ic hinge moment and rota

t ion

capncity.

These

effec ts

have

been

studied

by

Batho

16)

but

more research of th is type is needed.

6.

The

:Oes_ign ,9f e

t Q ~ l s

I t i s genera l ly

r ~ e c o g n i z e d t ha t

trle

most

important problems 1 n

s t ruc tura l des ign concern

design of

detai ls such connections

ra ther than the design of the main

members, Main

members

are

rather

thoroughly covered

by

speci f icat ions, but in

the

design

of

de

t a i l s tl1e e g i n e e l ~ i s ca l led llpon to exerc i se the greates t

a

mount of individual

judgment

and the

wisdom tha t comes

only

through

experience.

Here,

in

the

d e t a i l s ~

the engineer

departs

the fn r t ho s t fr om eltLstic s t re ss ana lys is procedures

and

e i the r

by

use of approximations based on his own experience

and

judgment

or by use of exis t ing

specif ica t ions where

these cover

the

case in

hand,

plas t ic

design in a res t r ic ted sense

has always

been

used.

A t yp ica l example i s

th8.t

of

tIle

d e s i € ~ n fo r tIle loca l c o m p l ~ e s s i v e

s t ress

in

bemil web c tbove a sllpport o r

ul1der

n conC811trrltion of



9/18/52

2 5 14

reaction

of the

beam

would have been

45.6 kips.

The

AISO

Speci

f ica t ion seems overly conservative

would automatically

l imi t

the design reactlon load) to 35

kips

in

th i s

case)

•

l\feilertheless,

in

the

t e s t

the

on.ly

evidence

of

fo i lure

was

a

grnducl.l

s p r ~ e a d

of

the

yielded

zone

from

the

end

of

tb.e

beam

towal ild

the

toe of

tJJ o

seat

t.l.ngls

lJ

T11is

spl lead

VVn

appreciable

a t

40

kip s b u t

the

beam

continued

to

take

1.oads

11p

to

80

kips

wi

tb.out

serious signs· of d i s t r e s s ~ Figure

10

shows the spread

of

yield

a t

the

70 kip

load and Figure 11 presents

curves

of reaction va.

deflec t ion a t

the connection fo r

the various

t es t s

t ha t

W01 )8 re

por t ed ii.bove 80 l{ips the

compression

y le ld in the web of the

beams had

spread

to S l l C h i n extent t b ~ t t be.rely p er ce pti ble l oc a l

buckling

developed as indicated by

dia l

gages but not to an

extent

easi ly noted by

eye.

4 t maximum load

of

90 kips

l a tera l buckling

amounted

to

a ~ p p r O X i l n Q t e l Y

1/10

of an inch. L-it tb.is

load

the beams

had

fa i led

ra ther

general ly

in

shear

and

the

tes ts

were

stopped.

Vii

tl1in the

rU11ge of

the

tes

t

pl Jogrnlu

the type of sea t

ha.d

no



205.14

shear ,

bearing, and

( in

the case of pins)

di rec t s t ress

due

to

bending. The h igh al lowable s t r ~ e s s . in pins fo r

d i r ec t

stress

due

to

bending

(30,000 psi

by AlSO Specif icat ions) may be jus t i f ied

by

the 11igh

shape fEte

to r

fo r

the c I J ~ c l t l a r s eo t ion Nl11ch i s

1 7

Considering plas t ic behavior there is thus a factor

of safety of

1.70 x 33 =

1.87

which is greator than

the

value of 1.65 as snnc-

30

tio11ed by

Ij,ISC

f or

t e l lS

iOl1.

members

t

In tl10

C

t lSe

of the

l \i

ve

ted

connect ion, t11 s t l ~ e S S 8 S [lllowed In

b ~ a r i 1 1 g

and sheCll l vV 111d p e ~ r -

mi t l oca l yield1rlg in an ill(11 vidllal

ve

t a.nd adj

aceXl

t plnt-;e J

were it

not

fo r

f r i c t ion

between

elements, and, f u r t h r m o r ~

i n

the case of a large connection with many r ive t s , tho end

r ive ts

are known to be stressed a t much higher IGvols

than

those in the

intel ior .

The outer r ~ i v e t s

mllst

y io ld 9 ncl

defoT m

f i J ~ s t ,

t l lUS

causing

a

l leclis tributlon

ofl

load to

tile v8.1 ious r i ve t s

th tt

i s

ent i re ly

analogous to the

successive

formation

of moment

hinges

assumed

i.n

the

plo.s t ic

n.nnlysis of tl1.0

continUOtlS

frrlmE.:.

Since the d8sign of s tr u ct ur al d e ta il s

is

already based

on

a



9/18/52

205.14

progrtess

in

the

p l l ~ s t i methods

of

s t ruc tura ; l nna .lys is ,

Symonds

and Neal (5) s ta te ft s

hec1.r

forces

can be neglected

except

in

cases

where

the ra t io of

span

l ength to beam depth 1s l e s s than ab l lt

4

to

J., which

i s

much smalJ.er

than commonly

used

u

• The authors

have

c o n f j ~ r m e d y correspondence

tha t

in using the

term span

they

had

been th ink ing

in tel nls of cant i levers or dis tnnces between

plas t i c

hinge locat ions in

genel altll)

This i11tol 1pretatioll

i s

corroborated y

the

fac t

that

may

be

shown th at ra tio s of

to ta l span length to depth of

8

to

1

or

more may be

controlled y

shear currentJ.y u s e ~ vvide flB.nge

sec t ions

under s y m m o t r ~ i c l

loading

when fixed a t each end.

In the

case of a

concentrated

load neo.r tIle StlPP01 1t of a e m

restrainEjd

a t

the

ends,

shear

may

be the primary design

cri ter ion in

some cases i f

the load

i s

at

a

distance less

than

four

times the

depth of the beam from the near

es t

s \ ~ p o r t

Such lond arrangements may OCCur in the use

of

off

se t

columns

in

building frame

construction.

Cur rent e las t ic design speci f ica t ions of ~ ~ I S

permit

a

lower



9/18/52

..

23-

205.14

f a i l u r e

of

these

beams

by shear.

n L it a t o t a l cen t e r ~ lOLl.d o f

170

k i p s

85

k i p s s l l e a l ~ each

beam

had

yielded ra ther

general ly th roughout the

beam

web

a r e a .

The aV81 )/lge s118ar s t r ~ e s s a t fail1.1re, based on

gJ, 1oss

\Iveb a l ~ e a

thCtt

i s

ber-un

depth d

l1

tiTnes t l 1ickness trw

1

gives an

Q Terage 8 h e t l l ~

st ress o_t f[111111' 'e

o f

19.1.

lclps

p e r

square

inchd

There i s thus

a fac tor of safety with

r e s ~

lJec t

to

the

al1owabJ.e

a v e l ~ o g e s t l ~ e 8 S

o f

13

k i p s

IJer

s q u a ~ e

i n c h of ol1.1y 1

0

47 as c o m p n . l ~ e d w i t h tIle l lsual s a f e t y

f a c t o r ~

of

1.65

:r eJ.ating

the permissab le tellsiJ_6

s t r e s s

of

20 l{si

t o the mininlUlll specifl:i .cation y i e l d

vD.lue of

33 k s i . II

ow-

about

40 kips

par square

inch,

therefore, the factor of

s a f e t y w0111d 0 1 1 1 ~ l be

1 . 2 1

i f ndjustecl to the nlin5.mull1

speci

f i c a t:i.o11 o f 33 k i p s

p e r

s q l 1 a r ~ e

inch..,

t

The

iOt l1al maXilTIUTIl s h e t ? t J ~

s

t l ~ e s s

a t

f C l i J . t l l 8

a

t tIle

cen t e r

o f

the

web

(neglecting

s tre s s

concentration

in

the

f i l l e t s

was

21

k ip s p e r square

inol1. by

·the f O l ~ l u l a ,



9/18/52

~

205.14

I f the allowable valuG

of

13

kips

per square inch

were

fo r

the

m ximum shorn )

stress

ra ther thun

the the factor of

safe ty

would be 1.61

fo r

the bertln tes ted \ ~ l i t h

n

web mate r i a l l:1aving

y i e ld of 40

kips

pel

sq.uare illCl1. ~ r i s

when adjus

ted

to

the

mimimtUTI : l i e ld

vnluo of

33 kips

1,)81 squB.re inch

gives

a

fc lC to r

safety

of

1.3 , Rven this

is

low

compared

with

tha t

usual

fo r

d. irec t stl )ess in ela.s t ic

dosign. m y

be noted tl:10.t

tllGSe beams

fa i led a t a shear stress level

loss

than tha t predicted y the

shear

str. ).ln

energy cl litel lion 1

1

U

oc

t ahed l 1al shen1

1

stressUcri t · ·

erion

of fa i lure which prodicts yie ld in pure shear a t 19.1

ks i

fo r

rna

t e r i a l

vvi th a y i e l d

of 33 ks i

I .d.ssuming

tl1 G

optim:i.stic



9/18/52 205.14

l imita t ion on design

of

beams

in the

plas t ic range is apparent

to a render

of

the

s l m ~ r y

report on University

of

I l l inois

fa t igue t es t s conducted

by

~ r o f e s s o r W.M. Wilson

and

h is

assoc-

i a t es as

repr i l l tod in the

VVe]

d ~ _ n g ~ ~ ~ n a l

1 8 ) ~ l here

I s never-

theless ,

some grounds fo r encouragement on the par t

of

tho.plas

t i c i ty

design

oxponent fo r the case

of

any structure designed fo r

100,000

cycles

of

load

or

less

in

which

the

lond

goes from

a

minilnl1l11 s

t re

s s of ze ro

to

TIla.ximUJ.i1 vr..lue (f

In

th i s range bo :.1m

sections fabricated

with

uniform cross-sect ions

and

with contin

110US Nelds had. fo. tlg11o stl aongths in

1tvJ:lich

the init i ,3.1

s t resses

were

[lbovo the y ie ld POi11

t

of tl1c mo.:torial..; On the other l1nnd,

b Llil

t

1.:tp beclms vITi

th r ) o . r ~ t i D . l 1.GIlg t;h

cover

pln

tes such

as , ~ l e

used

in

e las t ic

design.

proced,ul >oS to dlst l 1ibute the

mntel 1io..l

and

ll..tilize

a t as

higl l [I s t r ~ c s s Q.S

pos s i b l e

had low8r

fa t igue

s t rong ths

than the

bOCLms

vvlth

c onstfJ.nt

cross-sGctiona

On

th l s

ma.tter

tilo

a r t i c le

cOl lcludes

any

pJ.aj

n

ro l led

beam

\ lithout

a t

tachmonts 01 1

f lange

1101e8

wi l l

hCtve

gl eater

fD.tigue s t l ~ e n g t h



9/1S/52

26- 205.14

fo r f a i l u r e

Cl

t 190,000 rGIJO

t lons

of

l oad 1Jvere fa r below the. yi.e l<l

po in t of t110 ma t 8 1 ~ i n l Sj.mple nnc1 economical por ta l fl »ame

con

..

nections of the square knee

type

almost always include a connection

of

this type at n region

of

maximum moment

n

Fatigue fa i lure

in

such

u connection is l ikely within u few

thousand cycles of lond

bl1t th01

1

0

i s a I t lCk of

sufficien' l-;

i n f o r ~ m a t i o r l to

form

def in i t e

conclusions and

unt i l fur ther

t e s t ~ o r k is

carr ied out

scems

0

ssen

t i a l

t h ( : ~

t

the

nppl ic

Q

t l

on

p l l ~ L s

t i c

analys

is

to s

t rue

tu rn l

design

be

confinocl$' p o r f ~ ]

f l l n m e s . ~ to tIl.0se f ls s vI/here only

very· fevV l 1opetitio ls of

mG

i ~ 1 1 u l n 10.'].(18

aro to e

e.xpecto(l

dUPiIlg

th8 l . i i 'e o:f t l lo s t r 1 1 c t l l r 8 ~ lJJ 11'ltorlnodictto cond i t i on

l l ight

QJ:iso

wheroin Q

design fo r

r e p o ~ d

londs

a t

reasonablo e las t ic s t ress

levels

might be

mndo w ith very

occasional

overloads Qnticipnted

due

to

ab110rmetl

wind

01'

snovtT lOD d condi t ior ls .

Plas t i c

design

then might be used fo r

the

considerat ion of the heQvy overloads

be expec ted 0111y once or twico rlur:tns;

the;

l i f e of the s tl UC ture.,.

9,

Shako

down

The ques t ion

of

t S11C-lkod.o1J 111.

i

ho.s boen explored in de ta i l in



9/18/52

-27 ..

205.14

C 8. ted

111

terms 110t 1.1nlike tl10se used in sha.ke down fl lD.lys

i s

20 .

In somo cases the

c r i t i ca l

shakedown

load i s equal

to the

fu l l

load P

p

and in other casas

may be

as

low

as tho

elas t ic

ll1nit

load P

y

• Obvious ly , under repeated

load

cycles, shakodown

mny

be

an import[:\nt l imi ta t ion to

plas t ic

design. Shakedown st'lldles

nocessi tate

considoration

of

frame

analysis

in the

elas t ic

range,

hence,

i f required,

much

of

the

simplici ty

inherent

in

plast ic

analysis is

l os t

o

Detailed coverago of

the

problom of s t ra in aging,

l ike

that

of

Sllrtkedovvn i s outside the scope of

th i s

p n p o r ~ but

i s

mentioned

as

a possiblo l imitat ion

in

plas t ic dosign. In p ~ t i c u l a r

may incroaso the chance of br i t t l e

f rac ture ,

n l imitat ion to be

discussed

as the next item. In a general review, Epstein (21)

s tu t e s : u J ~ g i n g i s

chnnge

thf lt OCCllrs in tho

pl- oper'tios

of il on

or

s tee l

atmospheric

t e m p o ~ a t u r e

or

a t

a

moderntely

olevated

t e m p e l ~ t u r e

nf lter rrlpid

coolirlg or c ~ f t e r

co ld

W O l ~ l { i n g • • • strrltn



9/18/52

-28

..

205.14

has f J ~ a c t 1 . 1 r e d

with none of

the

dl lCt i l i ty lJ.ssocin.ted with the usual

Inborn

tory tensi le t es t in which cons ide rab le e longa tion,

both

t m i . f o l ~ m nd

locnl

tnkes plnee

pl )ior

f rac t U J ~ e • The typos of

fracture

occurring in

those disasters

has more

closely resembled

thClt

of glrtss than

that n l ~ l l y

to

be

expected

In

Et

s t ee l stru.c

ture Ono of the

most

recent

fai luros of

th is type is

thnt

of

tho

Duplessis

Bridgo

in

Cnnada

(6).

In the

oarly

correspondence

tho:c

led

to tIle cOllception

of

tho

presen t a r t i c l e

l

} }1 .II. Di l l

Welding

Engineer of the

~ o r i c a n

Bridge

Company, wrote as follows:

The 1 )].S8 of

the

iden tl1at the p la s t i c stJ: 8ngth

of s tee l may

be ut i l ized to gain greater economy in

tho design of

s tee l

structures

is

alarming when

i s

se t

agains t the long known and recontly reproved

fac t thqt s tr uc tu ra l s te el under many common circmn-

stn.nces

ht J.s

NO

plas t ic

act ion

I t is

a l a r ~ m i 1 1 g

even

when

I t

i s

intended

to

1.188

the

reserve

plas t ic

strongth

o n J ~ y

to

incl )ease

tho

allownblo elas t ic

worlring

s tresses



9/18/52

29-

205.14

qnd the designs

o r

s tr t lcturos

planned

o.ccordinglytt .

Whether

or not one agrees with

Mr

Dil l his viewpoint i s

held

by a numbor of

s t ructural

engineers. Some wi l l arguo

with

good

supporting

evidence

that

i t

is

impossible

even in ft ol

ns

t ic

t

de

sign to

g llnrd

completely t l g c ~ i l l S t

the

poss ib i l i ty

of l r i t t le f l ~ C t C -

tu re .

Such

fr1.c

tures seem

to bo c l ~ u s e d by an

1 111fort11na

te

coinc.i

dence

of

numlJer of

adverse

fete

tot s

the\

t

mn y in ten s true ture

occur

in combinat ion so rarely that tho poss ib i l i ty of such

br i t t l e fai luro must be accepted as a

calculated

r i sk . Others

may

argue tho.

t proper C olnbino

t lon

of

l

good m J:terial,

sk i l l ed

workmanship,

and adequate

s t ructural

design of d e t ~ i l s can be

achieved by

specified

good

practice

so as to insure

against

any

poss ib i l i ty of

bri t t lo

f racture within the rnnge

of allowable

loads including the po s s i b i l i ty of some

plD.stic f lo\v.

This

i s

cer ta inly a desirable

goal

but i t is Q di f f i cu l t one

to

achieve

as i s

at tes ted

by the

many

fa i lures on record. C ertain ly

seems

true t h ~ t

br i t t le fractures nre

cQused by

n

combination of

advorse



9/18/52

.. 30 ..

2 0 5 . 1 4

suI ted lnd i rec t ly froln f n . i lu r o s o f

vlolded

sh i.ps and

p r e s s u r e

vesse l s d u r ~ i n g ~ l n

s ubsequent

to th e

l a s t

~ a r These fa i lu ros

in

s p i t e

of

improvised meQsures

to

reduce them s t i l l occur o c c u ~

s iona l ly and

sev81 1al sh I p s

were

l o s t dU ring

th e

w i n t e r o f 1951-52.

However

as

has boen

p o i n t e d

o u t t hi s lim ita ti on ap p lies both

to

elas t ic and plas t ic

des ign.

12

c ~ n o m y

2f

l ~ s t i o

p e s i g ~

a

las

t

to m fo r

disC11ssion und er th e

g e n e r a l h e a d i n g

o f

l imita t ions tho q u estio n is ra ised as

to

whether o r

n o t

t h o re is

any

r ea l

econolny in plas t ic

clesign pl )ooeduros

assuming

tha t

alJ_

of

tho

foregoing

l i m i t a t i o n s are

adequately n s w e r e d ~

In t ~ h e

use

o f

x ollod

structur[l]. shapes

the r e i s I i t t l e oconomy

in

plas t ic de sign i f

the s t r u c t u r e

is

determinato

s i n c e i n this

c a s e

i f bending

of

wide

flange

beams

is

i n v ol v ed b o t h p r oc ed u re s

g i v e

e s sen t i a l l y

t

same answer

any

dif ference

bc;ing

due

to th e

shape

factor

alone.

The same

is

tru e

under

cer ta in

s p e c i a l

ses

o f

C011tinuous

beam s as

fo r example the f Ixed end boam wi th

a



9/18/52

.. 3)....

have cra.ne

runways in which misaJ. ignment

of

runways

would

create

malf'Lillc t ioning of cranes .

~ t l l o l \ l n b l e

s

t resses are increased in

the

elas t ic design considerat ion of unusual load combinations

tha t include wind. Plast ic design

procedures

would need the

same

considerat ion

to

effec t

great

saving over the procedures

now used. Nevortheless, the

ut i l iza t ion

of plas t ic design fo r

these unusual load

combinations

would

be

a more

rea l is t ic

approach

t11o.n the

p l ~ s n t procedure of si.mply incrreasing

the

o.llow[Lble

· s t resses . The

resul t would give

a structure of

balanced strength

and there would a t

leas t

be the poss ib i l i ty of

some

saving of

m t r i l ~ Design studios over

a

range

of variables

should be

made to actually

answer

the

l a t t e r question.

13.

~ e n d s in

~ ~ ~ ~ c t t } l ~ n l

DesiP;l1

~ s an intermediate

step

in

the

appl icat ion

of

plas t ic design,

as applied to t i e r buildings,

the

use of semi--r igid connect tons

should

be

menttoned

t

T11is h. J.s

been perm i

t ted

In

pr inc ip le

since

1946 by the / .ISC nSpec i f i ca t ions fo r the

Design,

Fabr ica t ion nnd



9/18/52

-32-

••For

the

purpose

of such design

C\ccurate

methods

of

s t ruc tura l

analysis

shal l

be employed

leading to

a load raotor of 2 , based on the calculated or other

wise ascertained fa i lure

load

of the structure or

any

of l t s par ts and duo

rogard shal l be paid

to the nc

compmlyi11g

defol 1mationsunder 1jvorking

loads so tha t

defloctio11S

and

othe r

movements

are

llot

111

exc()ss

of

the

l imi ts

impl ied in

th i s

Bri

t i sh

StQnd.o.rd

•

ilpparently, one of the f i r s t uses of t hi s s pe ci fic at io n was

in tho construction of tho gab led con tinuous weldod

frames

for

the

new

Inbo ra to rty o f

tho Bri t i sh \iVolding

I{esen.rch

i S f 3 c i ~ ] t i o n a t

Abington

(25). ~ c c o r d i n g to

the ci ted reference, the design

or

this frame showed a reduction of

approximately

45 percent

compared

wi t h t russ

t:ll1d

can t i l eve r colUlnn design and I? percont in comp-

arison with e las t ic design of u s imi la r

welded

continuous frame.

n

renson

ci ted

by

the au th ors

fo r

tho small

difference

is

the

fac t that greater load factors are required in the specif ica t ion



9/18/52

205.14

columns of 24,000

p s i

when th i s

s t l ~ e s s

i s ind.uced the

grav i ty

loading of ful ly

or par t ia l ly

restrained beams framing into the

columns .

I t

is

thus seen tha t two different approaches to the

u t i l i z ~

t lon of

plast ic

reserve strength are c urre ntly in process of de

velopmen t . 'I'he one as exom.plif ied

the Bri blsh Spec i f i c a

t i on

\ \Tould

e t e l ~ m i n e

actual

ttultimate or

tt.rulJ. or

l imi t

loads

arId

divide t he se

a load

fae tor , keeping in

mind

neces

sal 'Y

res -

t r ic t ions

as

to

deflect ion of the

s t ruc ture

poss ibi l i ty of

fatigue fa i lure

e tc . The

other, already par t ia l ly in

use in

the

tiISC Specif icat ion,

would

detormino variable

permissive

stresses

due

to

bending depending on

the

degroe

of

r es t r a in t and dist r ibu

t ion of load.

At the moment, possibly the

groates t

use for methods for analy

zing the

plas t ic

ultimate

strGngth

of s t e e l frames l i es in the

l ~ e l m

of miJ.i

t ry

appl ica

t

ons •

Such appl.1 0\9. t i.

ons

gave

j . lnpe

t ~ u s

to some of the developments

of plast ic

theory in England under



9/18/52

--34-

t ruc t ion wi th

SOlne poss ib le

except:i.ons

repeated

loads

are

a

poss ib i l i ty

PIns

t ic

analysis

should be applicabJ_e fo r design of

maxi-

mum

cOlnb:i.nations

of gra.vi ty l o d In

the

case of I n t { ~ r [ t l

wind loads, as has been pointed

out,

resul ts s imilar to

those obtained

by

l imi t des ign concepts

have

already been

in use for

many

yenrs

o

However the

l t e r l

dcflec-tions

tho. t wOl.l1d oocur i f

plcts

t ic

momel1ts

no t u ~ a l l y were de-

ve·loped

lJnder the

lo.teI1al 100. 18

t1S pp l ied

to t i e r

bui ld -

ings would

be

of

considorablo

mngxli

tud.e and

\ ~ o u l d

un-

doubtedly

cause

serious cracking

of

walls

cmd

p r t i t ions

2.

Tlle design of industl lin.l bui.lding

f l ~ o m e s

wherein pl.a.stic

analysis procedures might produce a

be t te r

distribution

of mater ia l for

effect ive

over-nIl s t rength against the

occns ionn l h igh wind and/or snow loads to be considered.

Special

t tent ion would be given to permissivo def lect ion

in the case

of

indus t r i l buildj ,ng

f r ~ l m e s

c f 1 r x ~ y i n g crane



9/18/52

-35 ..

205.].4

shear ax ia l load loca l b1.l..cklillg

l '1Gsidllal

s t r e s s

l a t e r a l

buckling,

etc . ;

the

problem

of

design

of

de ta i l s ;

shear

as

a

primary

design cr i ter ion; fat igue; shakedown; and

the possi

bi l i ty of br i t t l e frQcture. Many of

these problems

also exi s t

in conventional

c las t ic

design.

Pos sibl e app li cat ion s

fo r

plas t ic

design

have been outl ined in

br ief . Some

phases

of the

projects

in progress or completed

a t

Lehigh

University

have been

reviewed

where pert inent .

emphCtsizing

l i lni tat iol1S

the

authors do

not

mean to dis -

cred i t

the poss ibi l i ty

of

applicat ion of

plas t ic analysis to

s ign . c are ftl1 s tu dy of the problems he re in e n l l m e ] ~ . D . t e d s110uld

s t imula te

applicct.tion

to

those nreas of s t ructural Gllginoer

ing

where

in pIns

t ic

pl')ocod.ure

s do l1.Qve a

p lace . Tho

goal in

s t ruc

t u ra l

design

is ' to pr'ovide safe

and

enduring s t r u c t u l ~ e tha t

incorI)OI)a tes

ma:x.imum

poss ib le economy. I f plEts t ic a11o.1ysis can

be

app l ied to dosign to I ~ o n z e , these

gouls

i t wi l l be

. appl ied,

fo r the

laws

of evo lu t ion w o lk

as s111--ely

in the h i s t o l ~ r

of

man



9 /18/52

36

205 14

sequel to the

present

r t i le t some future date

wil l

present D cttlal des g stul1ios and empllasizG metllods

of

appl ica

t ion

to those

structures wherein

pl s t i analysis procedures do

seem to

have a place



9/18/52

(1) Timoshenko, s.

2)

Maier-Loibnitz

3 )

Vo n

Den Broek J. l..

4)

Baker,

J .F .

5 ) Symonds,.P.S.

Neal, B.G.

(6)

M e ~ r i t t , F. S.

References

S trength of

lVIaterials ,

Vol. 2,

Van Nostrand, 1s t edt 1930,

2nd edIt 1941 •

UContribution to the

p r o b ] ~ e m

of

u l

t ima

te c a r ~ r Y i n g CD pac i

of'

simple and C011tin1.101.1S

beams

of

s t ruc tu ra l s t ee l

and

tilubor

Die

Bnutechnik

1:6,

1927),

Tht.?-0ril ,9f

Limi

t

E

i g n t 1 , tTohn

Wiloy ~ o n s , ~ N e w

York, 1948).

ii l 1evie'N

of recent

invest iga-

tions in to the

behaviour of

s t ee l frames :In the

plast ic

<1nge •

J

Ins t

of

Civi l

Engs.

3:185

t

l

9

1

: :9

Recent

progress in

the

plas t ic

methods of s t ruc tu ra l

al1alysis

J Franklin

lus t

252:383-407,

469-492

1951)

Bridge collapse in Quebec

charged

to

bri t tJ e

s tee l

Eng News-Record

146:

23,.4, 1 9 5 1 j ~



9/18/52 -38-

(11)

Ruzek,

Jan M.

l\nudsen,

I'Cnud-E.

JOb,n.ston, E.

Beedle, Lynn

S.

(12) Horne,

M.

R.

(13) Ketter, R. L.

Be8dle,

L.

S.

Johnston B. G.

1.4

Y a n g ~ 9.

H ~

B e e d ~ l e IJ A S

•.

Johr stoll ,

B.

G.

(15) Beedle,

L. S.

Topractsoglou,

A. A.

205.14

u1jVelded

PortEll

F'r,9l118S Tested to

,Collapse

- Pl'ogress

Report

7

..

Welded Continuous

Frames

and

The Compo11el1

ts

To

be published

in SESA

Frac.

uTlle

p las t ic theory

of

bonding

-of s t e e l

ber:uns, Wi.tIl p ~ l r t i c u l a r

reference to

the

ef fec t

of

she

a

1

orce

s

Brit Weld Res ~ s s n Rep. (July,

1949).

Column Strengtl1.

l l11der conlbined

be11dix1g

and thrus

t -

P x ~ o g r e as

Report 6 -

Welded Continuous

l ~ x ~ a n l e s and T h e i r ~ Components

To

be

published

in

Welding

J

~ R 8 S

SUPPtI

R e s i d l ~ ~ s t ress

and the y le ld

s t r ~ e n g t s te e1

be

ams - P

rog

ress I1G 1ort

1AJelded

Cont inu-

ous Frames and Their Components

Publ i shed

:1.n

WelclJ.ng .J

3 : 2 5 s ~ 2 2 9 s (1952)

COIlnections

fo r

welded

cont inu-

ou.s po r t a l frau18s -

Progress



9/18/52

(19)

Conuni

t tee on Fat igue

lIe s

-tlng

(20)

Orowan, E.

(21) Eps te in , S.

(22) Bij lanrd ,

P. P.

(23) Hechtman,

R

~ .

Johnston, B. G

(24)

Pippard.9

. L ~ J . . J · . S .

Baker , J . F.

(25) ~ t k i n s w. S.

-39-

205.14

Fatigue

strongth of f i l l e t ,

plug

and

s lot

welds

in

ordinary

bridge

s teo l - i jeport No 4

COlnmi t toe

11

l ~ a t i g l l e Testi11g

Welding

J 2 4 ~ 3 ? 8 s - 4 0 0 s (1945)

Stress Concentrati.ons

in

Steel

Urlder

C:)Tclic L o a d ~

Weldirlg J 31: 2 7 3 s ~ 4

2828

(1952)

Itilging Ofl i ron and

s teeJ

Motals Handbook

(1948)

pp,438

443

Br i t t l e

f rac turos

in weJ.(led

b

l d Co) 1t

r

gos

Eng News-Rec.

146:46-48

(1951)

Riv eted

semi

r ig id

beam-to

e

1 tunrl

tn1i

1

(ling C

orU 8

c t i on s fl

dmorican Ins t i tu te of Steel

Corlst:l71.1ction

Publ ica t ion

No.

206,

(1947)

U ~ h 2 ) anaJ.ysis of ene;ineering

s

t 1

1

11C t l11- )e n

Longmans, Green & Co.,

New

York

1936

DeveloprrJ.en ts of design

and fab-



°0

STRAIN

tress straincurves fo r physicalproperty coupons

'1' '2.. of 8WF as delivered beam

401 P '

' I

I I I

321 I

r

J

L· : I

81----- -+1 I I /

I {

1 :

I

I

I I

(/)

X

241

I I I .. l I

...

I --y, I .. J .., f , f I

U)

U

161

I f J f I

I J I J I

f

I I

U )

,, -

. . .

R

~ . ,

E(;1=

E

STRAIN

T YPICA L SHAPE OF STRESS- STRAIN

DIAGRAM

FOR S TR UC TU RA L

STEEL.

~ ~

ELAST IC STRAIN INITIAL STRAIN HARDENING

PLASTIC STRAIN

=

10 ta

x

ELASTIC STRAIN

FLG.la

•

tJ )

en

w

a::

.-

fJ

FIG.lb ASSUMED S TR ES S D IS TR IB UT IO N

IN

STEEL BEAM

STRA1NED

BEYOND ELASTIC

RANGE.



ultimate

2

yield poin

ultimate

3

3124

3127

56,650 psi

91,140

ps i

31,090

psi

57 360psi

3127psi. 4998psi

2 1 0 9 P S i J 5 5 c r o I 3 3 7 I p s i ~ 5 2

7.89

ero 7.55

0

2

24

14

19

Results of mil l tests representing

approximately

30,000 tons

of

structural steel installed

at

vori :-

OU5 projects designedpy- Jocks·on

and M o r e l a n ~ t J r o m · t 9 8 to 1948.

Ratio ultimate

median strength

to yield

point median strength = 1.70

Structural

steel furnished

tJy :

Carnegie -lIlinois Steel Co.

Bethlehem Stee 1

Co

37

42

no. of mill

tests

high

point strengthllOw

standard

devration from

average

probability

error fr m average

coefficient

of

variation

186 1360 611 347 · 273 204 69

458

103

876

443 66 43 51

no ..

of

t e s t s ~ p e r

5

bracket

FIG.

3 RESULTS OF MILL TESTS

5( 1 I I I :AM:

011 - 5 W ' fa a 5 6 I I 5

to

5 1_ _1

« 3? rz to

45 i

deviation from median

·

3

eo

u

c 40 i I I \ I

\t

.2 E

0

._

c:

>

OJI-c

0

(U

'C

-c QJ

QI

4- U 30

---1----- --- ----i -i---Ir--T -tr--

~

average yield point

-g

I

strength

=

39,630 psi

0

'+

0 0

> fV rm==t=

g

20

r J ;

i'l

average

uttimate

~ g t ~ ~ 8 ~ Q J ·

\

strength =66,150 psi

00

II

c:

Q tj

(1) .0

g c: 10 G B

•

c

u q,p

E

Q

H

H

I

0' \



eo·

Calculated

initial ~ I d

-

60

I

40

.Ii

~

20

0

......

......

I l I I I I I l I I I l i I 1 I I I I I I I l I l l ~ - _

_ 1 l I I l I I I I i r i I m m 1 l l l l l l l l l l l m m _ 1 l I l i l I l I I l I / i ~ ~ ~ ~

1IIillIIIIIIIlI

02 04 0.6 1 12

l4

Inches

FIG. 4:

E X P F . J t l M E N T ~ t AND

THEORETI

elL Loan ..

OENTEBLINE DEFLECTION CURVES

FOR 14 IF 30

6 0 ~



F1

6

FRW 1

TESTED T 0 F41LUIll l:



p

P

4

W I

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8

6

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FIG. 11 DoueT/I)' tJF Su r ANtIU.

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Documents

Welded Continuous Frames and Their Components