Laterally Restrained Beam

8/13/2019 Laterally Restrained Beam

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Teaching Resource in Design of Steel Structures

IIT Madras, SERC Madras, Anna Univ., INSDAG 1

Laterally Restrained Beams


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Prof. Hardy Cross

.the structu ral elements are very

fai thfu l . They wou ld do what youexpect them to do ..But then you

have to asses whether they would be

ab le to do that.


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Conditions to Qualify as a Laterally

Restrained Beam

It should not laterally buckle

None of its elements should buckle until a

desired limit state is achieved

Limit state of serviceability must be satisfied

Member should behave in accordance with the

expected performance of the system


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Laterally Stability of Beams


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Local Buckling

In IS:800 (1984) the local buckling

is avoided by specifying b/t limits.

Hence we dont consider local

buckling explicitly

However in IS:800(2000??) limit

state design, the local buckling

would be the first aspect as far as

the beam design is concerned

How do we consider? By us ingsect ion classi f icat ion


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8 times Stronger!

K=4.0

K=0.425

Mr.Stiffened Mr.Unstiffened


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Local buckling

Full Section Capacity Full section capacity

eroded by local Buckling

Vent

Vent


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Unsitffened Elements


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Sitffened Elements


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Definition of Yield and Plastic Moment Capacities


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MP

MPMP

MP

My

My

PLASTIC

COMPACT

SEMI-COMPACT

SLENDER


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MP

MP

MP


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Section Classification

as per BS:5950 Part-5

No Slender sections

are rolledShare of plastic

sections is large

Section

classification

prevents the

inadvertent use of

sections less than

compact for plasticdesign


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Section al Classi f icat ion fo r Ind ian Cond it ions

Sect ion type Flange cri ter ion(b/T)

Web cr i ter ion(d/t)

Slender

Semi-compact

Compact

Plast ic

>15.75


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Curvature

MY

Rotational Capacity

Flexural member performance usin g sect ion classi f icat ion

Slender

Semi-Compact

Compact

Yield moment

MP

Moment M

Plastic momentfy

fy

fy

fy


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49

12

4plastic

compact

PLASTIC 49

COMPACT 12

SEMICOMPACT 4

Sect ion classif icat ion of Indian

standard rolled I beams


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Limit states for LR beams

Limit state of flexure

Limit state of shear

Limit state of bearing

Limit state of serviceability


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M

Radius of

curvature

Curvature of bending

(a) (b)

A

zM

h

c

Deflected

shapeN A


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Stress

1

strain

2 3 4fy

Plastic

range

Elastic

range

Idealised elasto - plast ic str ess

stra in cu rve for the pu rpose of

design

Ideal ised stress

stra in curve

f


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1


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3>y f3=fy

f3>y f4=fy

4AC

A

T

Zc

ZT

B

3

fy

T

d

t

d0

d0

zc

zT

StressStrain

Strain Stress


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1

2

4

3

fy

fy

fy

(b) Plastif ication

of cross section


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1 2 3 4

Plastic H inge

Simply supported beam and i ts def lection at various

stages


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Moment M

Curvature

MY

Moment curvature character istics of the simply supported beam

Yield moment

MP

Plastic momentEffect of strain hardening may

occur after large rotation


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ZfcM

ZyfyM

6

ytdf)tzcz)(t0dBT(yfcM

2

)t

Zt

Ac

Zc

A(y

ft

TZc

CZp

M

2

1

3

4


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2.0 1.7

1.27

1.14

1.5

Some typical shape factor


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Combined bending and shear in beams

Elastic

Bending

stress

Elastic Shear

stress

Plastic

range

a b c

LIMIT STATE OF SHEAR


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wdwt

Vav

yf58.03

yfy

wd

wt

yf6.0

cV

EQUATIONS FOR SHEAR CAPACITY


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Shear yielding near support

Web buckl ing Web cri ppling


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450

d / 2

d / 2 b1 n1

Effect ive width for w eb buck l ing

cft)1n1b(wbP

t

d5.2

t

32d7.0

yr

EL

32

t

t12

3t

A

yIyr

yr

d7.0

yr

EL


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b1 n2 1:2.5 slope

Rootradius

Ef fective width of web beari ng

ywft)2n1b(cripP

Web Crippling in beams


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LIMIT STATE OF SERVICEABILTY

yf

4923

325

1

yf6.0

510x2

5

24

d

L

Deflection (L/365 or L/200???)

Excessive vibration

Repairable damage due to fatigue

Limiting L/d ratio


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Secondary effects on beam behaviour

Residual Stresses

Qualitative change in the behaviourLittle more stringent b/t limits


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Secondary effects on beam behaviour

Combined bending and shear in

beams

Elastic

Bendingstress

Elastic Shear

stress

Plasticrange

a b c


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x

y

Unsymmetr ical bending

P

x

y

Mx

My

Mx

My


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Behaviour of point symmetric sections


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Deflect ion o f beams loaded through the

centro id

P

P

P

Centroid


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Def lec t ions of b eams loaded thro ugh

the shear canter

PP

Shear

centre


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Constrained bending


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IIT Madras, SERC Madras, Anna Univ., INSDAG44

Example of bu i l tup beams

Interface shear

to be considered

here

d/2

d/2Plate

area A

Rolled section

Moment ofinertia - Is

Modulus of

section - Zs

(a) (b)

x x

x x


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IIT Madras, SERC Madras, Anna Univ., INSDAG45

Load

w/metre

BM

Diagram

Rolled

beam

Cover

plate

Theoretical

Point of

cutoff

McMc

Curtai lment of cover plate

Actual

cutoff


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Teaching Resource in Design of Steel Structures46

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Laterally Restrained Beam

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