material ch21

8/12/2019 Material Ch21

1/38


2/38

Teaching Resource in Design of Steel Structures

IIT Madras, SERC Madras, Anna Univ., INSDAG 2

CONTENTS

INTODUCTION

ELASTIC BEHAVIOUR OF COMPOSITE BEAMS

SHEAR CONNECTORS

ULTIMATE LOAD BEHAVIOUR OF COMPOSITE

BEAM

SERVICEABILITY LIMIT STATES

CONCLUSION


3/38



INTRODUCTION

ADVANTAGES

effective utilisation of steel and concrete.

more economical steel section (in terms of depth and weight) is

adequate in composite construction when compared withconventional non-composite construction.

enhanced headroom due to reduction in construction depth

less deflection than steel beams.

efficient arrangement to cover large column free space.

amenable to fast-trackconstruction.

encased steel beam sections have improved fire resistance and

corrosion.


4/38



ELASTIC BEHAVIOUR OF COMPOSITE BEAMS

No interaction case

Effect of shear conn ect ion on

bend ing and shear stresses


5/38


6/38



ELASTIC BEHAVIOUR OF COMPOSITE BEAMS -2

Tensile strain at the bottom fibre of the upper beam and the

compression stress at the top fibre of the lower beam is

2

22

max

8

)4(3

Ebh

xw

EI

Myx


7/38




/2-/2

Typ ical Deflect ions, sl ip strain and sl ip.


8/38




Maximum bending stress

Maximum shear stress

maximum deflection

2

2

max

16

3

bh

w

I

Myf

bh

w

hb

wq

8

3

)2(

1

22

3max

3

4

256

5

Ebh

w

100% interaction case


9/38



Upli f t Forces

Shear s tress var iat ion over

span length


10/38



SHEAR CONNECTORS

Types of shear connectors

Rigid type

Flexible type

Bond or anchorage type


11/38



SHEAR CONNECTORS -1

r ig id connectors


12/38



SHEAR CONNECTORS -2

Flexible con nectors


13/38



SHEAR CONNECTORS - 4

( i i). Helical con necto r

Typic al bond o r anch orage

connectors


14/38



Characteristics of shear connectors


Load/Slip character ist ics

Typ ical load-sl ip cu rve for 19mm stud

connectors


15/38




k=

Idealised load-sl ip c haracter ist ics


16/38



push- out tests for

determining load-slip curve

Standard push test

[Eurocode4]



17/38

Teaching Resource in Design of Steel Structures IIT Madras, SERC Madras, Anna Univ., INSDAG 17

Standard test for s hear

connectors

(As per IS: 11384-1985)

SHEAR CONNECTORS -8


18/38


Load bearing mechanism of shear connectors


Trans fer of forc e at a shear

connector


19/38



Dowel mechanism of shear studs

dowel

Bear ing stress on the shank of a stud conn ector


20/38


Strength of connectors

dowel strength (D) is a function of the followingparameters: -

D = f [A d, fu,( fck)cy, Ec/Es]

design resistance of shear studs with h/d 4.


v

2u

Rd

4df80P

)/(.

v

21cmcyck

2

Rd

Efd290P

/))((.


21/38


ULTIMATE LOAD BEHAVIOUR OF COMPOSITE BEAM

The tensile strength of concrete is ignored.

Plane sections of both structural steel and reinforced

concrete remain plane after bending.

The effective area of concrete resists a constant stress of

0.85 (fck)cy/c (where (fck)cy)=cylinder strength of concrete;and c =partial safety factor for concrete) over the depth

between plastic neutral axis and the most compressed

fibre of concrete.

The effective area of steel member is stressed to its design

yield strength fy/a where fy is the yield strength of steeland ais the material safety factor for steel.


22/38


Reinforced concrete slabs, with profiled sheeting

supported on steel beams

IS: 113841985,gives no reference to profiled deck slab

and partial shear connection

Resis tance to sagging bending moment in plast ic or compact

sect ions fo r ful l interact ion .

0.85(fck)cy/ c 0.85(fck)cy/ c 0.85(fck)cy / c

D

T

t

B


23/38


Full shear connection

Neutral axis within the concrete slab

Neutral axis within the steel top flange

The neutral axis lies within web

)2/( xhhfA

M tga

ya

p

2/)()2/(. tcacctgplap hhxNhhhNM

2/)(

)2/2/()2/(

.

.

cftwa

cftacfctgplap

hthxN

hthNhhhNM


24/38


partial shear connections are provided

to achieve economy.

when there is problem of accommodating shear

connectors uniformly.

the force resisted by the connectors are

taken as their total capacity (Fc < Fc f)

between points of zero and maximummoment.

Partial shear connection


25/38


Degree of shear connection =

the neutral axis is within top flange

cf

c

f

p

FF

nn

22

ctac

ctga.plRd

xhxF)

xh(hNM


26/38

Teaching Resource in Design of Steel Structures IIT Madras, SERC Madras, Anna Univ., INSDAG

26

0.85(fck)cy/c

Resistance to sagging bending of com posi te

sect ion in class 1 or 2 for part ia l interact ion

If the neutral axis lies in web

2)

2(

2)(.

fta

aw

f

tcfcc

tgplaRd

thxN

thN

xFhhNM


27/38


27

Design method s of p art ial shear connect ion

MRd/ Mp

Map/ Mp

Fc/ Fcf 0.7


28/38


28

Moment of resistance reduces due to partial

shear connection.

The curve ABCis not valid for very low value ofshear connection.

At Fc/Fc f= 0.7, the required bending resistance

is slightly below Mp.

saving in the cost of shear connectors can beachieved without unduly sacrificing the

moment capacity.

for design purpose the curve ABC is replaced

by a straight-line ACgiven by

cf

app

ap

c FMM

MMS


29/38


29

SERVICEABILITY LIMIT STATES

For simply supported composite beams themost critical serviceability Limit State is

usually deflection.

the effect of vibration, cracking of concrete,

etc. should also be checked underserviceability criteria.

in exposed condition, it is preferred to design

to obtain full slab in compression to avoid

cracking in the shear connector region.


30/38


30

Stresses and deflection in service

elastic analysis is employed to check the serviceability

performance of composite beam.

concrete area is converted into equivalent steel area by

applying modular ratio m = (Es/Ec).

analysis is done in terms of equivalent steel section. It is assumed that full interaction exists between steel beam

and concrete slab.

effect of reinforcement in compression, the concrete in

tension and the concrete between rib of profiled sheeting are

ignored.


31/38


31

For distributed load w over a simply supported

composite beam, the deflection at mid-span is

For partial shear connections the increase in

deflection occurs due to longitudinal slip. Total

deflection,

with k= 0.5for propped construction

and k= 0.3for un-propped construction

a= deflection of steel beam acting alone

IE

wL

a

c384

5 4

111c

a

f

cN

Nk


32/38


32

The increase in deflection can be disregarded

either np/nf > 0.5or when force on connector

does not exceed 0.7 PRKwhere PRK is the

characteristic resistance of the shearconnector; and

when the transverse rib depth is less than 80

mm.


33/38


33

Effects of shrinkage of concrete and of temperature

In case of composite beam the slab is restrained from

shrinking by steel beam.

shear connectors resist the force arising out of shrinkage,

by inducing a tensile force on concrete which reduces the

apparent shrinkage of composite beam than the freeshrinkage.

no account of this force is taken in design as it acts in the

direction opposite to that caused by load.

the increase in deflection due to shrinkage may be

significant.


34/38


34

In an approximate approach the increase in deflection in

a simply supported beam is taken as the long-term

deflection due to weight of the concrete slab acting on

the composite member.

Generally the span/depth ratios specified by codes takecare of the shrinkage deflection.

check on shrinkage deflection should be done in case of

thick slabs resting on small steel beams, electrically

heated floors and concrete mixes with highfree

shrinkage.


35/38


35

Vibration

To design a floor structure, only the source ofvibration near or on the floor need be

considered.

Other sources such as machines, lift or cranes

should be isolated from the building.

In most buildings following two cases are

considered-

People walking across a floor with a pace

frequency between 1.4 Hzand 2.5Hz.

An impulse such as the effect of the fall of a

heavy object.


36/38


37/38


IIT Madras, SERC Madras, Anna Univ., INSDAG37

Natural frequency of beam and slab

Response factor

Cross-sect ion of vibrating f loor structure

show ing typica l fundamental mode


38/38


IIT Madras SERC Madras Anna Univ INSDAG38

CONCLUSION

the theory of composite beam and the

underlying philosophy behind its evolution

were discussed.

The design procedures of simply supported as

well as continuous beams have been

elaborately discussed.

material ch21

Documents