composit e beams2

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

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COMPOSITE BEAMS-II


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CONTENTS• INTRODUCTION• PROVISION FOR SERVICE OPENING IN

COMPOSITE BEAMS• BASIC DESIGN CONSIDERATIONS• DESIGN OF COMPOSITE BEAMS• EFFECT OF CONTINUITY• SERVICEABILITY• CONCLUSION


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INTRODUCTION

• Composite beam with profiled sheeting with concrete topping.• Profiled sheets are of two types• Trapezoidal profile• Re-entrant profile

(a) Trapezoidal profile deck (b) Re-entrant profile

Types of profile deck


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• The deck slab with profiled sheeting is of two types • The ribs of profiled decks running parallel to the beam.• The ribs of profiled decks running perpendicular to the beam.

Orientation of Profiled deck slab in a composite beam

(b) Ribs perpendicular to the beam

(a) Ribs parallel to the beam


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PROVISION FOR SERVICE OPENING IN COMPOSITE BEAMS

• Simple Construction with Rolled Sections• Fabricated Sections• Haunched Beams• Parallel Beam Approach• Castellated Sections

• Stub Girders

• Composite Trusses


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Fabricated Sections

Fabricated sections for commercial buildings

(a) Straight Taper

(b) Semi-Taper

(c)Cranked Taper

(d) Stepped Beam(where automatic welding is not crucial)


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Haunched Beams

(a) sections of different size(b) haunches cut from main beam

Haunched beams: Two types of haunches


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Parallel Beam Approach


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Castellated Sections


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Stub Girders


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Composite Trusses


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BASIC DESIGN CONSIDERATIONS

• Design Method suggested by Eurocode 4

• ultimate strength is determined from plastic capacity.• serviceability is checked using elastic analysis.• full shear connection ensures that full moment capacity of

the section develops. • in partial shear connection, the design should be adequate

to resist the applied loading.• partial shear connection is sometimes preferred due to

economy.


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• Span to depth ratio

Span to Depth ratio as according to EC4

EC4

Simply supported 15-18 (Primary Beams)18-20 (Secondary Beams)

Continuous 18-22 (Primary Beams)22-25 (end bays)


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• Effective breadth of flange

Use of effective width to allow for shear lag


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• For simply supported beam, effective breadth of simply supported beam is taken as o/8 on each side of the steel web

• For continuous beam,

Bbut4

beff

Value of 0 for continuous beam as per EC4

1 2 3 4

0.25(1+2) 0.25(2+3)

0.81 0.72 0.83-0.34

0.73

4+0.531.54


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• Modular ratio• Shear Connection

– The elastic shear flow at the interface increases linearly from zero at the centre to its maximum value at the end under uniform load.

– At the elastic limit of connectors, redistribution of forces occurs.

– At collapse load level it is assumed that all the connectors carry equal force.

– The design capacity of shear connectors is taken as 80% of their nominal static strength in EC4.

Shear flow at interface


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Load Partial safety factor, f

Dead load 1.35 Live load 1.5

Materials Partial safety factor, m

Concrete 1.5Structural Steel 1.15Reinforcement 1.15

• Partial Safety Factor


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Type of Element Type of Section

Class of Section

Plastic (1) Compact(2)

Semi-compact (3)

Outstand element of compression flange

Welded b/t 7.9 b/t 8.9 b/t 13.6

Rolled b/t 8.9 b/t 9.5 b/t 15.0

Internal element of compression flange

Welded b/t 24.2 b/t 26.3 b/t 29.4

Rolled b/t 27.3 b/t 33.6 b/t 41.0

Web with neutral axis at mid depth

All d/t 83.0 d/t 102.9

d/t 126.0

Web under uniform compression

Welded d/t 29.4

Rolled d/t 41.0

Single/double angle T-stems

Rolled b/t 8.9d/t 8.9

b/t 10.0d/t 10.0

b/t 15.8d/t 15.8

Circular tube with outer diameter D

D/t 442 D/t 632 D/t 882

yf250

• Section Classifications


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DESIGN OF COMPOSITE BEAMS

• Moment Resistance

• Reinforced Concrete Slabs, supported on Steel beams

Notations as per IS: 11384-1985

beff

ds

D

T

t

xu


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P o s i t i o n o fP l a s t i c N e u t r a l

A x i s

V a l u e o f x u M o m e n t C a p a c i t y M p

W it h i n s la b x u = a A a / b e f f M p = 0 . 8 7 A a f y ( d c + 0 . 5 d s – 0 . 4 2 x u )

P la s t i c n e u t r a la x i s i n s t e e lf l a n g e

Ba

dbaAdx seffa

su 2

M p = 0 . 8 7 f y [ A a ( d c + 0 . 0 8 d s ) – B ( x u– d s ) ( x u + 0 . 1 6 d s ) ]

P la s t i c n e u t r a la x i s i n w e b

at

dbAAaTdx sefffa

su 22

M p = 0 . 8 7 f y A s ( d c + 0 . 0 8 d s ) – 2 A f( 0 . 5 T + 0 . 5 8 d s ) – 2 t ( x u – d s – T ) ( 0 . 5x u + 0 . 0 8 d s + 0 . 5 T )

Moment capacity of composite Section with full shear interaction (according to IS:11384 - 1985)


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• Reinforced concrete slabs, with profiled sheeting supported on steel beams

• IS: 11384 – 1985, gives no reference to profiled deck slab and partial shear connection

Resistance to sagging bending moment in plastic or compact sections for full interaction.

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

D

Tt

B


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Resistance to hogging Bending Moment

hc+ hp

D

(a)

fy /afy /a

fsk /s

fy /a

FsFa1

Fa2

fy

/a

(b)

fsk /s

FsFa1

Fa2

a

(c)


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P o s i t i v e m o m e n t c a p a c i t y o f s e c t i o n w i t h f u l l s h e a r c o n n e c t i o n ( A c c o r d i n g t o E C 4 )

P o s i t i o n o f P l a s t i c N e u t r a l A x i s C o n d i t i o n M o m e n t C a p a c i t y M pP l a s t i c n e u t r a l a x i s i n c o n c r e t e s l a b

( F i g . 1 3 b )

a

yaceff

c

cyck fAhb

f

85.0 )2/( xhh

fAM tg

a

yap

P l a s t i c n e u t r a l a x i s i n s t e e l f l a n g e

( F i g . 1 3 c ) 2/)()2/(. tcacctgplap hhxNhhhNM

P l a s t i c n e u t r a l a x i s i n w e b( F i g . 1 3 d )

a

yaay

c

cyckceff γ

fA/ γB*T*f

γ

f0.85hb

2/)(

)2/2/()2/(

.

.

ctwa

ctac fctgplap

hThxN

hThNhhhNM

N e g a t i v e m o m e n t c a p a c i t y o f s e c t i o n w i t h f u l l s h e a r c o n n e c t i o n ( a c c o r d i n g E C 4 )

P o s i t i o n o f P l a s t i c N e u t r a l A x i s C o n d i t i o n M o m e n t C a p a c i t y M p

P l a s t i c n e u t r a l a x i s i n s t e e l f l a n g e( F i g . 1 4 b )

P l a s t i c n e u t r a l a x i s i n w e b( F i g . 1 4 c )

a

ya

c

cyckceff

fAfhb

85.0

a

yaw

s

s ks fAfA

a

ya

s

sks

a

yaw fAfAfA

a

fADfAM

s

s ks

a

yap

2

ays

s ks

s

s ksapp ft

fAaDfA

MM

/**42

2


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• Vertical Shear

The shear force resisted by the structural steel section should satisfy:VVp where, Vp is the plastic shear resistance given by,

• The shear buckling of steel web can be neglected if following condition is satisfied

)(

)(

sectionsIupbuiltfor

sectionsCH,I,rolledfor

3

ftd

ftD0.6V

a

y

a

yp

γ

concreteinencasedwebfor

concreteinencasednotwebfor

120td

67td


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• Effect of shape of deck slab on shear connection

Behaviour of a shear connection fixed through profile sheeting


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•Longitudinal Shear Force

• Full Shear Connection

• Single span beams

V = Fcf =Aa fy/a

orV = 0.85 (fck)cy beff hc/c whichever is smaller.

• Continuous span beams

V = Fcf + As fsk /s


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Full Shear Connection -I

• The number of required shear connectors in the zone under consideration for full composite action is given by:

nf = V /P• The shear connectors are usually equally spaced

• Minimum degree of shear connection• Ideal plastic behaviour of the shear connectors may be assumed

if a minimum degree of shear connection is provided.

• The minimum degree of shear connection is defined by the following equations:

btf AAwhere0.030.4nn 3/

btf AAwhere0.030.25nn /

btf AAwhere0.0nn 4/


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• Interaction between shear and moment

V

MMp

Vp

A

o

B

0.5Vp

Mf

Resistance to combined bending and vertical shear


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• Transverse reinforcement

Surfaces of potential shear failure

Truss model analysis


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EFFECT OF CONTINUITY

• Moment and Shear Coefficients for continuous beam

Bending moment coefficients according to IS: 456-1978

TYPE OF LOAD SPAN MOMENTS SUPPORT MOMENTSNear

middlespan

At middle ofinterior span

At support nextto the endsupport

At otherinteriorsupports

Dead load + Imposedload (fixed)

+ 1/12 +1/24 - 1/10 - 1/12

Imposed load (notfixed)

+1/10 +1/12 - 1/9 - 1/9

For obtaining the bending moment, the coefficient shall be multiplied by the total designload and effective span.


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EFFECT OF CONTINUITY-I

Shear force coefficients

At support next to the endsupport

TYPE OFLOAD

At endsupport

Outer side Inner side

At all otherinteriorsupports

Dead load +Imposed

load(fixed)

0.40 0.60 0.55 0.50

Imposedload(not fixed)

0.45 0.60 0.60 0.60

For obtaining the shear force, the coefficient shall be multiplied by the total designload


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• Lateral Torsional Buckling of Continuous Beams

Inverted – U frame Action


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SERVICEABILITY

• Deflection

– Influence of partial shear connection– Shrinkage induced deflections– Crack Control


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CONCLUSIONS

• Provision for service opening in composite beams was discussed.

• Basic design considerations of composite beams, connected to solid slab, as well as profiled deck slab was discussed.

• Effect of continuity on composite beam was discussed.• Serviceability Limit state for composite beam was discussed.

composit e beams2

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