Composite Beam Simply Supported Design

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DESIGN OF SIMPLY SUPPORTED COMPOSITE BEAM

Location : Primary Beam

Section Type :Welded Section Span L = 15700 mm

Ley = 15700 mm Average Space bo = 8000 mm

Original strength = 345 N/mm2 Design strength = 345.000 FPC Available

325 Welded Section ρy = 315 N/mm2

Effective Width, Be = 3925 Primary Beam

Ds = 175 Dp =57 Section Depth = 1700 D = Flange Width = 400 1700 Flange Thickness = 20 Web Thickness = 18 Ds, Overall Depth of slab = 175 Dp, Depth of deck profile = 57 Cube Strength of concrete, fcu = 30 Area of "I" Beam, A = 45880 Compressive and Tensile Capacities of Concrete and Steel

The Tensile Capacity of the steel

Rs = A ρy = 14452.2 kN

The Compressive Capacity of the concrete slab over its effective width

Rc = 0.45fcuBe(Ds-Dp) = 6252.53 kN

The axial Capacity of the web The axial Capacity of the Flange

Rw = Rs - 2Rf Rf = Btρy

= 9412.2 kN = 2520

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Check for fully Composite Moment capacity 03 =

= 12182.12 kNm Web compression depth= 258.63 mm

38tε = 639.10 mm

Stress Diagram for Fully Composite Beam (PNA lies in web of steel beam)

Check for Shear Connection Rs = 14452.2 kN Rc = 6252.53 kN Smaller of RC and RS is 6252.53 kN

Nominal Shank Diameter = 19 mm Welded Height = 95 mm Concrete Grade = 30 N/mm2

Design Capacity, Q = 80 kN Normal Concrete No of shear connector per trough = 2

Average trough width, br = 200 mm Overall Depth of the stud = 95 mm

Reduction factor for deck profile, k = 1 Primary Beam Resistance of a shear connector = 80 kN

Trough Spacing = 200 mm

No of connectors for fully composite = 78.2 (For half span of beam) No of connectors can accommodate = 78.5 (For half span of beam)

No of connectors can accommodate No of connectors for fully composite = 1.00

Degree of shear connection =

1

V C P S c s R dR D D D R M 4 2 2         Tension Rc, Compression Compression PNA Tension Rc, Compression Compression PNA p a N N 0 . 1 1 6 . 0                    p p r D h D b k

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Check for Partial Composite PARTIAL COMPOSITE NOT APPLICABLE Resistance of overall web depth, Rw = Rs - Rf

= 9412.20 kN Now Compression of Concrete, Rq = 6280 kN

Moment Capacity 04 =

= 12207.03 kNm

d/t= 92.22 < Moment Capacity 06 Not Applicable

Moment Capacity 06 =

= 10048.67 kNm NA

Stress Diagram for Partially Composite Beam PNA in Web

Check for Shear

Applied Shear force = 2254 kN Shear Resistance, 0.5x Pv = = 2891.7 kN OK

2

p a N N









4 2 2 2 T R R R D D R R D R D R f q s P S c q S q S           











4 2 2 2 0 2 d R R R R R R R D D R R D D R M V q V q V q P S C q S q S                Compression Tension R_q, Compression PNA R_q, Compression Tension PNA



0.6Dtpyw



5 . 0 v q

R



1

76 

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Check for Deflection (Unpropped Construction)

Length = 15.7 m During Construction

Dead Loads 8 m

Floor (Concrete Slab) = 33.60 kN/m Steel Beam Weight = 3.37 kN/m

Live Loads 8 m

Construction Loads = 1.5 kN/m2

= 12 kN/m

During Composite Stage

Dead Loads

Total Dead Load = 7.2 kN/m2 = 57.6 kN/m

Live Loads

Total Imposed Load = 20.0 kN/m2 = 160.0 kN/m

Serviceability Deflection (During the Construction Stage)

Construction stage Deflection, δ =

= 10.41 mm With Construction Live Load

Serviceability Deflection (During the Composite Stage)

Modular Ratio, Long term, αl = 18 Normal Concrete Modular Ratio, Short term, αs = 6

ρl = 1 Modular Ratio, Steel to Concrete, αe = 18

Ig =

= mm4

Actual Deflection, δ =

Composite Stage = 25.02 mm Full Composite Deflection Total Deflection = 35.43 mm

Allowable Deflection = 43.61 mm Deflection Satisfied 33564743016 EI WL 384 5 4















e e s p



p s p s e e p s e x D D B A D D D D D AB D D B I           4 ) ( 12 2 3 g

EI

WL

384

5

4

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Check for Service Stresss

= 1673.76 <A Section is Uncracked

Bending Stress in steel section (During the Construction Stage)

M = 1508.89 kNm Bending Stress, fbf = 70.66 N/mm2

Bending Stress in steel section (During the Composite Stage)

(Depth of neutral axis below top of the concrete flange)

Thus, Yg =

= 677.90 mm

M = 6704.528 kNm

Bending Stress in Concrete, fbc = 7.52 N/mm2 < Satisfied Bending Stress in Steel, fbs = 239.12 N/mm2

Total Stress in steel = 309.78 N/mm2 Satisfied

6



p



e e p s D D B D D



2 ) ( 2  







p



e e p s D D B D D A



2 2   











( )



2 2 2 p s e e p s e s e D D B A D D B D D A     



cu

f

5 .

0

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Web Classification - Composite Stage r = -0.71

Table 01

Flange/Web Classification - Construction Stage

Flange Classification Welded Section

ε = 0.934

Flange Class 1- Plastic

Table 02

Web Classification Welded Section

ε = 0.934

Web Class 2- Compact

Class 1, Plastic Class 2, Compact Class 3, Semi Compact 74.7 93.4 112.1 92.2 Class 1, Plastic Class 2, Compact Class 3, Semi Compact 9.55 26.16 29.90 37.37 92.2 208.0 247.0 Class 01 Compact Class 02 Compact

-51.4 Class 03 Semi Compact, When r < 0

-65.9 Class 03 Semi Compact, When r 0.66

-250.6 Class 03 Semi Compact, When 0.66 > r 0

9

10

t d r  1 64 r  1 76        _ 13 41 r _ r 2 1 114   









2 3 2 1 1 114 r r    T b



28



32



40 t d



80



100



120

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Table 03

Design Summary

APPLICABLE

PARTIAL COMPOSITE NOT APPLICABLE OK

Deflection Satisfied

Satisfied

Web Classification during

construction Web Class 2- Compact Web Classification during

composite Refer Table 01

Flange Classification during

construction Flange Class 1- Plastic Bending Stress in Concrete

during composite 7.52 N/mm

2

Total Stress in Steel during

composite 309.78 N/mm

2 Section Behaviour

70.66 N/mm2 Section is Uncracked Bending Stress in steel during

construction

Shear Resistance 2891.70 kN

Deflection 35.43 mm

Fully Composite Moment

Partially Composite Moment 12207.03 kNm 12182.12 kNm

10

1

2

3

4

5

6

7

8

9

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mm mm mm mm mm mm N/mm2 mm2 kN

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0 . 1 1 6 . 0                    p p r D h D b k

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Moment Capacity 06 Not Applicable

2

3 









4 2 2 2 0 2 d R R R R R R R D D R R D D R M V q V q V q P S C q S q S                v q

R



1

76 

r  1 64 r  1 76        _ 13 41 r r 2 1 114  

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4 













e e s p



p s p s e e p s e x D D B A D D D D D AB D D B I           4 ) ( 12 2 3









2 3 2 1 1 114 r r   

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(Depth of neutral axis below top of the Satisfied Satisfied

7

8

5

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



_         _s _p c s s s D D R R D D R 2 2









4 2 2 2 T R R R D D R D R f c s p s c s           V C P S c s R dR D D D R M 4 2 2        

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Tension Rc, Compression Compression PNA Rc, Compression Tension PNA RS, Compression Tension, RS PNA

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4 2 2 2 d R R D D R R D D R M v q P S c q S C S                









4 2 2 2 T R R R D D R R D R D R f q s P S c q S q S            0 . 1 1 85 . 0                    p p r D h D b k 8 . 0 1 6 . 0                    p p r D h D b k 6 . 0 1 5 . 0                    p p r D h D b k 0 . 1 1 6 . 0                    p p r D h D b k

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Compression Tension Rq, Compression PNA Rq, Compression Tension PNA

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