composite beam simply supported design

7/30/2019 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

y = 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= 30Area of "I" Beam, A = 45880

Compressive and Tensile Capacities of Concrete and Steel

The Tensile Capacity of the steel

R s = A y

= 14452.2 kN

The Compressive Capacity of the concrete slab over its effective width

R c = 0.45f cu B e (D s -D p)

= 6252.53 kN

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

R w = R s - 2R f Rf = Bt y

= 9412.2 kN = 2520

Ds-D

p= 118


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Check for fully Composite

Moment capacity 03 =

= 12182.12 kNm

Web compression depth= 258.63 mm

38t = 639.10 mm

Stress Diagram for Fully Composite Beam

(PNA lies in web of steel beam)

Check for Shear Connection

R s = 14452.2 kN

R c = 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

CPScs

R

dRDDDRM

42

2

Tension

Rc, Compression

CompressionPNA

aN

6.0

r

D

bk


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Check for Partial Composite PARTIAL COMPOSITE NOT APPLICABLE

Resistance of overall web depth, R w = R s - R f

= 9412.20 kN

Now Compression of Concrete, R q = 6280 kN

Moment Capacity 04 =

= 12207.03 kNm

d/t= 92.22 < Moment Capacity 06 Not Applic

Moment Capacity 06 =

= 10048.67 kNm NA

Stress Diagram for Partially Composite Beam

PNA in Web

Check for Shear

Applied Shear force = 2254 kNShear Resistance, 0.5x P v =

= 2891.7 kN OK

p

422

2

T

R

RRDD

R

RDR

DR

f

qsPS

c

q

SqS

22

2

R

RRRRDD

R

RD

DRM

V

qVqPS

C

q

SqS

Compression

ension

Rq, Compression

PNA

yw

Dtp6.05.0

v

q

R

R1

76


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Check for Deflection (Unpropped Construction)

Length = 15.7 m

During Construction

Dead Loads 8 mFloor (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 LoadsTotal Imposed Load = 20.0 kN/m

2

= 160.0 kN/m

Serviceability Deflection (During the Construction Stage)

Construction stage Deflection, =

= 10.41 mm With Construction Live Load

Serviceability Deflection (During the Composite Stage)

Modular Ratio, Long term, l = 18 Normal Concrete

Modular Ratio, Short term, s = 6

l= 1

Modular Ratio, Steel to Concrete, e = 18

I g =

= mm4

Actual Deflection, =

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

psee

pspse

e

pse

xDDBA

DDDDDABDDBI

4

)(

12

23

gEI

WL

384

5 4


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Check for Service Stresss

= 1673.76


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Web Classification - Composite Stage

r = -0.71

Table 01

Flange/Web Classification - Construction Stage

Flange Classification Welded Section

= 0.934

Flange Class 1- Plastic

Table 02

Web Classification Welded Section

= 0.934Web 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

-51.4Class 03 Semi Compact, When r r 0

9

10

t

d

r1

64

r1

76

13

41

r

r21

114

2

321

1114

r

r

T

b

28

32

40

t

d

80

100

120


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Table 03

Design Summary

APPLICABLE

PARTIAL COMPOSITE

OK

Deflection Satisfied

Satisfied

Satisfied

Web Classification during

constructionWeb Class 2- Compact

Web Classification during

compositeRefer Table 01

Flange Classification during

constructionFlange Class 1- Plastic

Bending Stress in Concrete

during composite

7.52 N/mm2

Total Stress in Steel during

composite309.78 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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9/21

mm

mm

mm

mm

mm

mm

N/mm

2

mm2

kN


10/21

0.11

pD

h


11/21

ble

2

3

4

2 0 dRRqV


12/21

4


13/21

of the

7

8

5


14/21


15/21

NOT APPLICABLE


16/21


17/21

ps

c

s

ssDD

R

RDDR

22

422

2T

R

RRDDR

DR

f

csps

cs

V

CPScs

R

dRDDDRM

42

2


18/21

Tension

Rc, Compression

Compression

PNA

Rc, Compression

Tension

PNA

RS, Compression

Tension, RS

PNA


19/21

422

2d

R

RDD

R

RD

DRM

v

qPS

c

q

SCS

422

2

T

R

RRDD

R

RDR

DR

f

qsPS

c

q

SqS

0.1185.0

pp

r

D

h

D

bk

8.016.0

pp

r

D

h

D

bk

6.015.0

pp

r

D

h

D

bk

0.116.0

pp

r

D

h

D

bk


20/21

Compression

Tension

Rq, Compression

PNA

Rq, Compression

Tension

PNA


21/21

composite beam simply supported design

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