Composite Beam Simply Supported Design

DESIGN OF SIMPLY SUPPORTED COMPOSITE BEAM Location : Primary Beam Section Type : Welded Section Span L = 15700 mm Ley = 15700 mm

Average Space bo = Original strength = Design strength = ρy =

8000

mm

345 345.000 325 315

N/mm2 FPC Available Welded Section N/mm

2

Effective Width, Be = 3925

Primary Beam

Ds-Dp = 118

Ds =

Dp = 57

175

D= 1700

Section Depth = Flange Width = Flange Thickness = Web Thickness = Ds, Overall Depth of slab =

1700 400 20 18

Dp, Depth of deck profile =

57

Cube Strength of concrete, fcu =

30

Area of "I" Beam, A =

45880

175

Compressive and Tensile Capacities of Concrete and Steel The Tensile Capacity of the steel

Rs = =

Aρy 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

R w = R s - 2R f = 9412.2 kN

The axial Capacity of the Flange

R f = Btρ y =

2520

Check for fully Composite 2  D  DS  D P  dRC M s  Rc    4R 2   V

Moment capacity 03 =

= 12182.12 kNm Web compression depth= 258.63 mm 38tε = 639.10 mm

Rc, Compr

1

Compress PNA

Rc, Compression Tension

Compression PNA

Tension

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 = Welded Height = Concrete Grade = Design Capacity, Q = No of shear connector per trough = Average trough width, br = Overall Depth of the stud = Reduction factor for deck profile, k = Resistance of a shear connector = Trough Spacing = No of connectors for fully composite = No of connectors can accommodate =

19 mm 95 mm 30 80 2 200 95 1 80 200 78.2 78.5

N/mm2 kN

Normal Concrete

mm mm Primary Beam kN mm (For half span of beam) (For half span of beam)

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

Degree of shear connection =

Np

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

Na Np

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 Rq D S  D P   R s  Rq  T  D  Rq  D S   2 Rc 2 Rf 4   2

Moment Capacity 04 = = d/t=

Moment Capacity 06 = =

RS

12207.03 kNm 92.22 <

76 Rq 1 Rv

2 Moment Capacity 06 Not Applicable

Rq DS  DP  Rq2  RV  Rq RV  Rq  2R0  d D M S  Rq   DS   RC 2 RV 4 2 

10048.67 kNm

NA

Rq, Compression

Compression

PNA

Tension

Stress Diagram for Partially Composite Beam

Rq, Compression

PNA in Web PNA

Check for Shear Tension Applied Shear force = Shear Resistance, 0.5x P v = =

2254 kN 0.5 0.6 Dtp yw 2891.7 kN



 OK

Check for Deflection (Unpropped Construction) Length =

15.7 m

During Construction Dead Loads Floor (Concrete Slab) = Steel Beam Weight =

8m 33.60 kN/m 3.37 kN/m

Live Loads

8m 1.5 kN/m 12 kN/m

Construction Loads = =

2

During Composite Stage Dead Loads Total Dead Load = =

2 7.2 kN/m 57.6 kN/m

Live Loads Total Imposed Load = =

2 20.0 kN/m 160.0 kN/m

Serviceability Deflection (During the Construction Stage) Construction stage Deflection, δ = =

5WL4 384 EI 10.41 mm

With Construction Live Load

Serviceability Deflection (During the Composite Stage) Modular Ratio, Long term, α l =

18

Modular Ratio, Short term, α s =

6

ρl =

1

Modular Ratio, Steel to Concrete, α e =

18

Normal Concrete

Be Ds  Dp 

3

Ig = = Actual Deflection, δ = Composite Stage = Total Deflection = Allowable Deflection =

Ix 

12e



ABe Ds  Dp (D  Ds  Dp )2



4 33564743016 mm

5WL4 384 EI g 25.02 mm 35.43 mm 43.61 mm



4 Ae  Be Ds  Dp 

Full Composite Deflection Deflection Satisfied

Check for Service Stresss ( D s  D p ) 2 Be

D  2 D  p

=

1673.76 r  0

-51.4

Class 03 Semi Compact, When r < 0

114 1  r  1  2r  3 2

Table 01

Flange/Web Classification - Construction Stage Flange Classification ε=

10

Welded Section 0.934

b T

9.55

28

26.16

Class 1, Plastic

32

29.90

Class 2, Compact

40

37.37

Class 3, Semi Compact

Flange Class 1- Plastic

Table 02

Web Classification ε=

Welded Section 0.934 Web Class 2- Compact

d t

92.2

80

74.7

Class 1, Plastic

100

93.4

Class 2, Compact

120

112.1

Class 3, Semi Compact

Table 03

Design Summary

1

Fully Composite Moment

12182.12 kNm

2

Partially Composite Moment

12207.03 kNm

3

Shear Resistance

2891.70 kN

4

Deflection

5

Section Behaviour

6 7 8

9 10

Bending Stress in steel during construction Bending Stress in Concrete during composite Total Stress in Steel during composite Web Classification during composite Flange Classification during construction Web Classification during construction

35.43 mm

APPLICABLE PARTIAL COMPOSITE NOT APPLICABLE OK Deflection Satisfied

Section is Uncracked 70.66 N/mm2 7.52 N/mm2

Satisfied

309.78 N/mm2

Satisfied

Refer Table 01 Flange Class 1- Plastic Web Class 2- Compact

mm mm mm mm mm mm N/mm2 mm2

kN

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

2

6 Not Applicable

 RV  Rq RV  Rq  2R0  d RV

4

76 Rq 1 Rv

64 1 r

3

76 1 r

 41   13   r  

114 1  2r

114 1  r  1  2r  3 2

 Ds  Dp )2



Ds  Dp 

4

5

is below top of the

Satisfied

7

Satisfied

8

COMPOSITE NOT APPLICABLE

  D R Rs Ds   s Ds  Dp  2 2Rc  

Rs

 Ds  Dp  Rs  Rc 2 T D    Rc  2 2 Rf 4  

2  D  DS  D P  dRC M s  Rc    4R 2   V

PNA

RS, Compression

Tension, RS

Rc, Compression PNA

Tension

Rc, Compression

Compression PNA

Tension

Rq  D S  D P D M S  RC   DS   Rc  2 2

 b  h  k  0.85 r    1  1.0   D p   D p

2   Rq d    Rv 4

Rq DS  DP  Rs  Rq  T  D RS  Rq  D S   2 Rc 2 Rf 4   2

 b  h  k  0 .6  r    1  0 .8   D p   D p

 b  h  k  0 .5  r    1  0 .6   D p   D p

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

Rq, Compression

PNA

Compression

Tension

Rq, Compression PNA

Tension