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
12e
ABe Ds Dp (D Ds Dp )2
4 33564743016 mm
5WL4 384 EI g 25.02 mm 35.43 mm 43.61 mm
4 Ae Be Ds Dp
Full Composite Deflection Deflection Satisfied
Check for Service Stresss ( D s D p ) 2 Be
D 2 D p
=
1673.76
Section is Uncracked
e
Bending Stress in steel section (During the Construction Stage) M= Bending Stress, f bf =
1508.89 kNm 70.66 N/mm2
6
Bending Stress in steel section (During the Composite Stage)
D D B A D 2 D 2
s
p
(Depth of neutral axis below top of the
e
p
concrete flange)
e
A e D 2 Ds Be Ds D p
2
Thus, Y g =
2 A e Be ( Ds D p )
= M= Bending Stress in Concrete, f bc =
677.90 mm 6704.528 kNm 7.52 N/mm2
Bending Stress in Steel, f bs =
2
239.12 N/mm
Total Stress in steel =
309.78 N/mm
2
<
0.5 f cu
Satisfied Satisfied
Web Classification - Composite Stage r=
9
-0.71
d t
92.2
64 1 r
208.0
Class 01 Compact
76 1 r
247.0
Class 02 Compact
41 13 r
-65.9
Class 03 Semi Compact, When r 0.66
114 1 2r
-250.6
Class 03 Semi Compact, When 0.66 > 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
