Design of Composite Beams to BS 5950. This is a excel based calculation sheet.
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Composite Slab and Beam Design:BM01 Member/Location
BM01
Drg. Ref. Made by
Date
Chd.
18/03/2010
Floor Details:
Reference are to BS EN 1994-1-1
Span L:
9
m
Beam spacing b:
3
m
Slab depth hS:
130
unless stated
mm
Profi Profile: le: 1.1 CF 60 Decking Profile Height hC:
70
mm
Decking Profile Height hP:
60
mm
bO =
139
mm
Connector diameter d =
19
mm
Overall height hSC =
100
mm
Ulti Ultima mate te Tens Tensil ile e Stre Streng nght ht fu =
450 450
N/mm
Shear Connectors:
2
Concrete: Conc Concre rete te Used Used::
Norm Normal al We Weig ight ht Conc Concre rete te Grad Grade e C30 C30/3 /37 7
BS EN 1992-1-1
N/mm
2
37
N/mm
2
Secant Modulus of Elasticity of concrete E CM:
33000
N/mm
2
Conc Concre rete te Volu Volume me::
0.09 0.097 7
m /m
3
2
Wet conr onrete density:
26
kN/m
3
Dry conr onrete density:
25
kN/m
f cd:
17
N/mm
Characteristic Cylinder Strenght f ck:
30
Characteristic Cube Strenght f ck,cube:
Table 3.1
Reinforcement: Bar Diameter:
10
mm
Spacing of bars:
200
mm
Area rea per unit unit widt width: h:
392 392
mm /m
Yield Strenght f sk:
500
N/mm
2
2
Section Se ction Properties:
Steel Building
Section: Depth ha:
398
mm
Width b:
141.8
mm
Web thickness tw:
6 .4
mm
Flange thickness tf :
8 .6
mm
Root Radius r:
10.2
mm
Depth between fillets Cw:
360.4
mm
Width of Compression Area Cf :
57.5
mm
12510
cm
Plastic Moment y-axis Wpl,y:
724
cm
Area Aa:
49.7
cm
Second moment of area y-axis Iy
39
275
N/mm
Design: Design Data
4 3 2
Modulu Moduluss of Elasti Elasticit city y E: 210000 210000 N/mm Mass per metre:
fy =
UB 406x140x39
2
2
BS EN 1993-1-1
kg
3.2.6(1)
1
Composite Slab and Beam Design:BM01 Member/Location
BM01
Drg. Ref. Made by
Date
18/03/2010
Chd.
Act ions Constru ctio n St age: Permanent Actions : Slab =
kN/m
2.522
Comflor Manual 2
Ponding =
0.252
kN/m
Decking =
0.15
kN/m
Total gK,1 =
2.924
kN/m
1
kN/m
Allowance for beam self weight gK,2=
2008
2
Variable Action s:
BS EN 1991-1-6
qcc =
0
kN/m
2
qca =
0.75
kN/m
2
qk,1 =
0.75
kN/m
2
NA.2.13
qcc is the construction load due to non-permanent equipment in position for use during construction qca is the construction load due to working personnel with hand tools or other small site equipment
Act ions Composi te Stage: Permanent Actions : Slab:
BS EN 1991-1-1 T. NA 2 BS EN 1990 Table NA.A1.2(B)
Partial Safety Factors:
BS EN 1990
γg =
1.35
Table
γq =
1.5
NA.A1.2(B)
Act ions Constru ctio n St age: Construction Stage @ ULS: Fd =
16.6
kN/m
Composi te Stage @ ULS: Fd =
30.16
kN/m
2
Composite Slab and Beam Design:BM01 Member/Location
BM01
Drg. Ref. Made by
Date
18/03/2010
Chd.
Design Bending Moments and Shear Forces: Construction Stage: Maximum Design Shear
VEd =
74.56
kN
Maximiun Design moment is
MEd =
167.75
kNm
Composite Stage: Maximum Design Shear
VEd =
135.73
kN
Maximiun Design moment is
MEd =
305.38
kNm
Cross Section Classification: Web: ε=
0.924
Cw/(twε) =
60.92
Class 1 Web!
Table 5.2
Cf /(tf ε)=
7.23
Class 1 Flange!
XSN = Class 1!
BS EN 1993-1-1
Flange:
Partial Factors For Resistance: Steel Section:
γMO =
1
BS EN 1993-1-1
Steel Section:
γM1 =
1
NA.2.15
γV =
1.25
NA.2.3.
Concrete:
γC=
1.5
BS EN 1992-1-1
Reinforcement:
γs=
1.15
Table NA.1
Shear Connector:
Design Resistance for the Construction Stage: Cross Section Resistance for the Construction Stage: BS EN 1993-1-5
Shear Buckling Check:
5.1(2)
hw/tw =
59.50
72ε/η =
66.56
Shear Buckling Ok
BS EN 1993-1-1 6.2.6(3)
Vertical Shear Resistance; AV=
2762
mm
VEd =
74.56
kN
VC,Rd =
438
kN
ηV =
0.17
MEd =
167.75
kNm
MC,Rd =
199.1
kNm
ηM =
0.84
6.2.6(2)
O.K.
Bending Moment Resistance: 6.2.5(1) O.K.
Buckling Resistance: The steel decking is connected to the steel beam by thru-deck welding of the stud connectors and provides continuous restraint to the top flange of the steel beam so the beam is not susceptible to lateral torsional buckling
3
Composite Slab and Beam Design:BM01 Member/Location
BM01
Drg. Ref. Made by
Date
18/03/2010
Chd.
Shear Connection: For n r = 1 PRd1 =
82
kN
BS EN 1994
PRd 2 =
83.33
kN
6.6.3.1(1)
PRd =
81.66
kN
BS EN 1994
Kt =
1.08
6.6.4.2(1)
KtMAX =
0.85
6.6.4.2(2)
Kt =
0.85
Reduction Factor Design Resistance per
PRd,ACT =
shear connector =
69.41
kN
1
nr = nr PRd,ACT =
69.41
ηMIN =
0.38
ηMIN >
0.4
ηMIN =
0.40
b0 =
0
mm
bei =
1125
mm
bi =
1500
mm
bei =
1125
mm
beff =
2250
mm
5.4.1.2(5)
NC,Rd = 2276 kN
Concrete Resitance:
Npl,a =
Steel Reistance:
1367
kN
NC,f = 1367 kN
no. of Shear connectors:
15
n=
studs
NC = 1041.12 kN η ACT =
0.76
nSC =
0.53
For nr =1
nr=1 is O.K.
O.K.
Design Resistances of the Cross-section for the Composite Stage: Plastic Resistance to Vertical Shear: VEd =
135.73
kN
Vpl,Rd =
438
kN
ηV =
0.31
O.K.
Bending Resistance: nr =
1
η=
0.76
χ C =
42.04
mm
Mpl,Rd =
421
kNm
Mpl,a,Rd =
199.1
kNm
N.A. In Concrete Flange
6.2.1.3(5)
Eq (6.1)
MEd =
305.38
kNm
MRd =
368
kNm
ηM =
4
0.83
O.K.
Composite Slab and Beam Design:BM01 Member/Location
BM01
Drg. Ref. Made by
Date
18/03/2010
Chd.
Longitudinal Shear Resistance of the Slab In practise it is usual to neglect the contribution of the steel decking:
νEd is the design longitudinal shear stress in the concrete slab: θ is the angle of the compression struts:
6.2.4(4)
BE EN 1992-1-1
For nr =
1
θ=
26.5
˚
νEd =
1.65
N/mm
(νEd*hf )/(f yd*Cotθ) =
0.133
Eq 6.21 2
6.2.4(3)
2
mm /mm 2
At =
133
mm /m
At,prov =
252
mm /m
For nr =1
2
O.K.
Crushing of th e Flange ν=
0.528
BS EN 1992-1-1
f cd =
17
Table NA.1
sin θ =
0.45
Cos θ =
0.90
ν*f cd*sinθ*cosθ =
3.58
BS EN 1992-1-1
Crushing of Flange is O.K.
6.2.4(4) Eq (6.22)
Deflection: Construction Stage: w=
12.0226
δ =
39.10
mm
45
mm
δallow =
kN/m
5
Composite Slab and Beam Design:BM01 Member/Location
BM01
Drg. Ref. Made by
Date
18/03/2010
Chd.
Deflection at Conmposite Stage:
Composite Stiffness:
r =
Aa beff hc
r=
0.03
Modular Ratio n=
6.36
n*r =
0.201
Second Moment Area of Composite Area:
I c
Ic=
=
Aa ( hc
+
2h p
+
4(1 + nr )
ha )
2
3
+
beff hc
12n
+
I a
4
492954442.1 mm
Case Self Weight: W=
1
N/mm
I =Iy
125100000
mm
δsw =
3.25
mm
W=
9.675
kN/m
I =Ic
492954442
mm
δ=
7.98
mm
δG=δsw+δg=
11.24
mm
W=
10.5
kN/m
I =Ic:
492954442
mm
δi =
8.67
mm
δiallow=
18
mm
δTOT =
19.90
mm
δallow =
45
mm
4
Case Permanent Weight: 4
Case: Imposed Load: 4
ηδ =
0.44
gk =
10.675
kN/m
10% of Imposed Load:
1.05
kN/m
δ =
12.10
mm
f=
5.17
hz
ηf =
0.77
O.K.
L/200 O.K.
Vibration:
6
Composite Slab and Beam Design:BM01 Member/Location Drg. Ref. Made by
