Spreadsheet Spreadsheet to t o Calculate Composite Beams Original by NCC Revised by LK Ng 5 May 2002 Project: PROMENADE II Level : Composite Beam-Simply Supported Beam :
Designed by: Checked by:
NCC
Steel Properties UB
45 4 57 x
Grade
43
Location
191 x
67 Kg/m
Internal
D=
453.6
mm mm
Ix =
29400
cm
4
B=
189.9
mm mm
Zx =
1300
cm
3
t=
8.5
mm mm
Sr =
1470
cm
3
T=
12.7
mm mm
A=
8540
mm
30 18 130 2.34
N/mm kN/m
0.50 0.50 1.00 1.50 5.00
kN/m kN/m kN/m kN/m kN/m
2
Design Data Normal concrete f cu cu = Density = Slab thickness = Slab UDL DL = Loading Imposed Construction Load = DL M+E = DL partition = Additional DL after construction construction = Total LL after construction = Beam Span , L = Effective Slab Width, Be = Supported Supported Slab W idth, b o = Bondek II
Steel
mm m m kN/m
12000 3000 3000
E= p y = Beam DL =
205000000 355 0.67
kN/m N/mm kN/m
mm mm mm
(steel sheeting)
br
Dp
Trough Spacing Section of Decking Formwork Thicknes Thickness, s, t = Profile Height, Dp = Deck UDL DL =
1 50 0.14
mm m m mm mm kN/m
19.0 90 0 95 100
mm mm nos. mm kN
Spacing = W idth, br =
300 150
mm mm
LL =
1.50
kN/m
LL =
15.00
m
Shear Connectors
Diameter = As-welded As-welded length length = Shear studs per rib = Stud height = Characteristic Strength, Qk =
Floor Loading A. Construction Stage Slab DL = 7.44 UB DL = 0.67
kN/m m
8.11
kN/m
B. Composite State Brickwall DL = 0.00 Dead Load = 12.61
kN/m kN/m
Total DL=
Total DL =
m
12.61
Check size of steel beam At Composite Stage Design l oad, w = 41.65 Design Shear Force, F v = 249.92 Design Moment, M = 749.77
kN/m kN kNm
Moment capacity capacity of steel, M s =
521.85
kNm
Resistance of concrete flange, R c = Rs = Rw = Rf =
3240.00 3031.70 1319.37 856.16
kN kN kN kN
<0.6 py (tD)=
492.7 kN
OK
Resistance of sl ab in compressi on Resistance of steel section i n tension
* Rc > Rs (Plastic neutral neutral axis lies in concrete slab) GO TO CASE 1
Date: Job No.
7-Nov-13 1
Moment Resistance of Composite Beam (for full shear connection): CASE 1
Rc > Rs - (plastic neutral axis lies in concrete slab) Mpc = Rs{D / 2 + D s - (Rs / Rc)(Ds - Dp) / 2} = 968.2 kN/m
CASE 2
Rs > Rc > Rw - (plastic neutral axis lies in steel flange) Mpc = RsD / 2 + R c(Ds + Dp) / 2 - (R s - Rc) T / 4Rf
CASE 3
Rc < Rw - (plastic neutral axis lies in web) Mpc = Ms + Rc (Ds + Dp + D) / 2 - R c D/ 4Rw
> Mu, O.K.
Design of Shear Connectors The smaller of Rc and Rs = Design Strength, Q =
3031.70 80.00
kN kN
Reduction factor for decking profile : No.Stud per trough 1 2 3 2
Calculated 2.04 1.44 1.20
Reduction Factor Limit 1.0 0.8 0.6 Selected
Resistance of one (1) shear connector = No. of connectors per half span required =
Allowable 1.0 0.8 0.6 0.8 64.00
kN
48
(Minimum)
Since there is 2 shear stud per Possible no. of connectors in full span =
300 80
mm (Maximum)
For full composite action, no .of studs req'd =
96
Check Stress: Stress due to self-weight Moment = Bendi ng stress = Modular Ratio = r= Elastic neutral axis depth, x e = Second moment of area, I c = Elastic section modulus-steel f lange, Z t = Elastic section modulus-concrete, Z c =
145.98 112.29 15 0.0356 150.25 861355521 1987655 85993701
kNm N/mm [ 10 for Normal Weight Concrete ; 15 for Light W eight Concrete ] mm mm mm mm
Service load on composite section: Service moment, M= 351.0 kNm Stress in steel
=
177 N/mm2
Total serv iceability stress =
289 N/mm2
OK
0.41 N/mm2
<
Stress in concrete
=
Additional stress on non-composite section
=
112 N/mm2
< Py 13.50 N/mm2
OK
Serviceability Deflection Deflection of beam at the construction stage : Deflection =
Deflection of beam at the composite stage : gamma e = short + p(long -short) =
0.00 mm
Ig = Deflection =
880213495 mm 0.00 mm
Total Deflection for fully composite beam for construction stage: constructi on stage (no pre-cam beri ng, and unpropped) = composite stage = Total = For unpropped construction, total deflection = Hence , unpropped
for normal weight concrete Modulus of Elasticity short term = 6 long term = 18 p= 0.64
13.65
0.00 mm < construction is recommended!
0.00 mm 0.00 mm 0.00 mm
<
L/ 360
L/ 360
33.33 mm
Check Natural Frequency of Beam Weight of F loor Considered in Dynamic Check self weight slab+beam+10% imposed load + SIDL w/o partitions =
11.11
Allowable frequency (minimum), f =
4.00
Ratio of dynamic to static in deflection =
1.10
Deflection due to instantaneously applied self load = Natural Frequency, f =
kN/m Hz
15.44
mm
4.58
Hz
OK !
33.33 mm