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ETABS 2013 0
BS-5950-90 Example-001 STEEL DESIGNERS MANUAL SIXTH EDITION - DESIGN OF SIMPLY SUPPORTED COMPOSITE BEAM EXAMPLE DESCRIPTION Design a composite floor with beams at 3-m centers spanning 12 m. The composite slab is 130 mm deep. The floor is to resist an imposed load of 5.0 kN/m2, partition loading of 1.0 kN/m2 and a ceiling load of 0.5 kN/m2. The floor is to be un-propped during construction. GEOMETRY, PROPERTIES AND LOADING
Member Properties UKB457x191x67 E = 205,000 MPa Fy = 355 MPa
Loading w = 6.67kN/m (Dead Load) w = 1.5kN/m (Construction) w = 1.5kN/m (Superimposed Load) w = 18.00kN/m (Live Load)
Geometry Span, L = 12 m
TECHNICAL FEATURES OF ETABS 2013 TESTED Composite beam design, including: Selection of steel section, camber and shear stud distribution Member bending capacities, at construction and in service Member deflections, at construction and in service
BS-5950-90 Example-001 - 1
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RESULTS COMPARISON Independent results are referenced from the first example, Design of Simply Supported Composite Beam, in Chapter 21 of the Steel Construction Institute Steel Designer’s Manual, Sixth Edition. ETABS
Independent
Percent Difference
211.3
211.3
0.00%
Construction Ms (kN-m)
521.9
521.9
0.00%
Construction Deflection (mm)
29.9
29.9
0.00%
Design Moment (kN-m)
724.2
724.3
0.01%
Full Composite Mpc (kN-m)
968.9
968.3
0.06%
Partial Composite Mc (kN-m)
919.0
919.6
0.06%
Shear Stud Capacity Qn (kN)
57.6
57.6
0.00%
Live Load Deflection (mm)
27.5
31.4
12.42%
Applied Shear Force Fv (kN)
241.4
241.4
0.00%
Shear Resistance Pv (kN)
820.9
821.2
0.03%
Output Parameter Construction Design Moment (kN-m)
COMPUTER FILE: BS-5950-90 EXAMPLE 001.EDB CONCLUSION The ETABS results show an acceptable comparison with the independent results.
BS-5950-90 Example-001 - 2
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HAND CALCULATION Properties: Materials: S355 Steel: E = 205,000 MPa, py = 355 MPa, γs = 7850 kg/m3 Light-weight concrete: E = 24,855 MPa, fcu = 30 MPa, γc = 1800 kg/m3 Section: UKB457x191x67 D = 453.6 mm, bf = 189.9 mm, tf = 12.7 mm, tw = 8.5 mm Asteel = 8,540 mm2, Isteel = 29,380 cm4 Deck: Ds =130 mm, Dp = 50 mm, sr = 300 mm, br = 150 mm Shear Connectors: d = 19 mm, h = 95 mm, Fu = 450 MPa Loadings: Self weight slab
= 2.0 kN/m2
Self weight beam
= 0.67 kN/m
Construction load
= 0.5 kN/m2
Ceiling
= 0.5 kN/m2
Partitions (live load)
= 1.0 kN/m2
Occupancy (live load)
= 5.0 kN/m2
Design for Pre-Composite Condition: Construction Required Flexural Strength: wult construction = 1.4 • 0.67 + (1.4 • 2.0 + 1.6 • 0.5 ) • 3.0 = 11.74 kN/m
BS-5950-90 Example-001 - 3
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wult construction • L2 11.74 • 122 = = = 211.3 kN-m M ult construction 8 8 M s = S z • Py = 1, 470 • 103 • 355 • 10−6 = 521.9 kN-m
Pre-Composite Deflection:
wconstruction = 2.0 • 3.0 + 0.67 = 6.67 kN/m = δ
5 • wconstruction • L4 5 • 6.67 • 12, 0004 = = 29.9 mm 384 • E • I 384 • 205, 000 • 29,380 • 104
Camber = 0.8 •= δ 24 mm, which is rounded down to 20 mm
Design for Composite Flexural Strength: Required Flexural Strength:
wult = 1.4 • 0.67 + (1.4 • 2.0 + 1.6 • 1 + 1.6 • 5 ) • 3.0 = 40.24 kN/m
= M ult
wult • L2 40.24 • 122 = = 724.3 kN-m 8 8
Full Composite Action Available Flexural Strength: Effective width of slab: B= e
L 12,000 = = 3, 000 mm ≤ 3,000 mmm 4 4
Resistance of slab in compression: Rc = 0.45 • f cu • Be • ( Ds − D p )= 0.45 • 30 • 3, 000 • (130 − 50 ) • 10−3 = 3, 240 kN
Resistance of steel in tension: Rs = Py = As • p y = 8, 540 • 355 • 10−3 = 3, 032 kN controls
Moment resistance of composite beam for full composite action:
D R ( Ds − D p ) M= Rs + Ds − s for Rs ≤ Rc pc Rc 2 2 3, 032 80 453.6 = 3, 032 + 130 − • = • 10−3 968.2 kN-m 3, 240 2 2
BS-5950-90 Example-001 - 4
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Partial Composite Action Available Flexural Strength: Assume 76% composite action: Rq = 0.76 • Rs = 2,304 kN
Tensile Resistance of web: Rw = tw • ( D − 2 • t f ) • p y = 8.5 • ( 453.6 − 2 • 12.7 ) • 355 • 10−3 = 1, 292 kN
As Rq > Rw, the plastic axis is in the steel flange, and
M c =Rs
Rq ( Ds − D p ) ( Rs − Rq ) 2 t f D + Rq Ds − − Rc Rf 2 2 4
( 3, 032 − 2,304 ) 12.7 • 10−3 453.6 2,304 80 = 3, 032 • 10−3 + 2,304 130 − • • 10−3 − 2 3, 240 2 ( 3, 032 − 1, 292 ) 4 2
= 919.6 kN-m Shear Stud Strength: Characteristic resistance of 19 mm-diameter studs in normal weight 30 MPa concrete: Qk = 100 kN from BS 5950: Part 3 Table 5 Adjusting for light-weight concrete:
Qk = 90 kN Reduction factor for profile shape with ribs perpendicular to the beam and two studs per rib:
k = 0.6 •
br ( h − D p ) 150 ( 95 − 50 ) • = 0.6 • • = 1.62 but k ≤ 0.8 50 50 Dp Dp
Design strength: Q p =k • 0.8 • Qk =0.8 • 0.8 • 90 =57.6 kN
Shear Stud Distribution:
= n
Rq 2,304 = = 40 studs from each end to mid-span 64 Qp
BS-5950-90 Example-001 - 5
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Live Load Deflection: The second moment of area of the composite section, based on elastic properties, Ic is given by:
= Ic
Asteel • ( D+ Ds + D p )
2
4 • (1 + α e • r )
+
beff • ( Ds − D p )
3
12 • α e
+ I steel
Asteel 8,540 = = 0.0356 beff • ( Ds − D p ) 3, 000 • (130 − 50 )
= r
For light-weight concrete:
αs = 10
α l =25 Proportion of total loading which is long term: = ρl
wdl + wsdl + 0.33 • wlive 6.67 + 1.5 + 0.33 • 18 = = 0.541 6.67 + 1.5 + 18 wdl + wsdl + wlive
α e = α s + ρl • ( α l − α s ) = 10 + 0.541 • ( 25 − 10 ) = 18.1
8,540 • ( 453.6 + 130 + 50 ) 3, 000 • 803 = + + 294 • 106 Ic 4 • (1 + 18.1 • 0.0356 ) 12 • 18.1 2
=
( 521 + 7 + 294 ) • 106=
822 • 106 mm 4
Live load deflection assuming full composite action:
5 • 18 • (12, 000 ) 5 • wlive • L4 = δc = = 28.9 mm 384 • E • I c 384 • 205, 000 • 822 • 106 4
Adjust for partial composite action:
5 • 18 • (12, 000 ) 5 • wlive • L4 = δs = 384 • E • I c 384 • 205, 000 • 294 • 106 4
= 80.7 mm non-composite reference deflection δ partial = δc + 0.3 • (1 − K ) • ( δ s − δc ) = 28.9 + 0.3 • (1 − 0.76 ) • ( 80.7 − 28.9= ) 32.6 mm
BS-5950-90 Example-001 - 6
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Design for Shear Strength: Required Shear Strength: = Fv
wult • L 40.24 • 12 = = 241.4 kN 2 2
Shear Resistance of Steel Section: P = 0.6 • p • A = 0.6 • 355 • 453.4 • 8.5 • 10−3 = 821.2 kN V y v
BS-5950-90 Example-001 - 7
