STEEL CONSTRUCTION INSTITUTE, Steel Designers Manual. 3. ... 4. BS 5950 Structural use of steelwork in building Part 3: Design in composite construction ...
Overall concrete depth 130mm (Grade 30) Depth of profiled decking 60mm Size beam with Z = ( Z for non-composite beam ) x F where F = 1.6 - 2.0 Typical maximum slab spans (m) Figures based on:
Decking gauge
1
"Ribdeck AL" (Richard Lees Ltd) 2 Imposed load of 4+1 kN/m (unfactored) 2 (including floor, ceiling and services = 6.7 kN/m ) Unpropped For other profiles see section D2
Lightweight concrete
Slab depth (mm)
Normal Weight Concrete
Simply Supported
Continuous
Simply Supported
Continuous
0.9 (A142 mesh)
130 150
2.95 2.88
3.11 3.22
2.78 2.66
3.03 3.00
1.2 (A193 mesh)
130 150
3.20 3.08
3.73 3.62
3.02 2.89
3.55 3.41
Design assumes 60 minute fire resistance, provided that the slab is continious (decking need not be)
•
Choice of beam system Likely span range (m) Scheme
Simple construction with rolled sections
As primary beams
As secondary beams
6-10.5
8-18
Economic and practical maximum ratios of span to structural depth
20 28
Accommodation of major services. Maximum xsectional area for 15m span m²
Estimated unit cost index for fabricated and erected steelwork
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4.5 Composite Steel and Concrete (2/11) 4.5.1
RULES OF THUMB (CONT’D)
•
Preferred beam layout Inefficient
2
Efficient
For maximum structural efficiency: Primary beams
Secondary beams
L secondary = 4/3 L primary
2.4-3.0m spacing
•
Initial scheming chart Universal beams, 125mm concrete slab (Dotted Line on upper graph indicates that a 150mm slab may be required).
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4.5 Composite Steel and Concrete (3/11) 4.5.1 RULES OF THUMB (CONT’D) Fabricated beams Castellated cellular beams (not very good for point loads): Span/depth < 20 Castellated beams, hole = 0.67D centres = 0.72D Cellular beams holes diameter = 0.6D - 0.8D centres = 1.1 -1.5 diameter Haunched beams (use as part of frame action): D = midspan depth Span/depth ≤ 35 (span/depth including slab = 26 – 28) Maximum overall depth at haunch = 2D Haunch length typically 7 - 10% of span Tapered beams: D = midspan depth Span/depth 15 - 25 Depth at support = 0.5D or maximum taper of 6 degrees
•
Openings in beams (non-seismic applications) Geometrical constraints : - Limit unstiffened openings to 0.6D depth by 1.5D length - Limit stiffened openings to 0.7D depth by 2D length - Space > D apart - Ideally positioned between L/5 and L/3 from support for beams with UDL - Position > D from any point load - Position > 2D (or L/10) from support - Openings should ideally be located mid-height. If not, the depths of the upper and lower sections of web should not differ by more than a factor of 2.
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4.5 Composite Steel and Concrete (4/11) 4.5.2
LOAD FACTORS As for non-composite steel (see section 4.4.2)
4.5.3
BENDING RESISTANCE (composite condition)
•
Approximate moment resistance calculation
P.N.A.
0.45f cu
3
Rc
yP
P.N.A.
yp
Ds- Dp
Rc y
p
P.N.A.
Py RC
D
Py y IN SLAB p
yp IN STEEL FLANGE
Case (c)
Case (b)
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æ Ds + Dp ö (Rs - Rc )2 T D ÷÷ = Rs + Rc çç 2 2 4 Rf è ø
where T = flange thickness Rf = axial capacity of one steel flange CASE (c) : Rc < Rw (P.N.A. lies in web)
Mpc
æ Ds + Dp + D ö Rc2 D ÷÷ = Ms + Rc çç 2 è ø Rw 4
where Ms = plastic capacity of steel section Rw = axial resistance of web only
4.5.4
4
SHEAR CONNECTORS
Design strength of headed studs in normal weight concrete (kN) Dimensions of stud shear connectors (mm) Diameter
Nominal height
As-welded height
100 100 100 75 75 65
25 22 19 19 16 13
95 95 95 70 70 60
Design strength of concrete (N/mm²) 25
30
35
40
117 95 76 66 56 35
123 101 80 70 59 38
129 106 83 73 62 39
134 111 87 77 66 42
For concrete of characteristic strength greater than 40 N/mm² use the values for 40 N/mm². For connectors of heights greater than tabulated use the values for the greatest height tabulated. rcon
= 0.9 for lightweight concrete = 1.0 for normal weight concrete
rprofile
=
0.85 ba (h- Dp) N Dp Dp
min 0.8 (N = 2 ) min 0.6 (N = 3 )
N h ba Dp
= no studs/trough = stud height = average trough width = depth profile
Design resistance = Design strength x rcon x rprofile
•
Spacing
Minimum longitudinal transverse
= 6φ = 4φ
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Maximum longitudinal = 600mm
4.5 Composite Steel and Concrete (6/11) 4.5.5
BENDING STRENGTH (DURING CONSTRUCTION)
•
Conform with requirements in section 4.4 for non-composite sections.
•
Decking perpendicular to beam (secondary) provides restraint to top flange.
•
Decking parallel to beam (primary) does not provide restraint.
4.5.6
STIFFNESS
3
Approximate ratio of second moment of area of composite section to that of the steel section.
α = 10
α = 15
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REFERENCES 1. RICHARD LEES Ltd, Steel Deck Flooring Systems 2. STEEL CONSTRUCTION INSTITUTE, Steel Designers Manual 3. STEEL CONSTRUCTION INSTITUTE, SCI-P-055 Design of Composite Slabs and Beams with Steel Decking 4. BS 5950 Structural use of steelwork in building Part 3: Design in composite construction
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15.0 x 6.0 15.0 x 7. 5 15.0 x 8.0 15. 0 x 9.0 15.0 x 10.0 15. 0 x 12.0 15.0 x 15.0 15.0 x 18.0
5 5 5 5 5 5 5 5
3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00
305 x 102 x 28 356 x 127 x 39 406 x 140 x 39 457 x 152 x 52 457 x 152 x 60 533 x 210 x 82 610 x 229 x 113 * 762 x 267 x 147 *
838 x 292 x 176 914 x 305 x 224 914 x 305 x 224 914 x 305 x 253 914 x 305 x 289 914 x 419 x 343 * FAIL FAI L
38.67 42.87 41.00 45.44 48.90 55.92
203 x 203 x 46 203 x 203 x 71 203 x 203 x 86 254 x 254 x 89 254 x 254 x 107 254 x 254 x 167* 305 x 305 x 240* 356 x 406 x 340*
COLCORE x 477* 356 x 406 x 551 356 x 406 x 551 356 x 406 x 634* 914 x 305 x 289* 914 x 419 x 388* FAIL FAIL
94.83 97.13 97.54 100.11 64.57 88.00
18.0 x 6.0 18.0 x 7.2 18.0 x 7.5 18.0 x 8. 0 18.0 x 9.0 18.0 x 10.0 18.0 x 12. 0 18.0 x 15.0 18.0 x 18.0
6 6 6 6 6 6 6 6 6
3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00
305 x 102 x 28 356 x 127 x 39 356 x 127 x 39 406 x 140 x 39 457 x 152 x 52 457 x 152 x 60 533 x 210 x 82 610 x 229 x 113 * 762 x 267 x 347 *
914 x 305 x 253 * 914 x 419 x 343 * 914 x 419 x 343 * 914 x 419 x 343 * FAIL FAIL FAIL FAIL FAIL
51.50 60.64 58.73 55.88
203 x 203 x 46 203 x 203 x 60 203 x 203 x 71 203 x 203 x 86 254 x 254 x 89 254 x 254 x 107 254 x 254 x 167* 305 x 305 x 240* 356 x 406 x 340*
356 x 406 x 634* 914 x 419 x 343* 914 x 419 x 343* 914 x 419 x 388* FAIL FAIL FAIL FAIL FAIL
121.00 67.64 69.40 77.1 7
(*) Natural frequency of the beam is less then 4.5Hz.
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4.5 Composite Steel and Concrete (9/11) SAFE LOAD TABLES (2) GRADE 43 - LIGHTWEIGHT CONCRETE SLAB 2 Imposed load = 4.0 + 1.0 kN/m Minimum Weight Bay size (m x m)
No. sec. beams per grid
Minimum Depth
Spacing of sec. beams
Secondary Beams
Primary Beams
Weight 2 (kg/m )
Secondary Beams
Primary Beams
Weight 2 (kg/m )
6.0 x 6.0 6.0 x 7.2 6.0 x 7.5 6.0 x 8.0 6.0 x 9.0 6.0 x 10.0 6.0 x 12.0 6.0 x 15.0 6.0 x 18.0
2 2 2 2 2 2 2 2 2
3.00 3.00 3 00 3.00 3.00 3.00 3.00 3.00 3.00
305 x 102 x 25 356 x 127 x 33 305 x 102 x 37 356 x 127 x 39 406 x 140 x 46 457 x 152 x 52 457 x 191 x 74 610 x 229 x 101 686 x 254 x 140*
406 x 140 x 46 457 x 152 x 52 457 x 152 x 52 457 x 152 x 60 457 x 152 x 67 457 x 191 x 74 533 x 210 x 82 610 x 229 x 101 610 x 229 x 113
15.0 x 6.0 15.0 x 7.5 15.0 x 8.0 15.0 x 9.0 15.0 x 10.0 15.0 x 12.0 15.0 x 15.0 15.0 x 18.0
5 5 5 5 5 5 5 5
3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00
305 x 102 x 25 305 x 102 x 37 356 x 127 x 39 406 x 140 x 46 457 x 152 x 52 457 x 191 x 74 610 x 229 x 101 686 x 254 x 140*
762 x 267 x 173 914 x 305 x 201 934 x 305 x 224 914 x 305 x 253 914 x 305 x 289 914 x 419 x 343 FAIL FAIL
37.37 39.13 41.00 43.44 46.23 53.25
203 x 203 x 46 203 x 203 x 60 203 x 203 x 71 203 x 203 x 86 254 x 254 x 107 254 x 254 x 167 305 x 305 x 198* 356 x 406 x 340*
356 x 406 x 393* 356 x 406 x 551 356 x 406 x 551 356 x 406 x 634* 356 x 406 x 634* 914 x 419 x 343 FAIL FAIL
80.83 93.47 92.54 99.11 99.07 84.25
18.0 x 6.0 18.0 x 7.2 18.0 x 7.5 18.0 x 8.0 18.0 x 9.0 18.0 x 10.0 18.0 x 12.0 18.0 x 15.0 18.0 x 18.0
6 6 6 6 6 6 6 6 6
3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00
305 x 102 x 25 356 x 127 x 33 305 x 102 x 37 356 x 127 x 39 406 x 140 x 46 457 x 152 x 52 457 x 191 x 74 610 x 229 x 101 686 x 254 x140*
914 x 305 x 253 * 914 x 305 x 289 * 914 x 419 x 343 * 914 x 419 x 343* 914 x 419 x 388* FAIL FAIL FAIL FAIL
50.50 51.14 58.07 55.88 58.44
203 x 203 x 46 203 x 203 x 52 203 x 203 x 60 203 x 203 x 71 203 x 203 x 86 254 x 254 x 107 254 x 254 x 167 305 x 305 x 198* 356 x 406 x 340*
356 x 406 x 634* 914 x 305 x 289* 914 x 419 x 343* 914 x 419 x 34 * 914 x 419 x 388* FAIL FAIL FAIL FAIL
121.00 57.47 65.73 66.54 71.78
(*) Natural frequency of the beam is less then 4.5Hz.
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Ver 3.1 / August 00
4.5 Composite Steel and Concrete (10/11)
SAFE LOAD TABLES (3) GRADE 50 - DENSE CONCRETE SLAB 2 Imposed load = 4.0 + 1.0 kN/m Minimum Weight Bay size (m x m)
No. sec. beams per grid
Spacing of sec. beams
Secondary Beams
Minimum Depth
Primary Beams
Weight 2 (kg/m )
Secondary Beams
Primary Beams
Weight 2 (kg/m )
6.0 x 6.0 6.0 x 7.2 6.0 x 7.5 6.0 x 8.0 6.0 x 9.0 6.0 x 10.0 6.0 x 12.0 6.0 x 15.0 6.0 x 18.0
2 2 2 2 2 2 2 2 2
3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00
305 x 102 x 25 305 x 102 x 33 305 x 102 x 33 356 x 127 x 33 406 x 140 x 39 457 x 152 x 52 457 x 191 x 67 533 x 210 x 92 686 x 254 x 125
406 x 140 x 39 406 x 140 x 46 457 x 152 x 52 457 x 152 x 52 457 x 152 x 60 457 x 152 x 67 533 x 210 x 82 533 x 210 x 92 610 x 229 x 101
15.0 x 6.0 15.0 x 7.5 15.0 x 8.0 15.0 x 9.0 15.0 x 10.0 15.0 x 12.0 15.0 x 15.0 15.0 x 18.0
5 5 5 5 5 5 5 5
3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00
305 x 102 x 25 305 x 102 x 33 356. x 127 x 33 406 x 140 x 39 457 x 152 x 52 457 x 152 x 67 533 x 210 x 92 686 x 254 x 125
762 x 267 x 147 * 838 x 292 x 176 * 838 x 292 x 194 * 914 x 305 x 201 * 914 x 305 x 224 * 914 x 305 x 289 * 914 x 419 x 343 * FAIL
32.83 34.47 35.25 35.33 39.73 46.42 53.53
152 x 152 x 37 203 x 203 x 52 203 x 203 x 60 203 x 203 x 86 254 x 254 x 89 254 x 254 x132* 305 x 305 x198* 356 x 406 x 340*
356 x 406 x 393* COLCORE x 477* 356 x 406 x 467* 356 x 406 x 551 356 x 406 x 634* 914 x 305 x 289* 914 x 419 x 343* FAIL
77.83 80.93 78.38 89.89 93.07 68.08 88.87
18.0 x 6.0 18.0 x 7.2 18.0 x 7.5 18.0 x 8.0 18.0 x 9.0 18.0 x 10.0 18.0 x 12.0 18.0 x 15.0 18.0 x 18.0
6 6 6 6 6 6 6 6 6
3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00
305 x 102 x 25 305 x 102 x 33 305 x 102 x 33 356 x 127 x 33 406 x 140 x 39 457 x 152 x 52 457 x 152 x 67 533 x 210 x 92 686 x 254 x 125
914 x 305 x 201 * 914 x 305 x 253 * 914 x 305 x 253 * 914 x 305 x 289 * 914 x 419 x 343 * 914 x 419 x 343 * FAIL FAIL FAIL
41.83 46.14 44.73 47.13 51.11 51.63
152 x 152 x 37 203 x 203 x 46 203 x 203 x 52 203 x 203 x 60 203 x 203 x 86 254 x 254 x 89 254 x 254 x 132* 305 x 305 x 198* 356 x 406 x 340*
356 x 406 x 634 * 914 x 305 x 253* 914 x 305 x 253* 914 x 305 x 289* 914 x 419 x 343* 914 x 419 x 343* FAIL FAIL FAIL
118.00 50.47 51.07 56.13 66.78 63.97
(*) Natural frequency of the beam is less then 4.5Hz.
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Ver 3.1 / August 00
4.5 Composite Steel and Concrete (11/11) SAFE LOAD TABLES (4) GRADE 50 - LIGHTWEIGHT CONCRETE SLAB 2 Imposed load = 4.0 + 1.0 kN/m Minimum Weight Bay size (m x m)
No. sec. beams per grid
Minimum Depth
Spacing of sec. beams
Secondary Beams
Primary Beams
Weight 2 (kg/m )
Secondary Beams
Primary Beams
Weight (kg/m2)
6.0 x 6.0 6.0 x 7.2 6.0 x 7.5 6.0 x 8.0 6.0 x 9.0 6.0 x 10.0 6.0 x 12.0 6.0 x 15.0 6.0 x 18.0
2 2 2 2 2 2 2 2 2
3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00
254 x 102 x 22 305 x 102 x 28 305 x 102 x 28 305 x 102 x 33 356 x 127 x 39 406 x 140 x 46 457 x 191 x 60 533 x 210 x 82 610 x 229 x 125*
356 x 127 x 39 406 x 140 x 46 406 x 140 x 46 457 x 152 x 52 457 x 152 x 52 457 x 191 x 60 457 x 191 x 74 533 x 210 x 82 610 x 229 x 101
15.0 x 6.0 15.0 x 7.5 15.0 x 8.0 15.0 x 9.0 15.0 x 10.0 15.0 x 12.0 15.0 x 15.0 15.0 x 18.0
5 5 5 5 5 5 5 5
3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00
254 x 102 x 22 305 x 102 x 28 305 x 102 x 33 356 x 127 x 39 406 x 140 x 46 457 x 152 x 60 533 x 210 x 82* 610 x 229 x 125*
762 x 267 x 147* 762 x 267 x 173* 838 x 292 x 176* 838 x 292 x 194* 914 x 305 x 224* 914 x 305 x 253* 914 x 419 x 343* 914 x 419 x 388*
31.83 32.40 33.00 34.56 37.73 41.08 50.20 63.22
152 x 152 x 37 203 x 203 x 46 203 x 203 x 52 203 x 203 x 71 254 x 254 x 73 254 x 254 x 132* 305 x 305 x 198* 356 x 406 x 340*
356 x 406 x 393* COLCORE x 477* 356 x 406 x 467* 356 x 406 x 551 356 x 406 x 634* 914 x 305 x 289 914 x 419 x 343* 914 x 419 x 388*
77.83 78.93 75.71 84.89 87.73 68.08 88.87 134.89
18.0 x 6.0 18.0 x 7.2 18.0 x 7.5 18.0 x 8.0 18.0 x 9.0 18.0 x 10.0 18.0 x 12.0 18.0 x 15.0 18.0 x 18.0
6 6 6 6 6 6 6 6 6
3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00
254 x 102 x 22 305 x 102 x 28 305 x 102 x 28 305 x 102 x 33 356 x 127 x 39 406 x 340 x 46 457 x 152 x 60 533 x 210 x 82 610 x 229 x 125
838 x 292 x 194* 914 x 305 x 224* 914 x 305 x 253* 914 x 305 x 253* 914 x 305 x 289* 914 x 419 x 343* 914 x 419 x 388* FAIL FAIL
39.67 40.44 43.07 42.63 45.11 49.63 52.33
152 x 152 x 37 203 x 203 x 46 203 x 203 x 46 203 x 203 x 52 203 x 203 x 71 254 x 254 x 73 254 x 254 x132* 305 x 305 x 198* 356 x 406 x 340*
356 x 406 x 634* 914 x 305 x 224* 914 x 305 x 253* 914 x 305 x 253* 914 x 305 x 289* 914 x 419 x 343* 914 x 419 x 388* FAIL FAIL
118.00 46.44 49.07 48.96 55.7B 58.63 76. 33
(*) Natural frequency of the beam is less then 4.5Hz.
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b > 10, then the digit A stands for 10, B for 11, etc. ...... When R is an equivalence relation then the equivalence class of an element a in A .... The set of letters in the English alphabet is nite. ...... The Guide to Available Mathematical Softwa
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