ST. ANDREWS
ROAD LESUIRE
CENTRE
I Simpson
Fully Fixed steel beam
calculations
TABLE
CALCULATIONS
RESULTS
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Table 1
LOADING
Page 10
(BS 8110)
Imposed Load (people and equipment)
7.5 x 1.6 (factor)
Total = 12 x (Area 20m2)
240 / 5m (Span)
Dead Load (structure and fittings)
100mm concrete floor screed
Ceiling and services
Flooring (beam and block)
Partitions are included within the imposed load
Total
8.92 x 1.4 (factor)
Total = 12.49 x (Area 20m2)
Total / 5m (span)
7.5KN/m2
12KN/m2
240KN
48KN/m
2.4KN/m2
0.5KN/m2
6.02KN/m2
8.92KN/m2
12.49KN/m2
249.8KN
49.96KN/m
AREA
The area the loads calculated act upon are:
4m (distance between beams) / 2
Multiply by 2 x 2
4m x 5m (span)
2m
4m
20m2
Assume self weight of steel beam as 1KN.m
1KN.m
This gives total loading of:
Imposed Load
Dead Load + Self weight
Total
48KN/m
49.96KN/m
97.96KN/m
The Maximum Bending Moment B (max) = WL2 / 12
M = 97.96 x 52 / 12
204.08Kn/m
1
SHEAR FORCE
Table 9
BS5950
Shear Force @ Supports
= 97.96KN/m x 5m/2
244.90KN
Mc = Py.S
Py = 265N/mm2
522.72KN.m x 106 Nm
265 N/mm2
Table11
Steel strength, py = 265N/mm2
265N/mm2
є = (265/py) 0.5 = 1.0
Section is Class 1 (Plastic)
1.0
1 (Plastic)
Sx = 1972.53cm3
1972.53 cm3
Try in Plastic Modulus table and check suitability of a
457 x 191 x 89 UB S265 section
Steel grade selected = S265
Thickness to be less than or equal to 16mm = Design strength py
265 N/mm2
Section
Tables
Universal
Beams
BS4
Part 1 – 1993
Section Properties
Depth of Section D
Depth between fillets d
Width of section b
Flange thickness t
Web thickness s
Ratio for local buckling Flange b/2t
Ratio for local buckling Web d/s
Torsional Index x
Buckling Parameter u
Plastic Modulus Axis x-x Sx
Elastic Modulus Axis x-x Zx
Radius of Gyration Axis y-y ry
463.40mm
407.60mm
191.90mm
17.70mm
10.50mm
5.42
38.80
28.3
0.880
2014cm3
1770 cm3
43mm
Table 9
BS5950
Flange Thickness t < 40mm therefore we can use py @ design
strength of 265N/mm2 & S265 grade steel
We checked the suitability of a 457 x 191 x 89 UB S265 section
to ensure the flange thickness was sufficient for the design strength
of S265 steelwork.
Cl 4.2.3
SHEAR AREA
Shear Area, Av = td
10.50mm x 463.40mm
= 4865.70mm3
4865.70mm3
2
Cl 4.2.3
SHEAR CAPACITY
Design shear force Fv = 435.60KN
Shear capacity Pv = 0.6pyAv
0.6 x 265N/mm2 x 4865.70mm
= 773646.30 N
Divide by 1000 to convert to KN
= 773.6463KN (which is greater than 435.60KN)
773.6463KN
Pv >> Fv
Therefore Section is adequate in shear
Cl 4.2.3
SHEAR RATIO
Shear Ratio Fv/Pv
244.90KN
773.6463KN
= 0.56
Therefore shear load is low
Cl 4.2.3
0.32
d/s < 70, therefore no need to check for web shear buckling
BENDING
Cl 4.2.5.1
Mc < 1.2py Zx for simply supported beams
= (1.2 x 265 x 1770 x 103)/ 106 = 562.86KNm
562.86KNm
The coincident shear at the point of maximum bending moment is
equal to zero; use Clause 4.2.5.2 for low shear.
Cl 4.2.5.2
Mc = Py Sx
= (265 x 2014 x 103)/ 106 = 533.71KNm
533.71KNm
Critical value of Mc = 533.71KNm
Maximum applied moment = Mx = 522.72KN.m
Therefore = Mc > Mx
DEFLECTION
Running the QSE analysis software for our fully fixed steel beam
we calculated our beams deflection was marginally over the
permissible value of 20mm. Therefore we increased the beam size
from a 457 x 191 UB89 to a 457 x 191 UB98 which gave a
deflection reading of 18mm which was sufficient.
 Provide 457 x 191 x 98 UB S265 section
3