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Beam Design SummaryThe following is a summary of the equations needed for beam design. This is applicable to rolled I and H
sections, and to Class 1 and 2 cross-sections.
Initial Choice of Section
Determine bending moments and shear forces to be resisted.
Use following formula to determine Section modulus needed
𝑊𝑝𝑙,𝑦 𝑓𝑦
𝑀𝑐,𝑦,𝑅𝑑 =
𝛾𝑀0
Look up Section tables to choose potential section.
Checking a suitability of a given Section
Is the beam fully restrained against lateral torsional buckling (LTB) or not?
Determine beam classification.
Clause 5.5.2, Table 6.2
Check bending resistance.
Clause 6.2.5, Eqn 6.13
𝑊𝑝𝑙,𝑦 𝑓𝑦
𝑀𝑐,𝑦,𝑅𝑑 =
𝛾𝑀0
Check shear resistance.
Clause 6.2.6, Eqn 6.18
𝐴𝑣 (𝑓𝑦 /√3)
𝑉𝑝𝑙,𝑅𝑑 =
𝛾𝑀0
Clause 6.2.6 (3)(a)
𝐴𝑣 = max(𝐴 − 2𝑏𝑡𝑓 + (𝑡𝑤 + 𝑟)𝑡𝑓 , 𝜂ℎ𝑤 𝑡𝑤 )
Check shear buckling.
Clause 6.2.6 (6) Shear buckling check
Need not be considered provided:
ℎ𝑤 72𝜀
≤
𝑡𝑤 𝜂
Does moment resistance need to be reduced due to shear?
Clause 6.2.8 (5)
2
2𝑉𝐸𝑑
𝜌=( − 1)
𝑉𝑝𝑙,𝑅𝑑
𝐴𝑤 = ℎ𝑤 𝑡𝑤
Eqn 6.30
𝐴2
(𝑊𝑝𝑙,𝑦 − 𝜌 4𝑡𝑤 ) 𝑓𝑦
𝑤
𝑀𝑦,𝑉,𝑅𝑑 = but 𝑀𝑦,𝑉,𝑅𝑑 ≤ 𝑀𝑦,𝑐,𝑅𝑑
𝛾𝑚0
Are there axial forces? If yes
Do we need to reduce plastic moment resistance due to the effect of axial forces?
Clause 6.2.9.1 (4)
For this not to be necessary for the y-y axis we need to satisfy the following two
conditions:
𝑁𝐸𝑑 ≤ 0.25 𝑁𝑝𝑙,𝑅𝑑
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