A steel beam having a span “L” of 7 m is simply supported at its ends and is laterally unrestrained over its whole length. It supports a uniformly distributed permanent action (dead load) (G) of 8 kN/m over its whole length, and a point load of 20 kN acting as an imposed action (live load) (Q) at midspan. Design information: • Load combinations: Strength limit state: WL = 1.2G + 1.5Q Serviceability limit state: WS = G + Q • Maximum deflection under serviceability conditionsis not to exceed L/400 • Effective length factors: kt = 1.0; kℓ = 1.4; kr = 1.0 • Elastic modulus for steel Esteel = 200 GPa • Self-weight of the beam can be disregarded in all calculations (a) Sketch the load diagram showing the loads on the beam for the strength limit state, and calculate the design moment (maximum bending moment) and the design shear force (maximum shear force) (b) Calculate the effective length (Le) of the beam from Le = kt×kℓ×kr×L and select from the Tables provided the lightest suitable Universal Beam (UB) section to fulfil strength limit state requirements. (c) Check if the selected beam fulfils the serviceability limit state of deflection. If it does not, select the lightest suitable UB section that would suffice. (UB section Dimensions and Properties are provided).
A steel beam having a span “L” of 7 m is simply supported at its ends and is laterally
unrestrained over its whole length. It supports a uniformly distributed permanent action
(dead load) (G) of 8 kN/m over its whole length, and a point load of 20 kN acting as an imposed
action (live load) (Q) at midspan.
Design information:
• Load combinations: Strength limit state: WL = 1.2G + 1.5Q
Serviceability limit state: WS = G + Q
• Maximum deflection under serviceability conditionsis not to exceed L/400
• Effective length factors: kt = 1.0; kℓ = 1.4; kr = 1.0
• Elastic modulus for steel Esteel = 200 GPa
• Self-weight of the beam can be disregarded in all calculations
(a) Sketch the load diagram showing the loads on the beam for the strength limit state, and
calculate the design moment (maximum bending moment) and the design shear force
(maximum shear force)
(b) Calculate the effective length (Le) of the beam from Le = kt×kℓ×kr×L and select from the
Tables provided the lightest suitable Universal Beam (UB) section to fulfil strength limit
state requirements.
(c) Check if the selected beam fulfils the serviceability limit state of deflection. If it does not,
select the lightest suitable UB section that would suffice. (UB section Dimensions and
Properties are provided).
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