a$)$ The maximum ULS Design Bending Moment in a steel beam is $550kNm$ and the maximum ULS Design Shear Force is $195kN.$ Select a suitable Universal Beam section in Grade $S355$ steel for this beam from the tables provided. Show that your chosen beam is adequate in moment, shear and combined moment and shear.

$(50$ marks$)$

b$)$ A simply supported steel beam with $f_y=275\frac{N}{m}{m}^2$ and $W_{el.y}($elastic section modulus$)=1,250c{m}^3$ has a span of $L=5m.$ The beam supports a Point Load $(P)$ at midspan with the following components: $G_k=100kN,Q_k=60kN,$ You may ignore the selfweight of the beam.

Check if the beam is behaving elastically under $G_k+Q_k$ loading Check if the deflection at midspan is less than the allowable for:

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$($i$)$ Variable Load only $)=(Q_k$

$($ii$)$ Permanent $+$ Variable $)=(G_k+Q_k.$

Given:

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Max Bending Moment in the beam $=P\frac{L}{4}$

Max. Deflection in the beam $=P\frac{L^3}{48EI}$ where

$E=200k\frac{N}{m}{m}^2$

I $(2{?}^{nd}$ moment of area about bending axis$)=50,000c{m}^4$