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QUESTION $1$

A simply supported beam subjected to a moment of $200kN.$m at support A and is also resisting a distributed load as shown in Figure $1,$ has a cross$-$sectional section given in Figure $2.$ The thickness of the rectangular hollow section is $20mm,$ and the thickness of the bottom and top steel plates is $8mm$ and $6mm$ respectively. Using the beam and the cross$-$section, answer the following questions:

a$)$ Determine the reactions at support A and $B$

b$)$ Determine the shear and moment functions and hence determine the maximum moment.

c$)$ Draw the shear force diagram and bending moment diagram.

d$)$ Draw the shear stress distribution.

e$)$ Determine the radius of gyration $(r_{}$ and $r_{yy}).$

f$)$ Determine the shape factor.

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QUESTION $2$

In Figure $3$ below, the frame is supported by pin support at A and roller at $C,$ point $B$ is fixed.

a$)$ Determine the reactions at support A and $C.$

b$)$ Draw the Axial force diagram, shear force diagram, and bending moment diagram.

c$)$ Draw the qualitative deflected shape.

Figure $3$: Inclined frame