Please kindly include all the working out and explanations. There is another upload for the same problem but it does not do a convincing job with the explanations. Thank you in advance!

A steel T$-$beam is to carry an applied moment as shown below. In addition, in the worst case, two bushwalkers with $850$N and

$600$N weight will be on the bridge, they can pass the bridge together or individually. You can ignore the self$-$weight of beam in your calculations.

a$)$ Determine the scenario$/$scenarios that will create the maximum bending moment and shear stress on the beam.

b$)$ Draw the shear force diagram and bending moment diagram based on the loading condition for the scenario of the maximum bending moment and derive the equations for bending moment and shear force.

c$)$ Determine the size of T beam and hollow square sections with specifications shown below with the smallest possible section that can carry the bending moment in the beam. Maximum allowable stress is $2$MPa.

$($d$)$ For the above sections with the loading condition specified in section $($b$),$ if the shearing stress is limited to $4$MPa, Which section is your preference? Explain your reason.

$($e$)$ Determine the maximum spacing between nails for T beam in section $($c$)$ if the shear strength of each nail is $60$N$.$

$($f$)$ Determine the largest tensile stress and the largest compressive stress in the beam.

$($g$)$ Considering T$-$section of Part$-$A$,$ calculate the plastic moment of the section, the yield moment of the section and the shape factor.

$($h$)$ Determine the deflection at mid$-$span of BC and the slope at point C using the integration method and discontinuity function methods. What is your judgement on the deflection? Is it acceptable or not?

If you require any specific information that has not been provided to you, you should make a reasonable hypothesis.

Please kindly include all the working out and explanations. There is another upload for the same problem but it does not do a convincing job with the explanations. Thank you in advance!