Problem #$1$: Refer to the simply supported beam below:

Find:

a$.(10$ pts$)$ Reactions at A and $C$

b$.(10$ pts$)$ Draw and clearly label Shear and Moment diagrams

c$.(10$ pts$)$ Identify the maximum shear and moment in the beam $($absolute values$).$

Problem #$2$: Refer to the simply supported beam and your solutions in Problem #$1.$

Find: $(15$ pts$)$ The most efficient $($i$.$e$.,$ the lightest$)$ wide flange section $($I$-$beam$)$ for the simply supported beam in problem #$1$ given:

A$992$ Steel

ONLY consider bending stress

Problem #$3$: Refer to the simply supported beam and your solutions in Problem #$1.$

Find: $(15$ pts$)$ The cross$-$sectional dimensions for the preliminary design of a concrete beam for the simply supported beam in problem #$1$ given:

Grade $40$ Rebar

F${}^{}$c?'=5000 psi

Problem #$4$: Refer to the simply supported beam and your solutions in Problem #$1.$

Find: $(15$ pts$)$ The cross$-$sectional dimensions of a wooden glu$-$lam beam for the simply supported beam in problem #$1.$

Problem #$5$: Refer to the simply supported beam and your solutions in Problem #$1.$

Find:

a$.(10$ pts$)$ The maximum moment that can be supported by the steel beam chosen in Problem #$2.$

b$.(15$ pts$)$ The largest overturning pressure that the cantilever section of the simply supported beam can withstand given the steel beam you chose for problem #$2.$