Problem $3$

Determine the factored design loads $($i$.$e$.,$ moment $($positive and negative$)$ and shear$)$ for a beam in a parking

garage that is continuous over two equal spans of $10m.$ Consider live and dead loads only. The tributary

width is $3m.$ Use a $3k\frac{N}{m}$ allowance for dead load $($includes self$-$weight$)$; there are significant height

restrictions and only small vehicles can get into the garage; only the live area load $($kPa$)$ needs to be

considered. Specifically, draw the shear force and bending moment diagram for:

a$)1\mathrm{.}25$D $+1\mathrm{.}5L($live load applied to both spans$)(11$ marks$)$

b$)1\mathrm{.}25$D $+1\mathrm{.}5L($live load applied to left span only$)(8$ marks$)$

c$)$ the envelope $($i$.$e$.,$ maximum and minimum of Case a$)$ and b$))-$ clearly state the maximum load

effect and which case it occurred in$.(11$ marks$)$

You may use a computer program $($e$.$g$.,$ Robot$)$ or design aids to obtain the shear and bending moment

diagrams. Use the principle of superposition when necessary.