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For the beam and loading shown, use discontinuity functions to compute:

$($a$)$ the deflection $v_A$ of the beam at $A,$ and

$($b$)$ the deflection $v_{\text{m}\text{i}\text{d}\text{s}\text{p}\text{a}\text{n}}$ of the beam at midspan $($i$.$e$.,x=3\mathrm{.}4m).$

Assume a constant value of $EI=1230kN-m^2$ for the beam; $M_A=7\mathrm{.}5kN-m,w_0=20\mathrm{.}8k\frac{N}{m},L_{AB}=1\mathrm{.}7m,L_{BC}=3\mathrm{.}4$m

Answer:

$($a$)v_A=$ mm $.$

$($b$)v_{\text{m}\text{i}\text{d}}=$ mm $.$

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