EXAMPLE: Method of Virtual Work in beams ft

Assume that

$(1)$ First assume that E&I are constant and find $V_c$ in terms of $E!$inI using the table of integrals

$(2)$ Then, consider that the material is steel, $E=29,000$ksi and $I=400i{n}^4,$ and find a numeric value for The vertical displacement at $c,V_c,$ in inches.

$(3)$ Finally, find the actual expressions of $M(x)!$inm$(x)$ and use them to perform the integuations by hand to corroborate previous results.