(Solved): Q2) Use Castigliano's theorem to verify the maximum deflection for the uniformly loaded beam 7 of A ...

Q2) Use Castigliano's theorem to verify the maximum deflection for the uniformly loaded beam 7 of Appendix Table A-9. Neglect shear. Table A-9 7 Simple supports_uniform load Shear, Moment, and Deflection of Beams (Continued) (Note: Force and moment reactions are positive in the directions shown; equations for shear force $V$ and bending moment $M$ follow the sign conventions given in Sec. 3-2.) $\begin{array}{rl}{R}_1& =R_2=\frac{wl}{2}V=\frac{wl}{2}?wx\\ M& =\frac{wx}{2}(l?x)\\ y& =\frac{wx}{24EI}\left(2l{x}^2?x^3?l^3\right)\\ y_{\max }& =?\frac{5w{l}^4}{384EI}\end{array}$ 8 Simple supports-moment load $\begin{array}{rl}{R}_1& =R_2=\frac{M_B}{l}V=\frac{M_B}{l}\\ M_{AB}& =\frac{M_{B}x}{l}{M}_{BC}=\frac{M_B}{l}(x?l)\\ y_{AB}& =\frac{M_{B}x}{6EIl}\left(x^2+3a^2?6al+2l^2\right)\\ y_{BC}& =\frac{M_B}{6EIl}\left[x^3?3l{x}^2+x\left(2l^2+3a^2\right)?3a^{2}l\right]\end{array}$