Question 7.8: Using moment-area method find out the slope at point C in th...

In the problem, the load P is applied such that symmetry is maintained. Naturally, the tangent at D is parallel to x-axis, that is, horizontal. Angle between tangent at D and tangent at C is the required slope. Using Theorem I, \theta_{ C / D } is equal to the area under M/EI diagram between points D and C, which is the summation of two areas: one triangle and one rectangle. Thus,

\theta_{ C / D }=\frac{P L}{8 E I} \cdot \frac{L}{4}+\frac{1}{2}\left\lgroup \frac{P L}{4 E I}-\frac{P L}{8 E I} \right\rgroup \frac{L}{4}

\theta_{ C / D }=\frac{3 P L^2}{64 E I} \quad \text { or } \quad \theta_{ C }=\frac{3 P L^2}{64 E I} ⦨

So, the required slope at C is 3PL²/64EI.