Chapter 14.2, Problem 14.24P

Determine the bending strain energy in the simply supported beam. Solve the problem two ways, (a) Apply Eq. 14–17. (b) The load w dx acting on the segment dx of the beam is displaced a distance y, where y = w(−x⁴ + 2Lx³ − L³x)/(24EI), the equation of the elastic curve. Hence the internal strain energy in the differential segment dx of the beam is equal to the external work, i.e., $d{U}_i=\frac{1}{2}(wdx)(-y)$. Integrate this equation to obtain the total strain energy in the beam. EI is constant.

Prob. 14–24