Determine the bending strain energy in the cantilever beam. Solve the problem two ways. (a) Apply Eq. 14-17. (b) The load \(w d x\) acting on a segment \(d x\) of the beam is displaced a distance \(v\), where \(v=w\left(-x^{4}+4 L^{3} x-3 L^{4}\right) /(24 E I)\), the equation of the elastic curve. Hence the internal strain energy in the differential segment \(d x\) of the beam is equal to the external work, i.e., \(d U_{i}=\frac{1}{2}(w d x)(-v)\). Integrate this equation to obtain the total strain energy in the beam. \(E I\) is constant.

Transcribed Image Text:

w dx +1-xp -L- -x- W