Determine the bending strain energy in the cantilevered beam due to a uniform load w
Chapter 14, Problem 14-23(choose chapter or problem)
Determine the bending strain energy in the cantilevered beam due to a uniform load w. Solve the problem two ways. (a) Apply Eq. 14-17. (b) The load w dx acting on a segment dx of the beam is displaced a distance y, where \(y=w\left(-x^4+4 L^3 x-3 L^4\right) /(24 E I)\), the equation of the elastic curve. Hence the internal strain energy in the differential segment dx of the beam is equal to the external work, i.e., \(d U_i=\frac{1}{2}(w d x)(-y)\). Integrate this equation to obtain the total strain energy in the beam. EI is constant.
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