Chapter 10, Problem 10.6.1P

Assume that the deflected shape of a beam AB with immovable pinned supports (see figure) is given by the equation v = - $-\delta \sin \pi x/L$, where $\delta$is the deflection at the midpoint of the beam and L is the length. Also, assume that the beam has constant axial rigidity EA.

Obtain formulas for the longitudinal force H at the ends of the beam and the corresponding axial tensile stress ${\sigma }_t$ .

1. For an aluminum-alloy beam with

E = 10 × 10⁶ psi, calculate the tensile stress ${\sigma }_t$when the ratio of the deflection S to the length L equals 1/200, 1/400, and 1/600.