Consider the general case of a prismatic beam subjected to bending-moment components M
Chapter 11, Problem 11-98(choose chapter or problem)
Consider the general case of a prismatic beam subjected to bending-moment components M, and M , as shown, when the x, y, z axes pass through the centroid of the cross section. If the material is linear elastic, the normal stress in the beam is a linear function of position such that u = a + by + cz. Using the equilibrium conditions 0 = JAudA, M,. = JAzudA, M, = JA- yudA, determine the constants a, b, and c, and show that the normal stress can be determined from the equation u = [- (M,I,. + M, I,,)y + (M/, + M,I,,)z]/(I,J, - I,,2), where the moments and products of inertia are defined in Appendix A.
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