Consider the general case of a prismatic beam subjected to bendingmoment components M_yand M_zwhen 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 σ = a + by + cz. Using the equilibrium conditions 0 = ˆ«_AσdA, M_y= ˆ«_AzσdA, M_z= ˆ«_A- yσdA, determine the constants a, b, and c, and show that the normal stress can be determined from the equation σ = [€“(M_zI_y+ M_yI_yz)y + (M_yI_z+ M_zI_yz)z]/(I_yI_z€“ I_yz²), where the moments and products of inertia are defined in Appendix A.

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AM, dA х