IK Consider the general case of a prismatic beamsubjected to bending-moment components M, and M., asshown, when thex,y,z axes pas throush the centruld of thecross section. Ir the material is nncar-clastic, the aormalstress in the beam is a lincar tunction of position such that=a+by + az. Using the equilibrium conditions0= f,wai, M, = Szat, M, = ,-ye dt, determinethe constants a, D. and c, and show that the normalbe determined trom the quationstree can=|-M, +My + (M, + M1/44,-4 wherethe moments and products of inertia are defined inAppendit A.Prob. 6-6

To find: The value of constants a,b and c and show that the normal stress is…

6-106. Consider the general case of a prismatic beam subjected to bending moment components M, and Me, as shown, when the x,y,z axes pass through the centruid of the cross section. If the material is linear-elastic, the normal stress in the beam is a linear function of position such that Using the equilibrium conditions S, M, ₁-yedt, determine =g+by+a. 0=f₁dA. M, show that the normal the constants a, b, and c, and stress can be determined from the equation 1-(M+M+M+Mly/-), where the moments and products of inertia are defined in Appendix A. Prob. 6-106

6-106. Consider the general case of a prismatic beam subjected to bending moment components M, and Me, as shown, when the x,y,z axes pass through the centruid of the cross section. If the material is linear-elastic, the normal stress in the beam is a linear function of position such that Using the equilibrium conditions S, M, ₁-yedt, determine =g+by+a. 0=f₁dA. M, show that the normal the constants a, b, and c, and stress can be determined from the equation 1-(M+M+M+Mly/-), where the moments and products of inertia are defined in Appendix A. Prob. 6-106

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter5: Stresses In Beams (basic Topics)

Section: Chapter Questions

Problem 5.11.11P: The three beams shown have approximately the same cross-sectional area. Beam 1 is a W 14 X 82 with...

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