From Mechanics of Materials (5th edition) by Beer, Johnston,DeWolf, and Mazurek,

Question

From Mechanics of Materials (5th edition) by Beer, Johnston,DeWolf, and Mazurek, ch.2 #33: A 250-mm bar of 15x30-mm rectangular cross section consists oftwo aluminum layers, 5-mm thick, brazed to a center brass layer ofthe same thickness. If it is subjected to centric forces ofmagnitude P = 30kN, and knowing that E(aluminum) = 70 GPa andE(brass) = 105 GPa, determine the normal stress in the aluminumlayers and also in the brass layer. I don't understand where to start; the modulus of elasticity,E, of aluminum and brass is included, but I don't understand whereto use it or how to start. From Mechanics of Materials (5th edition) by Beer, Johnston,DeWolf, and Mazurek, ch.2 #33: A 250-mm bar of 15x30-mm rectangular cross section consists oftwo aluminum layers, 5-mm thick, brazed to a center brass layer ofthe same thickness. If it is subjected to centric forces ofmagnitude P = 30kN, and knowing that E(aluminum) = 70 GPa andE(brass) = 105 GPa, determine the normal stress in the aluminumlayers and also in the brass layer. I don't understand where to start; the modulus of elasticity,E, of aluminum and brass is included, but I don't understand whereto use it or how to start.

Explanation / Answer

change in length is same => L = al*L/Eal =b*L/Eb al*Eb=bEal al*105= b*70 b = 1.5 al and P = Aal*al+Ab*b P = (2*5*30)*10-6*al+(5*30)*10-6*1.5al 30000 =( 300+225)*10-6al al = 57.14 MPa b =1.5*57.14 b =85.71 MPa

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