Question

A steel bar (E_s = 210 GPa) and an aluminum bar(E_a = 70 GPa) are bonded together to form the composite bar shown. Determine the maximum stress in (a) the aluminum, (b)the steel, when the bar is bent about a horizontal axis, with M =60 N-m

Answer 1

Calculate the ratio of modulus of elasticity of steel and aluminum.

Here, n is the ratio of modulus of elasticity of steel and aluminum, is the modulus of elasticity of steel, and modulus of elasticity of aluminum.

Substitute for and for .

Draw the equivalent system if aluminum and steel to the system by multiplying the horizontal dimension of the steel portion of the section by.

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Determine the distance of neutral axis from axis for the equivalent composite section.

Here, is the distance of neutral axis from axis , is the area of the steel section, is the area of the aluminum section which is equivalent to the aluminum and y is the distance of the section from the axis.

Substitute for , for , for , and for .

Determine the maximum distance from Neutral axis.

Substitute for .

Calculate the moment of inertia of the equivalent composite section about axis ,

Here, is the base of the aluminum section, is the height of the aluminum section, is the base of the steel section, is the moment of the section about its centroid, and is the height of the steel section.

Substitute for , for , for , for , for , for , for , and for .

Calculate the moment of inertia of the equivalent composite section about neutral axis.

Substitute for , , for , for , and for .

Calculate the maximum stress in aluminum section.

Here, is the maximum stress, is the moment, is distance of the top fiber of aluminum from the neutral axis, and is the moment of inertia.

Substitute for M, for C, and for I

Thus, the maximum stress in the aluminum is .

Calculate the maximum stress in steel section.

Here, is the is distance of the top fiber of steel from the neutral axis and is the maximum stress in the steel.

Substitute for M, for , 3 for n, and for I

Thus, the maximum stress in steel section is .