Question

An axial centric force of magnitude P=450kN is applied to the composite block shown by means of a rigid end plate.

Knowing that h=10mm, determine the normal stress in

(a) the brass core,

(b) the aluminum plates.

Answer 1

Step-by-step explanation:

To determine the normal stress in the brass core and aluminum plates, we can use the equation of equilibrium:

F = P = A_core * sigma_core + 2 * A_aluminum * sigma_aluminum

where F is the applied force, P is the magnitude of the force, A_core is the cross-sectional area of the brass core, sigma_core is the normal stress in the brass core, A_aluminum is the cross-sectional area of the aluminum plates, and sigma_aluminum is the normal stress in the aluminum plates.

We know that h = 10 mm, and since the cross-sectional area of the brass core is the same as that of the aluminum plates, we can find the cross-sectional area by multiplying h by the width of the block.

A_core = A_aluminum = h * width

We can now use the equation of equilibrium to find the normal stress in the brass core and aluminum plates:

450kN = A_core * sigma_core + 2 * A_aluminum * sigma_aluminum

sigma_core = P / A_core

sigma_aluminum = (P - A_core * sigma_core) / (2 * A_aluminum)

Note that you would need to know the width of the block in order to complete the calculation.