Problem 2

A rigid plate sits on top of two steel rods, as shown in Figure 2. An additional rod made of

aluminum is located below the center of the plate; the initial gap between the aluminum rod and

the plate is 0.006 in. The steel rods are 12 in long and the cross-sectional area of each rod is shown

in the figure.

The modulus of elasticity of aluminum is Ex-10 psi and the modulus of elasticity of steel is Es

-30×10° psi.

A = 3 in²

A = 5 in²

A 3in²

St

Al

St

Figure 2: Rigid plate on rods

a) Find the normal stress in the aluminum rod if a point load P-200 kips is applied at the

middle of the rigid plate at the top.

b) For the same load (P-200 kips) calculate the axial deformation, i.c., the change of

length, of the steel rods.

e) The yield stress of the aluminum rod is dy A = 40 ksi and the yield stress of the steel

rods is dy st = 60 ksi. Find the maximum load Pas that can be applied without causing

any of the rods to yield.

Note: the symmetry of the geometry, material properties and applied loads implies that the rigid

plate at the top will remain horizontal as the rods deform.