# Axial Deformation

## Solution to Problem 246 Statically Indeterminate

**Problem 246**

Referring to the composite bar in Problem 245, what maximum axial load P can be applied if the allowable stresses are 10 ksi for aluminum and 18 ksi for steel.

## Solution to Problem 245 Statically Indeterminate

**Problem 245**

The composite bar in Fig. P-245 is firmly attached to unyielding supports. Compute the stress in each material caused by the application of the axial load P = 50 kips.

## Solution to Problem 244 Statically Indeterminate

**Problem 244**

A homogeneous bar with a cross sectional area of 500 mm^{2} is attached to rigid supports. It carries the axial loads P_{1} = 25 kN and P_{2} = 50 kN, applied as shown in Fig. P-244. Determine the stress in segment BC. (Hint: Use the results of Prob. 243, and compute the reactions caused by P_{1} and P_{2} acting separately. Then use the principle of superposition to compute the reactions when both loads are applied.)

## Solution to Problem 243 Statically Indeterminate

**Problem 243**

A homogeneous rod of constant cross section is attached to unyielding supports. It carries an axial load P applied as shown in Fig. P-243. Prove that the reactions are given by R_{1} = Pb/L and R_{2} = Pa/L.

## Solution to Problem 242 Statically Indeterminate

**Problem 242**

The assembly in Fig. P-242 consists of a light rigid bar AB, pinned at O, that is attached to the steel and aluminum rods. In the position shown, bar AB is horizontal and there is a gap, Δ = 5 mm, between the lower end of the steel rod and its pin support at C. Compute the stress in the aluminum rod when the lower end of the steel rod is attached to its support.

## Solution to Problem 241 Statically Indeterminate

**Problem 241**

As shown in Fig. P-241, three steel wires, each 0.05 in.2 in area, are used to lift a load W = 1500 lb. Their unstressed lengths are 74.98 ft, 74.99 ft, and 75.00 ft.

(a) What stress exists in the longest wire?

(b) Determine the stress in the shortest wire if W = 500 lb.

## Solution to Problem 240 Statically Indeterminate

**Problem 240**

Three steel eye-bars, each 4 in. by 1 in. in section, are to be assembled by driving rigid 7/8-in.-diameter drift pins through holes drilled in the ends of the bars. The center-line spacing between the holes is 30 ft in the two outer bars, but 0.045 in. shorter in the middle bar. Find the shearing stress developed in the drip pins. Neglect local deformation at the holes.

## Solution to Problem 239 Statically Indeterminate

**Problem 239**

The rigid platform in Fig. P-239 has negligible mass and rests on two steel bars, each 250.00 mm long. The center bar is aluminum and 249.90 mm long. Compute the stress in the aluminum bar after the center load P = 400 kN has been applied. For each steel bar, the area is 1200 mm2 and E = 200 GPa. For the aluminum bar, the area is 2400 mm2 and E = 70 GPa.

## Solution to Problem 238 Statically Indeterminate

**Problem 238**

The lower ends of the three bars in Fig. P-238 are at the same level before the uniform rigid block weighing 40 kips is attached. Each steel bar has a length of 3 ft, and area of 1.0 in.^{2}, and E = 29 × 10^{6} psi. For the bronze bar, the area is 1.5 in.^{2} and E = 12 × 10^{6} psi. Determine (a) the length of the bronze bar so that the load on each steel bar is twice the load on the bronze bar, and (b) the length of the bronze that will make the steel stress twice the bronze stress.