# deformation

## Thermal Stress

Temperature changes cause the body to expand or contract. The amount δ_{T}, is given by

where α is the coefficient of thermal expansion in m/m°C, L is the length in meter, T_{i} and T_{f} are the initial and final temperatures, respectively in °C. For steel, α = 11.25 × 10^{-6} m/m°C.

If temperature deformation is permitted to occur freely, no load or stress will be induced in the structure. In some cases where temperature deformation is not permitted, an internal stress is created. The internal stress created is termed as thermal stress.

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## Solution to Problem 257 Statically Indeterminate

**Problem 257**

Three bars AB, AC, and AD are pinned together as shown in Fig. P-257. Initially, the assembly is stress free. Horizontal movement of the joint at A is prevented by a short horizontal strut AE. Calculate the stress in each bar and the force in the strut AE when the assembly is used to support the load W = 10 kips. For each steel bar, A = 0.3 in.^{2} and E = 29 × 10^{6} psi. For the aluminum bar, A = 0.6 in.^{2} and E = 10 × 10^{6} psi.

## Solution to Problem 256 Statically Indeterminate

**Problem 256**

Three rods, each of area 250 mm^{2}, jointly support a 7.5 kN load, as shown in Fig. P-256. Assuming that there was no slack or stress in the rods before the load was applied, find the stress in each rod. Use E_{st} = 200 GPa and E_{br} = 83 GPa.

## Solution to Problem 255 Statically Indeterminate

**Problem 255**

Shown in Fig. P-255 is a section through a balcony. The total uniform load of 600 kN is supported by three rods of the same area and material. Compute the load in each rod. Assume the floor to be rigid, but note that it does not necessarily remain horizontal.

## Solution to Problem 254 Statically Indeterminate

**Problem 254**

As shown in Fig. P-254, a rigid bar with negligible mass is pinned at O and attached to two vertical rods. Assuming that the rods were initially stress-free, what maximum load P can be applied without exceeding stresses of 150 MPa in the steel rod and 70 MPa in the bronze rod.

## Solution to Problem 253 Statically Indeterminate

**Problem 253**

As shown in Fig. P-253, a rigid beam with negligible weight is pinned at one end and attached to two vertical rods. The beam was initially horizontal before the load W = 50 kips was applied. Find the vertical movement of W.

## Solution to Problem 252 Statically Indeterminate

**Problem 252**

The light rigid bar ABCD shown in Fig. P-252 is pinned at B and connected to two vertical rods. Assuming that the bar was initially horizontal and the rods stress-free, determine the stress in each rod after the load after the load P = 20 kips is applied.

## Solution to Problem 251 Statically Indeterminate

**Problem 251**

The two vertical rods attached to the light rigid bar in Fig. P-251 are identical except for length. Before the load W was attached, the bar was horizontal and the rods were stress-free. Determine the load in each rod if W = 6600 lb.

## Solution to Problem 249 Statically Indeterminate

**Problem 249**

There is a radial clearance of 0.05 mm when a steel tube is placed over an aluminum tube. The inside diameter of the aluminum tube is 120 mm, and the wall thickness of each tube is 2.5 mm. Compute the contact pressure and tangential stress in each tube when the aluminum tube is subjected to an internal pressure of 5.0 MPa.

## Solution to Problem 248 Statically Indeterminate

**Problem 248**

Solve Problem 247 if the right wall yields 0.80 mm.