A uniform steel rod of cross-sectional area A is attached to rigid supports and is unstressed at a temperature of 458F. The steel is assumed to be elastoplastic with sY 5 36 ksi and E 5 29 3 106 psi. Knowing that a 5 6.5 3 1026 /8F, determine the stress in the bar (a) when the temperature is raised to 3208F, (b) after the temperature has returned to 458F.

Explanation:

As the given rod is attached to rigid supports as a result, the deformation occurring due to the change in temperature will cause stress in the rod.

Let us assume that P is the compressive force in the rod due to change in temperature.

So,        

                          =

                          =

Now, we will calculate the actual change in temperature as follows.

This means that the actual change in temperature is more than required for yielding.

(a)   Formula to calculate yielding stress is as follows.

                        =

                        =

                        =

Hence, stress in the bar when temperature is raised to is .

(b)  Now, we will calculate the residual stress as follows.

                          = 15.837 ksi

Therefore, stress in the bar when the temperature has returned to is 15.837 ksi.

(a). The stress is

(b). The residual stress is 15.83 ksi

Explanation:

Given that,

Initial temperature = 45°F

Raised temperature = 320°F

We need to calculate the actual change in temperature

We need to calculate the stress

Using formula of stress

Put the value into the formula

(b). We need to calculate the residual stress

Using formula of stress

Put the value into the formula

Hence, (a). The stress is

(b). The residual stress is 15.83 ksi

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explanation: