The strain gauge is placed on the surface of a thin-walled steel boiler as shown. The gauge is 0.5 in. long and it elongates 0.19(10-3) in. when a pressure is applied. The boiler has a thickness of 0.5in . and inner diameter of60 in. Est = 29(103) ksi, ?st = 0.3. Determine the pressure in the boiler. Determine the maximum x,y in-plane shear strain in the material.

Answers

Answer 1

The pressure in the boiler can be determined by using the formula for stress, which is the force per unit area. In this case, the force is caused by the elongation of the strain gauge, and the area is the cross-sectional area of the boiler.

To determine the pressure, we can use the following steps:

1. Calculate the change in length of the strain gauge:
Change in length = 0.19(10^-3) in.

2. Calculate the strain in the strain gauge:
Strain = Change in length / Original length
Strain = (0.19(10^-3) in.) / (0.5 in.)

3. Calculate the stress in the strain gauge:
Stress = Strain * Young's modulus
Stress = Strain * Est

4. Calculate the force on the strain gauge:
Force = Stress * Cross-sectional area of the strain gauge
Cross-sectional area of the strain gauge = thickness of the boiler * length of the strain gauge
Cross-sectional area of the strain gauge = 0.5 in. * 0.5 in.

5. Calculate the pressure in the boiler:
Pressure = Force / Cross-sectional area of the boiler
Cross-sectional area of the boiler = π * (inner diameter/2)^2
Cross-sectional area of the boiler = π * (60 in./2)^2

Now let's calculate the values:

1. Change in length = 0.19(10^-3) in.

2. Strain = (0.19(10^-3) in.) / (0.5 in.)

3. Stress = Strain * Est

4. Cross-sectional area of the strain gauge = 0.5 in. * 0.5 in.

5. Cross-sectional area of the boiler = π * (60 in./2)^2

6. Force = Stress * Cross-sectional area of the strain gauge

7. Pressure = Force / Cross-sectional area of the boiler

Finally, we can determine the maximum x, y in-plane shear strain in the material. The maximum shear strain occurs at a 45-degree angle to the x and y axes. It can be calculated using the formula:
Shear strain = (Change in length / Original length) / 2

In this case, the change in length is already known as 0.19(10^-3) in., and the original length is 0.5 in.
Let's calculate the shear strain:
Shear strain = (0.19(10^-3) in. / 0.5 in.) / 2

Please note that the above calculations are based on the information provided in the question. It's important to double-check the values and formulas used, as well as units, to ensure accuracy.

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Related Questions

a scuba tank is being designed for an internal pressure of 2640 psi with a factor of safety of 2.0 with respect to yielding. the yield stress of the steel is 65,000 psi in tension and 32,000 psi in shear.

Answers

The scuba tank should be designed to withstand an internal pressure of 2640 psi with a factor of safety of 2.0, considering the yield stress of the steel, which is 65,000 psi in tension and 32,000 psi in shear.

To design a scuba tank that can safely withstand the specified internal pressure, we need to consider the factor of safety and the yield stress of the steel. The factor of safety is a measure of how much stronger the tank is compared to the expected load, and it ensures that the tank can handle unexpected variations or stress concentrations without failure.

Given a factor of safety of 2.0, we can calculate the maximum stress that the tank should experience without yielding. To do this, we divide the yield stress by the factor of safety:

Maximum stress = Yield stress / Factor of safety

For tension, the maximum stress would be 65,000 psi / 2.0 = 32,500 psi, and for shear, it would be 32,000 psi / 2.0 = 16,000 psi.

Therefore, the scuba tank should be designed to withstand a maximum internal pressure of 32,500 psi in tension and 16,000 psi in shear, ensuring that the stresses exerted on the steel do not exceed the yield limits. This design will provide a factor of safety of 2.0, meaning that the tank can handle twice the specified internal pressure before the material starts to yield.

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