Chapter 1, Problem 1.5.1P

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6th Edition

Segui + 1 other

ISBN: 9781337094740

Textbook Problem

A tensile test was performed on a metal specimen with a circular cross section. The diameter was measured to be 0.550 inch. Two marks were made along the length of the specimen and were measured to be 2.030 inches apart. This distance is defined as the *gage length*, and all length measurements are made between the two marks. The specimen was loaded to failure. Fracture occurred at a load of 28,500 pounds. The specimen was then reassembled, and the diameter and gage length were measured to be 0.430 inch and 2.300 inches. Determine the

a. Ultimate tensile stress in ksi.

b. Elongation as a percentage.

c. Reduction in cross-sectional area as a percentage.

To determine

**(a)**

The ultimate tensile stress of metal specimen.

Answer

Explanation

**Given:**

The diameter of metal specimen is

The load at facture is

**Concept Used:**

Write the equation to calculate the ultimate tensile stress.

Here, ultimate tensile stress is

**Calculation:**

Calculate the cross-sectional area of specimen.

Here, diameter of the specimen is

Substitute

Calculate the ultimate tensile stress.

Substitute

**Conclusion:**

Thus, the ultimate tensile stress on the metal specimen is

To determine

**(b)**

The elongation of the metal specimen.

Answer

Explanation

**Given:**

The original gage length is

The change in gage length is

**Concept Used:**

Write the equation to calculate the elongation.

Here, the elongation is

**Calculation:**

Calculate the elongation of the metal specimen.

Substitute

**Conclusion:**

Thus, the elongation of the metal specimen is

To determine

**(c)**

The reduction in the cross-sectional area of the metal specimen.

Answer

Explanation

**Given:**

The original diameter of metal specimen is

The diameter after fracture load is

**Concept Used:**

Write the equation to calculate reduction in cross-sectional area.

Here, the reduction in cross-sectional area is

**Calculation:**

Calculate the cross-sectional area after fracture load.

Substitute

Calculate the reduction in the cross-sectional area.

Substitute

**Conclusion:**

Thus, the reduction in the cross-sectional area is

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