Chapter 1, Problem 1.5.5P

### Steel Design (Activate Learning wi...

6th Edition
Segui + 1 other
ISBN: 9781337094740

Chapter
Section

### Steel Design (Activate Learning wi...

6th Edition
Segui + 1 other
ISBN: 9781337094740
Textbook Problem

# The results of a tensile test are shown in Table 1.5.2. The test was performed on a metal specimen with a circular cross section. The diameter was 3 8 inch and the gage length (The length over which the elongation is measured) was 2 inches.a. Use the data in Table 1.5.2 to produce a table of stress and strain values.b. Plot the stress-strain data and draw a best-fit curve.c. Compute the, modulus of elasticity from the initial slope of the curve.d. Estimate the yield stress.

To determine

(a)

The stress and strain values.

Explanation

Given:

The diameter of metal specimen is 38inch.

The gage length is 2inches.

Concept Used:

Write the equation of tensile stress.

f=PA      ...... (I)

Here, tensile stress is f, load is P and the cross-sectional area is A.

Write the equation to calculate strain.

ε=eL      ...... (II)

Here, the elongation is e and the gage length is L and the strain is ε.

Calculation:

Calculate the cross-sectional area.

A=π4×d2      ...... (III).

Here, the diameter of metal specimen is d.

Substitute 38inch for d in Equation (III).

A=π4×(0.375inch)2=0.4417inch24=0.1104inch2

Calculate the stress and strain values by substituting corresponding elongation and load values in the Equation (I) and Equation (II).

The following table shows the stress and strain values.

 Load (lb) Elongation (×10−6 in) Stress f=PA Stress (lb/in2) Strain ε=eL Strain (×10−6) 0 0 f=00.1104 0 ε=02 0 550 350 f=5500.1104 452.898 ε=3502 175 1100 700 f=11000.1104 996.376 ε=7002 350 1700 900 f=17000
To determine

(b)

A plot of the stress-strain curve.

To determine

(c)

The modulus of elasticity from the initial slope of curve.

To determine

(d)

The yield stress in the metal specimen.

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