Question
Asked Mar 11, 2020
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A steel specimen is tested in tension. The specimen is 1.0 in. wide by 0.25 in. thick in the test region. By monitoring the load dial of the testing machine, it was found that the specimen yielded at a load of 12.5 kips and fractured at 17.5 kips.
a. Determine the tensile stresses at yield and at fracture.
b. Estimate how much increase in length would occur at 60% of the yield stress in a 2-in. gauge length.

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Expert Answer

Step 1

Given:

Width of specimen = 1 in

Thickness of specimen = 0.25 in

Yield load = 12.5 kip

Fracture load = 17.5 kip

 

Also,

Modulus of Elasticity of steel, E = 29 x 103 ksi

Step 2

a)

The formula for tensile stress is given by,

Civil Engineering homework question answer, step 2, image 1

Where,

P = load

A = area of cross section

 

The tensile stress at yield point is calculated as,

Civil Engineering homework question answer, step 2, image 2

The tensile stress at fracture point is calculated as,

Civil Engineering homework question answer, step 2, image 3

Step 3

b)

Gauge length , l = 2 in

60% of yield stress is calculated as,

Civil Engineering homework question answer, step 3, image 1

The formula for modulus of elasticity is given by,

Civil Engineering homework question answer, step 3, image 2

Civil Engineering homework question answer, step 3, image 3

The formula for longitudinal strain is given by,

Civil Engineering homework question answer, step 3, image 4

Civil Engineering homework question answer, step 3, image 5

 

The longitudinal strain is calculated as,

Civil Engineering homework question answer, step 3, image 6

 

The increase in length is calculated as,

Civil Engineering homework question answer, step 3, image 7

...

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