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Civil EngineeringQ&A LibraryA tensile load of 50,000 lb is applied to a metal bar with a 0.6 in. * 0.6 in.cross section and a gauge length of 2 in. Under this load, the bar elastically deforms so that the gauge length increases to 2.007 in. and the cross section decreases to 0.599 in. * 0.599 in. Determine the modulus of elasticity and Poisson’s ratio for this metal.Question

Asked Mar 9, 2020

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A tensile load of 50,000 lb is applied to a metal bar with a 0.6 in. * 0.6 in.cross section and a gauge length of 2 in. Under this load, the bar elastically deforms so that the gauge length increases to 2.007 in. and the cross section decreases to 0.599 in. * 0.599 in. Determine the modulus of elasticity and Poisson’s ratio for this metal.

Step 1

Given:

The tensile load is 50,000 lb.

The area of the metal bar is 0.6 in x 0.6 in.

The gauge length is 2 in.

The increase in the gauge length is 2.007 in.

The decrease in area is 0.599 in x 0.599 in.

Step 2

The formula to calculate the modulus of elasticity is,

The formula to calculate the stress is,

The formula to calculate the strain is,

Here, P is the load, A_{1} is the initial area of the bar, l_{1} is the initial length, and l_{2} is the final length.

The formula to calculate the Poisson’s ratio is,

Step 3

Calculate the stress.

Calculate the strain.

Calculate the modulus of elasticity.

...

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