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A test specimen in a tensile test has a gage length of 2.0 in and an area = 0.5in^2. During the test the specimen yields under a load of 32,000 lb. The corresponding gage length = 2.0083 in. This is the 0.2% yield point. The maximum load of 60,000 lb is reached at a gage length = 2.6 in. Determine a) yield strength, b) madulus of elasticity, and c) ten

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Answer:

yield strength is 64000 lb/ in²

modulus of elasticity is 29.76 ×[tex]10^{6}[/tex] lb/in²

Explanation:

given data

length L = 2 in

area A = 0.5 in²

load = 32000 lb

gage length L1 = 2.0083 in

yield point = 0.2%

maximum load = 60000 lb

to find out

yield strength and modulus of elasticity

solution

we apply here yield strength that is express as

yield strength = [tex]\frac{load}{area}[/tex]  ...........1

yield strength =  [tex]\frac{32000}{0.5}[/tex]

yield strength = 64000 lb/ in²

and

modulus of elasticity  is calculated as

modulus of elasticity =  [tex]\frac{yield strength}{strain}[/tex]    ..........2

here strain = [tex]\frac{L1 - L}{L}[/tex]  

strain = [tex]\frac{2.0083 - 2}{2}[/tex]  

strain = 0.00415

so new strain after offset is here 0.00415 - 0.002

new strain = 0.00215

so from equation 2

modulus of elasticity =  [tex]\frac{yield strength}{strain}[/tex]  

modulus of elasticity =  [tex]\frac{64000}{0.00215}[/tex]  

modulus of elasticity is 29.76 ×[tex]10^{6}[/tex] lb/in²

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