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Problem on strain energy for gradually applied load.

A steel specimen 150 mm^2 in X-section stretches 0.05 mm over a 50 mm gauge length under an axial load of 30 kN. Calculate the strain energy stored in the specimen at this stage. If the load at the elastic limit for the specimen is 50 kN, calculate the elongation at the elastic limit and proof resilience.

2 Answers
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Data:

A=150mm2

δl=0.05mm

l=50mm

P=30KN

δl=plE and stress p=PA=30103150

p=200N/mm2

0.05=20050E

E=2105N/mm2

Strain energy=u=p22EAl=20022210515050

u=750Nmm

For 30KN δl=0.05mm

For 50KN, δl=?

δl=0.053050

δl=0.0833mm

Strain energy at elastic limit=proof resilience=

=5010315021505022105

=2083.33Nmm

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