GATE CE 2017 Set 2 — Question 43
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Structural Engineering → Determinate Structures & Energy Methods → Strain Energy
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Question
A long, axially loaded mild steel rod of diameter exhibits the load-displacement (-) behavior as shown in the figure.
Assume the yield stress of steel as . The complementary strain energy (in N-mm) stored in the bar up to its linear elastic behavior will be ____________
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Solution
1.Calculate the cross-sectional area of the rod ():
The diameter ..
2.Calculate the yield load ():
Given yield stress ..
(Note: The graph label '(kN)' appears to be a typo for '(N)' given the axis values and material properties).
3.Determine the displacement at yield ():
From the given graph, the linear elastic behavior ends at a displacement .Verification: , which is standard for steel.
4.Calculate the complementary strain energy ():
For linear elastic behavior, the complementary strain energy is equal to the strain energy, which is the area under the - curve..Rounding to the nearest integer, we get .
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