A compressive load P is transmitted through a rigid plate to three magnesium-alloy bars that are identical except that initially the middle bar is slightly shorter than the other bars (see figure). The dimensions and properties of the assembly are as follows: length L = 1.0 m, cross-sectional area of each bar A = 3000 mm2, modulus of elasticity E = 45 GPa, and the gap s = 1.0 mm.
(a) Calculate the load P1 required to close the gap.
(b) Calculate the downward displacement δ of the rigid plate when P = 400 kN.
(c) Calculate the total strain energy U of the three bars when P = 400 kN.
(d) Explain why the strain energy U is not equal to Pδ/2.

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