재료역학 2과 6번째

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Problem 2.7-9 A slightly tapered bar ABof rectangular cross section
and length Lis acted upon by a force P(see figure). The width of the
bar varies uniformly from b2 at end Ato b1 at end B. The thickness t
is constant.
(a) Determine the strain energy U of the bar.
(b) Determine the elongation . of the bar by equating the strain
energy to the work done by the force P.
Solution 2.7-9Tapered bar of rectangular cross section
144 CHAPTER 2 Axially Loaded Numbers
b2
b1
L
A B
P
(a) STRAIN ENERGY OF THE BAR
Apply this integration formula to Eq. (1):
From Appendix C: .
<중략>
Problem 2.7-10 A compressive load Pis 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 mm
2, modulus of elasticity
E . 45 GPa, and the gap s . 1.0 mm.
(a) Calculate the load P
1 required to close the gap.
(b) Calculate the downward displacement . 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 notequal to P./2.
(Hint:Draw a load-displacement diagram.)

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