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Unformatted text preview: 07Ch07.qxd 9/27/08 612 1:20 PM Page 612 CHAPTER 7 Analysis of Stress and Strain STRAIN ENERGY
Eq. (7-50): u U
(s2 + s2
2E x (0.03234 MPa)(125 * 103 mm3) uV0 ; 4.04 J 2 sxsy) 0.03234 MPa 0.1)
3.0 * 106 psi,
is compressed in biaxial stress by means of a framework that is loaded as
shown in the figure.
Assuming that each load F equals 20 k, determine the change ¢ V in
the volume of the cube and the strain energy U stored in the cube. Problem 7.5-9 A 4.0-inch cube of concrete (E F F Solution 7.5-9 Biaxial stress – concrete cube
CHANGE IN VOLUME b
E Eq. (7-47): e 4 in.
6 3.0 * 10 psi F 12 ¢V sy eV0 (4 in.)3 0.0009429 64 in.3 0.0603 in.3 ; (Decrease in volume) Eq. (7-50): u P
(s2 + s2
2E x 2 sxsy) 0.9377 psi 28.28 kips
sx b3 (sx + sy) STRAIN ENERGY Joint A: P 20 kips 2
E V0 0.1
F 1 U uV0 ; 60.0 in.-lb 1768 psi Py Problem 7.5-10 A square plate of width b and thickness t is loaded by
normal forces Px and Py, and by shear forces V, as shown in the figure.
These forces produce uniformly distributed stresses acting on the side
faces of the place.
Calculate the change V in the volume of the plate and the strain
energy U stored in the plate if the dimensions are b 600 mm and
t 40 mm, the plate is made of magnesium with E 45 GPa and
v 0.35, and the forces are Px 480 kN, Py 180 kN, and
V 120 kN. t V
V V bO
b x V
Py Probs. 7.5-10 and 7.5-11 Px ...
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