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Unformatted text preview: 07Ch07.qxd 9/27/08 622 1:24 PM Page 622 CHAPTER 7 Analysis of Stress and Strain Plane Strain y
sy When solving the problems for Section 7.7, consider only the in-plane strains (the
strains in the xy plane) unless stated otherwise. Use the transformation equations
of plane strain except when Mohr’s circle is specified (Problems 7.7-23 through
7.7-28). sx h Problem 7.7-1 A thin rectangular plate in biaxial stress is subjected to b stresses sx and sy, as shown in part (a) of the figure on the next page. The
width and height of the plate are b 8.0 in. and h 4.0 in., respectively.
Measurements show that the normal strains in the x and y directions are
Px 195 * 10 6 and Py
125 * 10 6, respectively.
With reference to part (b) of the figure, which shows a two-dimensional
view of the plate, determine the following quantities: (a) the increase ¢ d in the
length of diagonal Od; (b) the change ¢ f in the angle f between diagonal Od
and the x axis; and (c) the change ¢ c in the angle c between diagonal Od and
the y axis. x
O x b
(b) Probs. 7.7-1 and 7.7-2 Solution 7.7-1 Plate in biaxial stress
¢d f 26.57°, âx1 âx1L d 6 130.98 * 10 0.00117 in. ; (b) CHANGE IN ANGLE f
Eq. (7-68): a
Ld h 8.0 in.
125 * 10 1b 2 + h2 h
b âx 4.0 in. 6 gxy 195 * 10 6 0 ây âx
+ 2 6 128 * 10 6 rad (decrease) 2 cos 2u + ¢c
2 sin 2u rad ; Angle c increases the same amount that f
decreases. 8.944 in. âx + ây 128.0 * 10 (c) CHANGE IN ANGLE c (a) INCREASE IN LENGTH OF DIAGONAL
âx1 26.57°: a gxy sin2u ây) sin u cos u Minus sign means line Od rotates clockwise
(angle f decreases).
¢f 26.57° f (âx 128 * 10 6 rad (increase) ; ...
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