Page 603 - Rock Mechanics For Underground Mining

Answers to problems

Chapter 2

1 (a) 200 kN, with clockwise moment.
(b) xx =−15 MPa, yy = 16 MPa, xy = 10 MPa.
(c) ll = 1.41 MPa, mm =−0.41 MPa, lm = 18.42 MPa.
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(d) 1 = 8.95 MPa, 2 =−17.95 MPa,
= 73.6 .
−2
−2
(e)
= 0 ; t x = 15 MN m , t y =−10 MN m .
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−2
−2

= 60 ; t x =−1.16 MN m , t y =−18.86 MN m , R = 18.90 MPa
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−2
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= 90 ; t x =−10 MN m , t y =−16 MN m −2
2 (a) xx = 7.825, yy = 6.308, zz = 7.866;
xy = 1.422, yz = 0.012, zx =−1.857.
(b) mm = 9.824; nl = 0.079.
(c) I 1 = 22.0, I 2 = 155.0, I 3 = 350.0;.
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1 = 10.0( 1 = 43.4 , 1 = 73.9 , 1 = 129.05 );
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2 = 7.0( 2 = 108.5 , 2 = 131.8 , 2 = 132.4 );
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3 = 5.0( 3 = 51.8 , 3 = 132.4 , 3 = 66.2 ).
2
1 y 2x y
4 (a) ε xx = − + .
2G r 2 r 4
1 y 2y 3
ε yy = (1 − 4 ) + ,
2G r 2 r 4
2
1 x 4xy
xy = 2(1 − 2 ) + .
2G r 2 r 4
2
y 2x y
(b) xx =−(1 − 2 ) + .
r 2 r 4
y 2y 3
yy = (1 − 2 ) + ,
r 2 r 4
x 2xy 2
xy = (1 − 2 ) + .
r 2 r 4
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5 (a) 1 = 25.0, 2 = 7.1, 1 = 58 , 2 = 148 .
n = 21.0, = 7.2.
(b) ll = 20.9, lm = 7.46.
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(c) 1 = 24.94, 2 = 7.10, 1 = 58.3 , 2 = 148.3 .
Chapter 3
1 (a) ¯ x 0A = 0.369 m; ¯ x 0B = 0.274 m.
(b) ¯ x = 0.288 m.
(c) RQD = 95.2.
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