Chapter 10
2
1 y x y x 2
10.1 a. xy
3 2 2
x = 162 kN/m2; y = 128 kN/m2; xy = +32 kN/m2
2
1 128 162 128 162
(32) 2
3 2 2
1= 181.23 kN/m2; 3 = 108.76 kN/m2
y x y x
b. n cos 2 xy sin 2 ; 35
2 2
128 162 128 162
n cos[(2)(35)] 32 sin[( 2)(35)] 169.25 kN/m 2
2 2
y x
n sin 2 xy cos 2
2
128 162
sin[( 2)(35)] 32 cos[(2)(35)] -26.92 kN/m 2
2
10.2 a. x = 72 kN/m2; y = 121 kN/m2; xy = 39 kN/m2; = 147º
2
1 121 72 121 72
(39) 2
3 2 2
1= 142.55 kN/m2; 3 = 50.45 kN/m2
121 72 121 72
b. n cos[(2)(147)] 39 sin[( 2)(147)] 131.33 kN/m 2
2 2
69
2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, 121 72
n sin[( 2)(147)] (39) cos[(2)(147)] 38.24 kN/m 2
2
10.3 a. The Mohr’s circle is shown below.
550 350
OO1 450 lb/ft 2 ; O1O2 550 450 100 lb/ft 2
2
2
350 550
O1 B ( 175) 2 201.5 lb/ft 2
2
3 OS 450 201.5 248.4 lb/ft 2 ( )
1 ON 450 201.5 651.5 lb/ft 2 ( )
1 175
BO1O2 tan 60.25
100
b. n OO1 O1 D cos(29.75) 450 201.5 cos(29.75) 275.1 lb/ft 2 ( )
n O1 D sin(29.75) 99.98 lb/ft 2 ( )
70
2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
2
1 y x y x 2
10.1 a. xy
3 2 2
x = 162 kN/m2; y = 128 kN/m2; xy = +32 kN/m2
2
1 128 162 128 162
(32) 2
3 2 2
1= 181.23 kN/m2; 3 = 108.76 kN/m2
y x y x
b. n cos 2 xy sin 2 ; 35
2 2
128 162 128 162
n cos[(2)(35)] 32 sin[( 2)(35)] 169.25 kN/m 2
2 2
y x
n sin 2 xy cos 2
2
128 162
sin[( 2)(35)] 32 cos[(2)(35)] -26.92 kN/m 2
2
10.2 a. x = 72 kN/m2; y = 121 kN/m2; xy = 39 kN/m2; = 147º
2
1 121 72 121 72
(39) 2
3 2 2
1= 142.55 kN/m2; 3 = 50.45 kN/m2
121 72 121 72
b. n cos[(2)(147)] 39 sin[( 2)(147)] 131.33 kN/m 2
2 2
69
2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, 121 72
n sin[( 2)(147)] (39) cos[(2)(147)] 38.24 kN/m 2
2
10.3 a. The Mohr’s circle is shown below.
550 350
OO1 450 lb/ft 2 ; O1O2 550 450 100 lb/ft 2
2
2
350 550
O1 B ( 175) 2 201.5 lb/ft 2
2
3 OS 450 201.5 248.4 lb/ft 2 ( )
1 ON 450 201.5 651.5 lb/ft 2 ( )
1 175
BO1O2 tan 60.25
100
b. n OO1 O1 D cos(29.75) 450 201.5 cos(29.75) 275.1 lb/ft 2 ( )
n O1 D sin(29.75) 99.98 lb/ft 2 ( )
70
2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
