Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

(c) φ E/C = 0.1408 rad
(d) T A = 232 N · m, 34.3 Hz
P6.39 (a) T max = 84.7 kip · in.
(b) T 1 = 45.4 kip · in., T 2 = 39.3 kip · in.
(c) φ = 0.0769 rad
P6.41 (a) τ 1 = 4,230 psi
(b)τ 2 = 5,090 psi
(c) τ 3 = 9,780 psi
(d) φ B = 0.0446 rad
(e) φ C = −0.01043 rad
P6.43 (a) T allow = 73.8 lb · ft
(b) T 1 = 44.7 lb · ft, T 2 = 29.1 lb · ft
(c) φ B = 0.1103 rad
P6.45 (a) T 0,allow = 14.02 kip · in.
(b) τ 1 = 7.27 ksi
(c) τ 2 = 1.082 ksi
P6.47 (a) τ 1 = 36.0 MPa
(b) τ 3 = 23.3 MPa
(c) φ E = −0.0208 rad
(d) φ C = 0.0776 rad
P6.49 τ = 40.4 MPa
P6.51 r min = 0.25 in.
P6.53 T max = 310 N · m
P6.55 (a) T max = 11.23 kip · in.
(b) φ = 0.0988 rad
P6.57 (a) τ 1 = 103.9 MPa, τ 2 = 68.0 MPa, τ 3 = 85.8 MPa
(b) φ 1 = 0.223 rad, φ 2 = 0.0907 rad, φ 3 = 0.1399 rad
P6.59 t min = 0.0726 in.
P6.61 τ A = 41.8 MPa, τ B = 83.7 MPa, τ C = 50.2 MPa
w0 P7.7 (a) A
6( a b) [ a 2 3ab 3 b 2
y =
+ +
+
]
0 ≤ x < a:
wx 0 wx
V A
2 0
= y − , M = Ayx
−
3
2a
6a
a ≤ x < a + b:
wa 0
V = Ay
− − w0
( x − a),
2
w0 wa a
M A x x a x
2 ( ) 2 0 ⎛ 2 ⎞
= y − − − ⎜ − ⎟
2 ⎝ 3 ⎠
P7.9
13.50 kips
Units: kips
Units: kip·ft
P7.11
y
3 ft
13.50 13.50
40.50
@x=6.00 ft
60.75
4.5 kips/ft
9 ft 3 ft
40.50 kips
13.50
–27.00
–20.25
x
Chapter 7
P7.1 (a) V = w0
( L − x);
w0 M =− L + x + wLx
2 ( 2 2
) 0
wa
P7.3 (a) x a V w x M x
2
0 ≤ < : =− a , =−
2
a ≤ x < a + b: V = −( wa − wb) a − wx b ,
wb
( w w ) a
M x
2
( w a w b)
ax
a − b
=− − − +
2
2
P7.5 (a) 0 ≤ x < a: V =− P,
M =−Px
a ≤ x < a + b: V = − P, M = MB
− Px
834
2