Mecanica de Materiales - 7ma.Ed_James

1010 Respuestas a los problemas
9.5.19 d C 0.120 in
9.5.20 q 16cEI/7L 4
9.5.21 d h Pcb 2 /2EI, d v Pc 2 (c 3b)/3EI
9.5.22 d PL 2 (2L 3a)/3EI
9.5.23 (a) b/L 0.4030; (b) d C 0.002870qL 4 /EI
9.5.24 a 22.5°, 112.5°, 67.5°, o 157.5°
9.6.4 u B 7qL 3 /162EI, d B 23qL 4 /648EI
9.6.5 d B 0.443 in, d C 0.137 in
9.6.6 d B 11.8 mm, d C 4.10 mm
9.6.8 P 64 kN
9.6.9 u A M 0 L/6EI, u B M 0 L/3EI,
d M 0 L 2 /16EI
9.6.10 u A Pa(L a)(L 2a)/6LEI,
d 1 Pa 2 (L 2a) 2 /6LEI, d 2 0
9.6.11 u A M 0 L/6EI, u B 0, d M 0 L 2 /27EI (hacia abajo)
9.7.1 (a) d B PL 3 (1 7I 1 /I 2 )/24EI 1 ;
(b) r (1 7I 1 /I 2 )/8
9.7.2 (a) d B qL 4 (1 15I 1 /I 2 )/128EI 1 ;
(b) r (1 15I 1 /I 2 )/16
9.7.3 (a) d c = 0.31 in (hacia arriba)
(b) d c = 0.75 in (hacia abajo)
9.7.4 v qx(21L 3 64Lx 2 32x 3 )/768EI para
0 x L/4;
v q(13L 4 256L 3 x 512Lx 3
256x 4 )/12,288EI para L/4 x L/2;
u A 7qL 3 /256EI; d máx 31qL 4 /4096EI
9.7.5 u A 8PL 2 /243EI, d B 8PL 3 /729EI,
d máx 0.01363PL 3 /EI
9.7.6 v 2Px(19L 2 27x 2 )/729EI para 0 x L/3;
v P(13L 3 175L 2 x 243Lx 2 81x 3 )/1458EI
para L/3 x L;
u A 38PL 2 /729EI, u C 34PL 2 /729EI,
d B 32PL 3 /2187EI
9.7.7 v
3
PL
L 3x 1
ln
L x
EI A 2(L x) 8L
8 2L
;
d A
3
PL
(8 ln 2
8EIA
5)
9.7.8 v
PL 4L(
2L 3x) 2x 7
2 ;
24EI A ( L x) L
d A
PL 24EI A
9.7.9 v
3
8PL
L 2x 1
ln 2L x
EIA
2L x 9L
9 3L
;
3
8PL
d A ln 3 7
EI
2 18
A
9.7.10
9.7.11
vx
d A
vx
d B
9.7.12 (a) v
v
( )
( )
3
19,683PL
⎛ 81L
⎜
2ln
2000EI
A
81L
40x
⎛
⎛ 81 40x
⎞ 6440x 3361 ⎞
⎜ ⎟
⎟
121 121L
14641L 14641
⎛
3
19,683PL
⎛
⎛11⎞⎞
⎜ 2820 14,641 ln ⎜ ⎟⎟
7,320,500
⎛
⎛
EI
A
9
3
19,683PL
⎛ 81L
⎛ 40x
⎞
⎜
2ln
⎜1
⎟
⎛
2000 ⎛ EI
A
81L
40x
81L
6440x ⎞
1⎟
14,641L
19,683
7,320,500
3
2
qL
8Lx
1
16EI A (L x) 3 para 0 x L,
4
qL
(9L 2 14Lx x 2 )x x
ln 1
2EI
8L(L x) 2
L
A
3
PL
EI
⎛
A
⎛11⎞⎞
2820 14,641 ln ⎜ ⎟⎟
9
para 0 x L;
3
qL
qL 4 (3 4ln2)
(b) u A , d C
16EI A 8EI A
9.8.1 U 4bhL s 2 máx/45E
9.8.2 (a) y (b) U P 2 L 3 /96EI; (c) d PL 3 /48EI
9.8.3 (a) y (b) U
2 5
qL
15EI
9.8.4 (a) U 32EId 2 /L 3 ; (b) U p 4 EId 2 /4L 3
9.8.5 (a) U P 2 a 2 (L a)/6EI;
(b) d C Pa 2 (L a)/3EI;
(c) U 241 in-lb, d C 0.133 in
9.8.6 U
L
Lq qL M
15 360 EI (
4 2 2
17 280 2560M
9.8.7 d B 2PL 3 /3EI 8 2PL/EA
9.9.2 d D Pa 2 b 2 /3LEI
9.9.3 d C Pa 2 (L a)/3EI
9.9.6 d C L 3 (2P 1 5P 2 )/48EI,
d B L 3 (5P 1 16P 2 )/48EI
9.9.7 u A 7qL 3 /48EI
9.9.8 d C Pb 2 (b 3h)/3EI, u C Pb(b 2h)/2EI
9.9.9 d C 31qL 4 /4096EI
9.9.10 u A M A (L 3a)/3EI, d A M A a(2L 3a)/6EI
9.9.11 d C Pa 2 (L a)/3EI P(L a) 2 /kL 2
9.9.12 d D 37qL 4 /6144EI (hacia arriba)
9.10.1 s máx s est [1 (1 2h/d est ) 1/2 ]
9.10.2 s máx 18WEh/AL
⎛
⎛
⎜
⎛
⎛
⎛
⎛
⎛
⎛
⎛
⎛
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