Análisis Estructural, 8va Edición - R. C. Hibbeler-FREELIBROS.ORG

S o l u c io n e s pa r c ia l e s y r e s pu e st a s a l o s pr o b l e m a s fu n d a m e n t a l e s 629

F 2 -5 . I + ? M a = O. F s c ( i) ( 4 ) + F K (ÍX 3 ) - 3 0 0 (2 ) = 0 P K = 125 Ib

X YF, = G A , - 125(1) = 0 = 100 Ib Resp.
Resp.
+ T 2 F , = 0; A , + 1 2 5 (|) - 300 = 0 A , = 225 Ib Resp.
Resp.
B , = C , = 1 2 5 (|) = 100 Ib
Resp.
B , = C , = 125( ^) = 7 5 .0 Ib Resp.
Resp.
F 2 -6 . l+ Z M c = G 6 ( 2 ) + 2 ( 2 ) - N a( 4 ) = 0 iV ^ = 4 .0 0 k N
X Z P M= G C , - 2 = 0 C , = 200 kN
+ Í 2 F , = 0;
C . + 4 .0 0 - 6 = 0 C , = 2 0 0 k N

*2 -7 .

8kN 8 kN

E le m e n to A B
Í + S M a = G B , ( 4 ) - B y( 3 ) - 3 ( 5 ) ( 2 . 5 ) = 0

H c m c n to BCD

Í+ 'L M d = G 8 (2 ) + 8 (4 ) - B ,(4 ) - B ,(6 ) = 0

B , = 10.25 k N f l 4 = 1.16 7 k N = 1.17 k N Resp.

E le m e n to A B - A t + 3 ( 5 ) ( j) - 10.25 = 0 A , = 1 .7 5 k N /te sp .
XZF, = G - ( 3 ) ( 5 ) ( ^ ) - 1 .1 6 7 = 0 A r = 10 .1 67 k N = 1 0 .2 k N Resp.
+ t 2 f r = 0;
Resp.
E le m e n to B C D 10.25 - D m = 0 D , = 10.25 k N Resp.
X*F, = G D , + 1.167 - 8 - 8 = 0 Dy = 14.833 k N = 14.8 k N
+ T 2 F , = 0;

www.FreeLibros.me

630 S o l u c io n e s pa r c ia les y r e s pu e st a s a l o s p r o b l e m a s f u n d a m e n t a l e s

F 2 -8 .

i

6m

-o,

M0
D-

Elemento A B 5 ,( 6 ) - 4(3) = 0 B , = ZOO kN Resp.
4(3) - -4,(6) = 0 A , = ZOO kN Resp.
1 + 2 *4 -0 ;
\,+ Z M h = 0; ZOO - C , = 0 C , = ZOO kN Resp.
6(2) + 6(4) - 5,(6) = 0 5 , = 6.00 kN Resp.
Elemento B C Resp.
C ,(6) - 6(2) - 6(4) = 0 C , = 600 kN
X XF, = o.
A y - 6 0 0 = 0 A y = 6.00 kN Resp.
l +XA#c = 0;
ZOO - D x = 0 D , = ZOO kN Resp.
l+ X A /« = 0; Dy - 600 = 0 Dy = 600 kN Resp.
M d ~ Z 0 0 ( 6 ) = 0 M d - 12.0 k N • m Resp.
Elemento A B

+ tX 5 , = 0;

Elemento CD

- Í 2 F , = 0.
+ ÍX F , = 0;
l+ X M o = 0 ;

www.FreeLibros.me

S o l u c io n e s pa r c ia l e s y r e s pu e st a s a l o s pr o b l e m a s fu n d a m e n t a l e s 631

F 2 -9 .

0 .5 (6 ) k

E le m e n to A fí B ,(6) - 0.5(6)(3) = 0 B , = 1.50k Resp.
i+ 2 M A = 0; 0.5(6)(3) - -4,(6) = 0 A , = 1.50 k Resp.
= 0;
Resp.
E le m e n to B C 2(8)(4) - By(8) - 0 B y = 8.00k Resp.
Cy{S) - 2(8)(4) = 0 C y = 8.00k Resp.
i+2Mc = 0;
[t+2Mfí = 0\ 1-50 - C , = 0 C, = 1.50k Resp.

2Fm= Ot Resp.
Resp.
E le m e n to A B A y — 800 = 0 A y = 8.00k Resp.

+t 2Fy = 0;

E le m e n to C D 1.50 - D , = 0 D , = 1.50k
D y - 8.00 = 0 D y = 8.00k
0;X 2 . F , = M d - 1.50(4) = 0 MD = 6.00 k -pie
t 0;+ 2 F y =
www.FreeLibros.me
i,+ 2 M D = 0,

632 S o l u c io n e s par ciales y respuestas a lo s p r o b l e m a s f u n d a m e n t a l e s
F 2-10.

E le m e n to B C C , ( 6 ) - 8 ( 2 ) - 8 ( 4 ) - 6 ( 6 ) = 0 C y = 1 4 .0 k N Resp.
|,+ 2 M b = 0 ; 8 ( 2 ) + 8 ( 4 ) + 6 ( 6 ) - B y{6 ) = 0 B , = 1 4 .0 k N Resp.
1 + 2 M c = 0;

E le m e n to A B B, =0 Resp.
= 0; A, =0 Resp.
A y - 14 .0 = 0 A , = 14 .0 k N Resp.
X * F , = O.
+ U F , = 0;

E le m e n to B C C ,= 0 Resp.
X Z E , = O.
D , - 1 .5 (6 ) = 0 D , = 9.0 0 k N Resp.
E le m e n to C D
- Í Z F , = 0; D y - 1 4 .0 = 0 D y = 14.0 k N Resp.
+ U F f = 0;
l+ Z A f 0 = 0; 1.5(6)(3) - M o = 0 M o = 27.0kN • m Resp.

www.FreeLibros.me

S o l u c io n e s pa r c ia l e s y r e s pu e st a s a l o s pr o b l e m a s fu n d a m e n t a l e s 633

F3-I. Ju n ta C Resp.
Resp.
'LF, = 0 ; 4 0 - Fcb{Í) = 0 FCB= 5 0 .0 k N ( C )
5 0 . 0 ( 3 ) - FCA = 0
40 + 1 = 0 ; F Ca = 3 0 .0 k N ( T )

Jum a B X Z F , = 0; 5 0 .0 (3 ) - F ,,* = 0 F BA = 4 0 . 0 k N ( T ) Resp.
VCB = 5 0 .0 k N + T2Fw = 0; JV« - 5 0 .0 (3 ) = 0 = 3 0 .0 k N

N*

F3-2. J u n ta F

£ + TS Fy = 0; F acsen 45° - 6 = 0 = 8 .4 8 5 k N ( T ) = 8 4 9 k N ( T ) Resp.
± > 2 F , = 0;
fm F fl„ - 8 . 4 8 5 e o s 4 5 ° = 0 F BA = 6 . 0 0 k N ( C ) Resp.

R
6kN

J u n ta C Í 2 F , = 0; 8.48 5 e o s 4 5 ° - F c o = 0 F Cd = 6 .0 0 k N ( T ) Resp.
+ Í2 F ,, = 0; - 8485 sen 45° = 0 F ca = 6 .0 0 k N (C ) Resp.
JFfO C
\|4 5 "
8.485 k N

13-3. J u n ta C

Í Z F , = 0; 10 - F c „c o s 4 5 ° = 0 F Cn = 1 4 .1 4 k N ( T ) = 14.1 k N ( T ) Resp.
+ U F y = 0; F CB - 14 .1 4 s e n 4 5 ° = 0
C 10 kN F cb = 10 .0 k N ( C ) Resp.
4 y /3 ■

Fco Fc»

Junta D

14J4kN V í F * = O. 1 4 .1 4 - F D a = 0 F D,* = 1 4 .1 4 k N ( T ) = 14.1 k N ( T ) Resp.
\ü / \ + 2 / y = 0; F /ib ~ 0 Resp.

www.FreeLibros.me

634 S o l u c io n e s pa r c ia les y r e s pu e st a s a l o s p r o b l e m a s f u n d a m e n t a l e s

J u n ta fí 10 kN X 2 F , = 0; Faa = 0 Resp.
- + fZ F , = 0; N h - 1 0 .0 = 0
R / V „ = 1 0 .0 kN
1

,

F 3 -4 . Ju n ta D •ÍEF, = 0; F o c - 2 = 0 F ^ = 200k(T) Resp.
2 k n foc +ÍSF, = 0; F DA = 0 Resp.

F #>x

Ju n ta C

X Z F , = 0; ^ Ca ( | ) “ 2 = 0 F ca = 3 .3 3 3 k ( C ) = 3 .3 3 k ( C ) Resp.
+ 1 l F r = 0; ^ c a = 2 .6 6 7 k ( T ) = 2 6 7 k ( T ) /fe sp.
3 .3 3 3 {|) - F CB = 0
F CB

J u n ta .4

3333 k = F x fl - 3 .3 3 3 (Í) = 0 Fxa = Z 0 0 k (T ) Resp.
Fx» N x - 3 .3 3 3 (|) = 0 Na = 2667 k
+T2F,*0;

Nx

F 3 -5 . Ju n ta /) X l . F , = 0; Foc = 0 Resp.
Fw + t 2 F r = 0; *D A « 0 Resp.

Fox

Ju n ta C

■ i 1 F , = O, 8 e o s 6 0 ° - F C x e o s 4 5 ° = 0 F CÁ = 5 .6 5 7 k N ( T ) = 5 .6 6 k N ( T )Resp

+ T 2 F , = 0 ; F Ch - 5 .6 5 7 s e n 4 5 ° - 8 s e n 6 0 “ = 0 F c a = 1 0 .9 3 k N ( C ) = 1 0 .9 k N ( C )R esp .

60°
8kN

www.FreeLibros.me

S o l u c io n e s pa r c ia l e s y r e s pu e st a s a l o s pr o b l e m a s fu n d a m e n t a l e s 635

Ju n ta fí 10.93 k N ± > X F , = 0; F ab = 0 Resp.
+ Í Z F r = 0; N b = 10.93 k N
I1A B

Ns

F 3 -6 . T o d a la a rm a d u ra l+ S A f4 = 0 ; E¿8) - 6 0 0 (2 ) - 8 0 0 (4 ) - 6 0 0 (6 ) = 0 E, = 10 00 N
J u n ta E
+ T2F , = 0 1 0 0 0 - F e f s e n 4 5 ° = 0 F EF = 1 4 1 4 .2 1 N ( C ) = 1.41 k N ( C ) Resp.
= 0; 1 4 1 4 2 1 e o s 4 5 ° - F ED = 0 F ED = 1 0 0 0 N ( T ) = 1 .0 0 k N ( T ) Resp.

J u n ta F

2 F , = 0; F f c - 1414.21 e o s 4 5 ° = 0 P K = 1 0 0 0 N ( C ) = 1.0 0 k N ( C ) Resp.
+ ] l F y = O, 1 4 1 4 .2 1 s e n 4 5 ° - F FD = 0 F n = 1 0 0 0 N ( T ) = 1.0 0 k N ( T ) Resp.

J u n ta D 1000N + T 2 F r = 0 1000 - 60 0 - F 00X 0 4 5° = 0 F ¡x ; = 5 6 5 .6 9 N ( C ) = 5 6 6 N ( C ) Resp.
~ ix

1000N ^ = °*> 1(K W + 5 6 5 . 6 9 e o s 4 5 ° - F p c = 0 F q c = 1 4 0 0 N ( T ) = 1 . 4 0 k N ( T ) Resp.

600 N

Junta C

fe a + Í 2 F , = 0. F c c - 8 0 0 = 0 F qq = 8 0 0 N ( T ) Resp.
800 N
D e b id o a la s im e tría ,
F b c » F d c = 1 .4 0 k N ( T ) P & = F dg = 5 6 6 N ( C ) F HG = F f c = 1 .0 0 k N ( C ) Resp.
F h b = F f d = 1 .0 0 k N ( T ) F a h = F e f = 1.41 k N ( C ) F ^ = F ED = 1 .0 0 k N ( T ) Resp.

www.FreeLibros.me

636 S o l u c io n e s pa r c ia les y r e s pu e st a s a l o s p r o b l e m a s f u n d a m e n t a l e s

rv -7 . P ara to d a la a rm a d u ra

l+ Z M # r = 0 ; 2 (5 ) + 2 (1 0 ) + 2 (1 5 ) - /l.(2 0 ) = 0 Ay = 3.0 0 k
= L41 k (C )
+ ' I F , = O. A, = 0
P a ra e l s e g m e n to iz q u ie rd o

+ í 2 F , = 0; 3 .0 0 - 2 - ^ flC s e n 45 ° = 0 Resp.
Resp.
t+ S A ffl = 0; F H<!( 5 ) - 3 ( 5 ) = 0 F H G = a 0 0 k ( C ) Resp.

l+ Z A fc = 0 ; F w .(5 ) + 2 (5 ) - 3 .0 0 (1 0 ) = 0 = 400 k (T )

2 .0 k

F3-8. P ara to d a la a rm a d u ra
l+ S M f = 0; 600(16) + 600(12) + 6 0 0 (8 ) + 6 0 0 (4 ) - .4 ,(1 6 ) = 0
Ay = 1500 Ib
¿ 1 ^ = 0; A, = 0
F ,„ = 1600 Ib (C )
P a ra e l s e g m e n to iz q u ie rd o F bc = 1200 Ib (T )

l+ 2 A /c = 0; F „ ,(3 ) + 6 0 0 (4 ) + 6 0 0 (8 ) - 1500(8) = 0

1 + 2 M , = 0; F flc< 3 ) + 6 0 0 ( 4 ) - 1 5 0 0 (4 ) = 0 Resp.

6001b 6001b

Ju n ta H

6001b ^ * F , = 0; 1600 - F „ c = 0 F hg = 1600 Ib (C ) Resp.
+ T S F , = 0; F „c - 600 = 0 F „ c = 6 0 0 Ib (C ) Resp.

16001b F „o

F „c

www.FreeLibros.me

S o l u c io n e s pa r c ia l e s y r e s pu e st a s a l o s pr o b l e m a s fu n d a m e n t a l e s 637

F 3 -9 . P ara to d a la a rm a d u ra
t+ 2 iV /^ = 0 ;
N c (4 ) - 8 (2 ) - 6 (2 ) = 0 N c = 7.0 0 k N

C o n s id e re e l s e g m e n to d e re c h o I 'bd = 9 £ 9 9 k N ( T ) = 9 . 9 0 k N ( T )

+ l2 .F y = 0; 7 .0 0 - F a „ s e n 45 ° = 0 F ed = 1.0 0 k N ( C ) Resp.
F bc = 0 Resp
= 0; 7 .0 0 ( 2 ) - 6 ( 2 ) - F ED( 2 ) = 0 Resp.

l+ 2 M D = 0 . 0 - F bc( 2 ) = 0

1 3 -1 0 . P a ra to d a la a rm a d u ra N E = 1 0 0 0 Ib
= 0; N e (3 2 ) - 4 0 0 (8 ) - 4 0 0 (1 6 ) - 4 0 0 (2 4 ) - 4 0 0 (3 2 ) = 0

C b n s id e re e l s e g m e n to d e re c h o

t + X iW £ = 0 ; 4 0 0 ( 8 ) - F c , ( $ ) ( 1 6 ) = 0 F c f = 3 3 3 .3 3 I b ( C ) = 3 3 3 I b ( C ) Resp.

i+ S M c = 0 ; 1 0 0 0(16) - 40 0 (1 6 ) - 4 0 0 (8 ) - F c f(Í)[ 16 ) = 0 F g f = 6 6 6 6 7 Ib ( C ) = 6 6 7 Ib (C ) Resp.
i + l M F = (y. 1 0 0 0 (8 ) - 4 0 0 (8 ) - F cd(6 ) = 0 F CD = 8 0 0 Ib ( T ) Resp.

www.FreeLibros.me

638 S o l u c io n e s pa r c ia les y r e s pu e st a s a l o s p r o b l e m a s f u n d a m e n t a l e s

F 3-11. P ara to d a la a rm a d u ra
1+ 1M a = 0;
N d { 6 ) - 2(6) - 4 ( 3 ) = 0 ND= 4 0 0 k N

C o n s id e re e l s e g m e n to d e re c h o Ffc = 2 8 2 8 k N (C ) = 2 8 3 k N (C )

+ 1 2 F y = 0; 4 .0 0 - 2 - F K se n 45° = 0 Resp.
Resp.
[+SM f = 0; 4 .0 0 (3 ) - 2 ( 3 ) - F flC (1 .5 ) = 0 f W = 4 .0 0 k N (T ) Resp.
|,+ 2 :M C = 0; 4 .0 0 (1 .5 ) - 2 (1 .5 ) - F fe(I.S ) = 0
F f e = 2 0 0 k N (C)

2 kN

Para toda la armadura

t + XAf * = 0; N d 16) - 500(4) - 500(8) - 500(12) = 0 NB = 750 Ib

Considere el segmento derecho Fc o = 10(K) Ib (T )

1,+ X iW f = 0; 750(4) - Fc/)(3 ) = 0 Resp.
Resp.
= 0; 750(8) - 500(4) - F 0#^ - J = ) ( 1 6 ) = 0 Fg f = 1030.78 Ib = 1.03 k (C ) Resp.

(,-fSA/o = 0; FC/r(|)(16) + 500(12) - 750(8) = 0 Fc f = 0

www.FreeLibros.me

S o l u c io n e s p a r c ia l e s y r e s p u e s t a s a l o s p r o b l e m a s f u n d a m e n t a l e s 639

F 4 -L t+ 2 M „ = 0; B ,( 2 ) + 20 - 10(4) = 0 B y = 10.0 kN
Segmento CB
X Z F x = 0; A/c = 0 Vc = 0 Resp.
Vc + 10 - 1 0 = 0 Mc = - 2 0 k N -m Resp.
+ Í2 F , = 0; Mc + 10(1) - 10(3) = 0 Resp.

t+ 2 M c = 0;

F 4 -2 . \,+ 2 M a = 0; B y(3 ) - 4 (1 .5 )(0 .7 5 ) - 8 (1 .5 )(2 .2 5 ) = 0 B y = 10.5 kN
Segmento CB
X ZFX= 0 Nc = 0 Resp.
+ t 2 F , = 0; V c + 10.5 - 8 (1 .5 ) = 0 V c - 1.50 kN Resp.
l + 2 i Mc = 0; 10.5(1.5) - 8(1.5)(0.75) - M c = 0 M c = 6.75 k N -m Resp.

F 4 -3 . t+ S V /8 = 0; - ( 6 ) ( 6 ) ( 3 ) - Ay(6 ) = 0 Ar = 9.00 kN Resp.
■ i.2 F x = 0: A, = 0 Resp.
Segmento AC Resp.
X Z F x = b. Nc = 0
+ T 2 F , = 0; 9.00 - ^ (3 )(1 .5 ) - V c = 0 Vc = 6.75 kN
Wc + |( 3 ) ( 1 .5 ) ( 0 .5 ) - 9.00(1.5) = 0 M c = 12.4 k N - m
t+ 2iW c = 0;

F 4 -4 . L+2/W * = 0; 300(3)(1.5) - -(3 0 0 )(3 )(1 )- Ar (3 ) = 0 A ,= 3001b

X Z F , = 0: A, =0 Resp.
Segmento AC Resp.
Nc= 0 Resp.
X Z F , = 0. 300 - 300(1.5) - Vc = 0 Vc = -1501b
M c +300(1.5 )(0 .7 5 ) - 300(1.5) = 0 M c = 112.5 Ib Resp.
+ t 2 F , = 0; Resp.
Resp.
(,2M C = 0;

F 4 -5 . R eaccion es
Í + Z M A = 0;
X 2F, = F a sen 4 5"(3 ) - 5 (6 )(3 ) = 0 F a = 42.43 kN
+ í 2 F , = 0; 4243 eo s 45° - A , = 0 A , = 30.0 kN
Segmento A C
X Z F , = O, 42.43 s e n 45° - 5 (6 ) - A , = 0 A , = 0
+ T 2 F , = 0;
t+ 2 M c = 0; N c ~ 30.0 = 0 N c = 30.0 kN
-5 (1 .5 ) - Vc = 0 Vc = -7.50 kN

M c + 5 (1 .5)(0.75) = 0 Mc = -5.625 kN • m

www.FreeLibros.me

640 S o l u c io n e s pa r c ia les y r e s pu e st a s a l o s p r o b l e m a s f u n d a m e n t a l e s

F4-6. R eaccio n es
1+ 1 M a = 0 ; By( 15) - 150(9)(10.5) - 6 0 0 (6 ) - 8 0 0 (3 ) = 0 By = 1345 Ib

Segmento CB

X X F , = 0, Nc = 0 Resp.
+ TX F, = 0; Vc + 1345 - 150(6) = 0 V c = -4 4 5 Ib Resp.
Resp.
|,+ 2 M c = 0; 1345(6) - 150(6){3) - M c = 0 M c = 5370 Ib - pie = 5.37 k • pie

F4-7. Segmento izquierdo " 6 ■ K t x) w " v = 0 v = <_3^ ' 6>kN Resp.
+ ? X F , = 0; M + + 61 = 0 M = m Resp.
\.+ 2 M 0 = 0;

F4-8. Reacción -( 1 2 )(6 )(2 ) - -4,(6) = 0 A y = 12.0 kN
l+ X M fl = 0;
Segmento izquierdo 120 ■ K r > > " v = ° v = {i20" x2>k N Resp.
+ Í X F , = 0; Resp.
m
i,+2 M 0 = 0; Resp.
M = { , 2 a t " l x3} k N ' Resp.
,w + K fH f ) " nox=0 Resp.
Resp.
F4-9. R eaccio n es
L + X A ^-0;
\,+ 2 M b = 0; B y(S) - 8 (4 )(6 ) = 0 B , = 24.0 kN
8 (4 ) (2 ) - A r{&) = 0 A , = 8.00 kN

Segmento izquierdo.0 < x < 4 8.00 - V = 0 V = (8 ) kN
+ Í X F , = 0; M - 8.00* = 0 M = {8.*} k N -m
l+ X M o = 0;

Segmento derecho. 4 m < í < 8 m

+ í X F , = 0; V + 24.0 - 8 (8 - . t ) = 0 V = {40 - 8*} kN

l+ X M 0 = 0; 24.0(8 - x ) - 8(8 - ~ w = 0 W = {“ 4z2 + 40.r - 64} k N • m

F 4 -1 0 . -= x < 2 m
t X F , = 0;
- XA/0 = 0; V' = 0 M = -2 0 kN -m Resp.
m < * s4m Resp.
tX F , = 0; M + 70 = 0

■ XA/0 = 0; M + 5(* - - 5 ( * - 2 ) - V = 0 1/ = {10 - 5x} kN Resp.
+ 15 + 20 = 0 M = { - I * 2 + 10* - 45J kN • m Resp.

www.FreeLibros.me

S o l u c io n e s pa r c ia l e s y r e s pu e st a s a l o s pr o b l e m a s fu n d a m e n t a l e s 641

14-11. Reacciones A y - 5 (2 ) - 15 = 0 A y = 25.0 kN
+ t 2 F r = 0; - 5(2)(1) - 15{4) = 0 M a = 70.0k N -m
Í + Z M a = 0;

Segmento izquierdo, ( ) s t < 2 m

+ t 2 F , = 0: 25.0 - 5x - V = 0 V = {25 - 5*} kN Resp.
Resp.
t+ X M 0 = 0; M + 5 x ( | ) + 70.0 - 25.0* = 0 M = j - 1 x 2 + 25* - 70J k N -m

Segmento derecho, 2 m < j < 4 m

+ Í 2 F , = 0; V - 15 = 0 V = 15 kN Resp.
t + S W 0 = 0; - M - 15(4 - x ) = 0 M = { 15x - 60} k N -m Resp.

14-12. Reacciones en los soportes

l+ 1 M a = 0; B y{2 4 ) - 2<12)(6) - 1 8 (1 2 ) = 0 B y = 15.0 k
t+ S A ffl = 0; 18(12) + 2(12)( 18) - -4,(24) = 0 A , = 27.0k

Segm ento iz q u ie rd o .0 S r < 12 pies

+ T = 0; 27.0 - 2x - V = 0 V = {27 - 2 x } k Resp.
Resp.
t+ 2 W 0 = 0; A/ + 2 x ( | ) - 27.0* = 0 M = { - x 2 + 27*} k -pie

Segm ento derech o . 12 p ies < x < 24 pies

+ T 2 F , = 0; V + 15.0 = 0 V = { -1 5 k} Resp.
L+2,V/G = 0; 15.0(24 - x ) - M = 0 M = ( - 1 5 * + 360} k -p ie Resp.
14-13.

y (kN) M (kN -m )

II

-x(m )

14-14. M (kN-m)
k'(kN)
8.5
0
Ü5
•6
— *(m)

46

www.FreeLibros.me

642 S o l u c io n e s pa r c ia les y r e s pu e st a s a l o s p r o b l e m a s f u n d a m e n t a l e s

F4-16.

V k)

63

i a s 12 24 x (p ie s )

'- 's i
-2 7

F4-17.

M (kN -m )

i(m )

F 4 -I8 . M (kN -m )

V(1cN) 0 .5 3 .5 5

F4-19. 1 .5 • x(m )

V (kN) wH----- f— -1 .5
-1 .5

M (kN-m )

www.FreeLibros.me

S o l u c io n e s pa r c ia l e s y r espu e st a s a l o s pr o b l e m a s fu n d a m e n t a l e s 643

P t-2 0 .

W (kpie)

x (pies) *<pics)

F6-2. M„
F6-3.
F6-4. BDC Md D
B

Va M a

n i.

www.FreeLibros.me

644 S o l u c io n e s pa r c ia les y r e s pu e st a s a l o s p r o b l e m a s f u n d a m e n t a l e s

F6-5.

¥6-6. Ma
'-------- 1— x
¥6-7.
ec n

( * c W ;(>+) = -8v(*1 /) +• I| 12 '( 6 - 2 ) ( 1 ) 1(1-5) + (2) + - ( 6 - 2)(1) (2)
- 13.0 k N -m
Resp.
(VVW ) = 8(0-5) ^ (2 )(0 .5 )](1 .5 ) + [ ^ ( 6 - 4 )(0 .5 )]( 1.5) Resp.

2 (2 )(0 .5 ) ( 2 ) + - ( 4 - 2 ) ( —0.5) (2 ) -(6 - 4)(0.5) (2)

= 650 kN

www.FreeLibros.me

S o l u c io n e s pa r c ia l e s y r e s pu e st a s a l o s pr o b l e m a s fu n d a m e n t a l e s 645

FÓ-8.

-*<m)

«> ( C r ) = 6 ( 2 ) 4 1 (9 - 3 )(2 )](2 ) + [1 (9 - 3)(2)]< 4) = 48 kN Resp.
Resp.
b) (A /aU „-> = 6 (-3 ) f - ( 6 - 0 ) ( - 3 ) (2) + ¿ ( 6 - 0 ) { - 3 ) |(4 )-f l(9-6)(3)](4)

= -5 4 kN -m

re-L -z r

J

www.FreeLibros.me

646 S o l u c io n e s pa r c ia les y r e s pu e st a s a l o s p r o b l e m a s f u n d a m e n t a l e s

FH-2.

www.FreeLibros.me

S o l u c io n e s pa r c ia l e s y r e s pu e st a s a l o s pr o b l e m a s fu n d a m e n t a l e s 647

F 8 -4 . Para 0 < x t < y

P
M \ = 2*i

F , d2v' - P .

£ ,^ = f ; + C' <"

E l v, = + C,x, * C 2 (2)

Para | < x2 * L

M 2 = ^ ( L - x 2) = ^ - Z X2

4 7o2 P L P

U dx\ 2 2 X7

dvj PL (3)
E l dxj = - y * 2 ~ ~jx\ + C 3

El 1>2= -j7¿2 - —x\ + Cj*2 + C 4 (4 )

o, = 0 en x , = 0. D e la ecuación (2), C2 = 0

dvi L PL2
—dx—i = 0 en x , = —. De la ecuación (1), C\ = — —
2 16

~ ^ = 0 en x} = D e la ecuación (3). C j = - ^ 7 ~
axi 2 16

PL?

Vj = 0 e n x j = L . De la ecu ació n ( 4 ) , C4 = — -

*i = i “ 3 ¿2 ) *"P
ü2 = - ¿ ¡ ( - 4 * 1 + l 2 L x l - 9 ¿ 2j 2 + ¿ 3) fosp.

F 8-5. M = Px - PL Resp

d 2v
E .-^ -P x -P E

E l —d v = -Px , - P L x -f C , (1)
dx 2 2

£/ v = f 13 “ T 1*2+ c >* + c? (2)

dx = 0 en .r = 0. D e la ecu ació n (1 ), C i = 0

o = 0 en x = 0. D e la ecuación (2), C2 - 0

v = { e 1 {x * ~ 3 L x )

www.FreeLibros.me

648 S o lu c io n e s p arciales y re sp u estas a lo s p ro b lem a s fu n d a m e n ta le s

F8-6. M = M 0 - ~ x
L

. . Mo
d? " "T *

E , t = !2 * - & + C 'x + C 2 (O

v = 0 en x = 0. D e la ecuación (1). C2 = 0

v = Q en x = L. D e la ecuación (1), =

• - 6i f c - * + 3L' ' - R" r
F8-7. Para 0 £ x t < y

m = - t x>

d 2Vy M„
L X‘

£ /* , = - ^ ? + C ,* l + C2 (2)

Para ^ < x 2 * L

M = M 0 — — *2

,/® 2 , , W0
""T * 1

f i n +Ci «3>

E/t, = * Cj*2+ c . («)

ü , = 0 e n Xi = 0. D e la ecuación (2), C2 = 0

üj = 0 en x 2 = L. D e la ecuación (4). 0 = C jL + C4 + (5)

dt)\ dih L MfíL

d 7 ,= 772 en Xí = Xj = 2 ’ De lasecuaciones 0 ) y (3)- c >- c 3 = ~ y ~ (^)

/ Mn L?
t>i = t»2 e n x \ = x 2 = y . D e las ecu acio n es (2 ) y (4),C \ L - C jL - 2C4 = ■ (7)

www.FreeLibros.me

S o l u c io n e s pa r c ia l e s y r e s pu e st a s a l o s pr o b l e m a s fu n d a m e n t a l e s 649

Resolviendo las ecuaciones (5), (6 ) y (7)

_ 11MpL _ MoL
~~ ~24~
~ I Cj 24“

M Rr$p

Pi = 24£ / I^ "4x' +

** = 7¿ E H {~AX* + ULX*" U/A? + 3¿3) RCSp

F8-8. M = - j x 2 + w L x -

d 2v _- | * 2 + K ’L x 2
dx2

dv _ * 3 + * — ■H■-■■L■21\

dx 6 2 2'

H -/.2 .

"■ 5 * * + T * * - ~ x

dv
— = 0 en .t = 0. D e la ecuación (1). C , = 0
ax

v = 0 en x = 0. D e la ecuación (2 ), C } = 0

W ' - x * + 4 ¿ x 3 - 6Z.2*2) Resp.
24E l

FX-9. — a*

«S~a*

« • - - á f e » ’ + « * ♦ < * (2) Resp

= o en x = L D e la ecu ació n (1), C \ = ^ 7 -
ax 24

WnL
f = ü en x = L . D e la ecuación (2 ), C j = — —

- - M’° < - * 5 + 5 L *x - 4 L 5)
120E I L

www.FreeLibros.me

650 S o l u c io n e s pa r c ia les y r e s pu e st a s a l o s p r o b l e m a s f u n d a m e n t a l e s

r e - 10. M
n

AA = \ia / b\ 27 k N - m? Resp.
Resp.
ra -ii. El 0 = El 7

54 kN • m?
El

+tSF, =0: n . i ( ü ^ ) ( 3 m ) = „ El Resp.
Resp.
l + £ M „ = 0 ; - M \ - [ i ( MkEN/ ' 11) ( 3 , n ) ] [ l ( 3 , n ) ] = 0
Resp.
MA ~ 54 k N -m 3 54 k N -m 3 , Resp.

ir ,---------- ¡r.----- i

ra-12.

w
F.I

8 kN-m

El

f— x (m )

32 k N • m?
El

¿<4m ) 64 k N -m 3
El

www.FreeLibros.me

S o l u c io n e s pa r c ia l e s y r e s pu e st a s a l o s pr o b l e m a s fu n d a m e n t a l e s 651

r e - 13. / 8 k N -m v „ .

( El ) 1 1

♦ T S P ,-* (SJga),4.,-V..-0 Resp.
Resp.
(,+ Z M s = 0 ; M ¿ - [ ( ^ í ) ( 4 m ) ] ( 2 n . ) = 0 A T » = a , =
r e - 14. Resp.
Resp.
M

t-x (m )

tan A

Í1 / 5 kN • m V xl f 2 #, .1 15 k N -m 3

¡b/a = [2 v e7 / ][j J= E /

4.6875 k N - m 1
El

1 1 (1 5 kN • m3\ 7.5 kN •m3
A = 2 ^ = 2 Í “ £ r “ j = — £7“

I'r/aI 15kN -m 3/ E / 5 kN -m 2 _

Ai 3m El
E ab

7.5 k N • m 3 4.6875 kN • m3 281 k N • m 3
Ac = A - fc//4 =
El El i
El

www.FreeLibros.me

652 S o l u c io n e s pa r c ia les y r e s pu e st a s a l o s p r o b l e m a s f u n d a m e n t a l e s

r e - 15.

F.I

+ Í 2 F , = 0; - V 'A - 5 k NE.l! m ~ = 0 iA = v A = 5 k N ' m2 = 5 k N ‘ m2 ^ Resp.
Resp.
El El

^ 25 k N - m 2' 1(1.5 m ) - M ’c = 0

5 m) (0.5 m ) -

Ac = M c 28125 kN -m 3 281 kN-m 3 ,
-----------E—l --------- — -------*
r e - 16. F.I

12 kN -

1 /1 2 kN -m V 18 k N - m 2 Resp.
Resp.
Ba ~ °C/A ~ 2 { — ¡ n — p m ) ~ — é i — ^

[1 /1 2 kN »1 18 kN • n

'c' - ~ [2\— El

= oa l c = 18 kN •m~ ^ (3 m) = 54 kN -m 3

ei r F!

A c = A ' - IC /A = 54kN-m3 18 k N - m 3 3 6 kN- m 3i

El El El

re -1 7 .

f * < !* £ = )« » ->

18 kN - T

El 18 kN -m '

El

www.FreeLibros.me

S o l u c io n e s pa r c ia l e s y r e s pu e st a s a l o s pr o b l e m a s fu n d a m e n t a l e s 653

18 k N - m 2 18 k N - m 2 - . Resp.

* U F , - 0; - k í - . ^ V - o • a = Va -------- E l E~ l----- ■ Resp.

t+ 2 W c = 0; M f c + ( H 1 ^ 5 Í ) ( 3 « n ) - [ j

M i = Ac = - 36 k N -m 3 36 kN -m 3 ,

El El

M

= j» ^ « k N - m \ (2 m ) || 2 m + - (2 m ) | + r )(2 m ) ( l m ) = 37.33 k N -m ' Resp.
[2 \ E l ) Resp.
tC,A B El

24 k N *m2\ . 96 kN -m 3

y = * a L m: = ( = — i¡—

ac = y 96 k N -m 2 37.33 k N -m 3 58.7 k N -m 3
- ic /A = El 1

El El

H l-19.

(S ^ S )« 4 -,+ i * ( “ * = ) < 2 « , ( 8- ^ ) ( 2 m ,
F.l El
-Im H

2.667 m

4m J 1 ""

24kN -m a
El

El El Resp.
l+ S W c. * M, + ( 2 ^ ( 4 - , -
- ( 2 ^ = )p -K .- ) - o
Ac = W{r = 58.7 kN • m3 ,
Resp.
El

www.FreeLibros.me

654 S o lu c io n e s p arciales y re sp u estas a lo s p ro b lem a s fu n d a m e n ta le s

r e - 20. M
n

Resp.

“M 2 m + j (2 m) 60 kN -m
El
I

R i-2 1 .

■ftSF, = 0; -V » - m) = 0

18 k N - m 2 18 k N • m 2 v Resp.
El El Resp.

= 0; M'„ + [ | ( 18 f / m ) ( 2 m ) ] [ |( 2 n .) + 2 m = 0

60 kN -m * 60 k N -m 3 ,
Mu = d» = E” l ---- = -------E l i

www.FreeLibros.me

S o l u c io n e s pa r c ia l e s y r e s pu e st a s a l o s pr o b l e m a s fu n d a m e n t a l e s

« 9 -1 . □em ento nflb) N flb ) i- (pies) nNL ( b 2-pie)

AB -1.667 -250 10 4166.67
AC 1 150 6 900.00
BC 200 8
1.333 2133.33

2 7200

Entonces,,

v nNL 7200 Ib2-pie
llb -A * ,= AE

^ AE

7200 Ib-pie.

AE

¥9-2. XN
XP
Sem entó N N ( P = 150 Ib) L (pies) N (
--1.667 , s O l ( l b ’pie)
A B 1.667P 1 -250
AC P 150 10 4166.67
B C 1.333P 1.333 200 6 900.00
8 2133.33

2 7200

, 7200 Ib -p ie.
i» . - - ■ AE

¥9-3. N (kN) nNL (kN2-m )

□em ento n (kN) -4.041 Mm) -8.0829
8.0829 0
AB 1 2 0
AC 0 -8.0829 2 0
BC 0 8.0829 2
CD 0 1 2 -8.0829

Entonces. 8.0829 kN 2-m
nNL AE

lk N -A ^ 2
AE

808 k N • m 8.08 k N -m Resp

4* = --------J e - = — ¿ e ----------

FV-4. SN

□ e m e n to N (kN) SP N (P = 0) (kN) Mm)
N ( s ) L (kN ' m)

A B P - 4.041 1 -4.041 2 -8.083

A C 8.083 0 8.083 2 0

BC -8.083 0 -8.083 2 0

C D 8.083 0 8.083 1 0

2 -8.083

SN\ L 8.083 k N - m 8 . 0 8 k N - m

www.FreeLibros.me

656 S o l u c io n e s p a r c ia l e s y r e s p u e s t a s a l o s p r o b l e m a s f u n d a m e n t a l e s

F 9 -5 .

E lem ento n (kN) N (kN) L nN L (kN 2 -m )

AB 0 0 3_ 0
AC 1.414 8 .4 8 5 3 \/2 50.91
BC -1 -6 3 18.00
AD 0 -6 3
CD -1 0 3 0
0

2 68.91

v n \L 68.91 k N 2 -m
1 k N • A Dí ■ AE

AE

\ — 68.9 k N -m R esp .
A />. “ R esp .
AE

F 9 -6 . cSN

E le m e n to N (kN) SP N ( P = 0 ) (kN) L(m ) 0
50.91
AB 0 0 0 3 18.00
A C V Í ( P + 6) Vi 6V 2 3V 2
B C -(/> + 6) -i 0
A D -6 -6 3 0
CD -P 0 -6 3
-1 0 3 2 68.91

A D, = 2 N |
\6 P ) A E

68.9 k N -m
AE

F 9 -7 . E lem ento n(kN ) N (kN ) L (m) nNL (kN 2 • m )

AB 0.375 18.75 3 21.09
BC 0.375 18.75 3 21.09
AD -0 .6 2 5 -3 1 .2 5 5 97.66
CD -0 .6 2 5 -3 1 .2 5 5 9 7 .6 6
BD 0 50 4
0

2 237.5

237.5 kN -m , Resp.

A° - = ■ - A E " 1

www.FreeLibros.me

S o l u c io n e s pa r c ia l e s y r e s pu e st a s a l o s pr o b l e m a s fu n d a m e n t a l e s 657

F 9-8. 8N
8P
Sem entó N(kN) N ( P = 0)(kN) L(m) N ( ^ ) L ' kN-m >
0.375
AB J/» + 18.75 0.375 18.75 3 21.09
BC ¡ P + 18.75 -0.625 18.75 3 21.09
AD - ( ¡ r + 31.25) -0.625 -31.25 5 97.66
CD - ( ¡ P + 31.25) 0 -31.25 5 97.66
BD 50 4
50 0
2 237.5

237.5 kN • mi Resp.
A E

F9-9. Sem entó n(kN ) N (kN) L(m) nNL (kN 2-m )

AB 0 -6 1.5 0
BC 0 -6 1.5 0
BD 1 2 0
CD 0 0 2.5 0
AD -1 .2 5 10 2.5 31.25
DE 0.75 -1 0 1.5 13.5
12
1 4 4 .7 5

nN!. 44.75 kN 2 *m
1 k N • Afl, - 2 A E AE

44.75 k N -m Resp.
A». A E

W -10. 8N

Sem entó N ( kN) 8P N (P = 0)(kN ) H m) 0
0
AB -6 0 -6 1.5 0
BC -6 0 -6 1.5 0
BD P 1 2 31.25
CD 10 0 0 2.5 13.5
AD - ( 1 .2 5 P + 10) -1.25 10 2.5
DE 0 .75P + 12 075 -1 0 1.5 144.75
12

A», = 5 > 5N ' 44.75 kN • m Resp.
8p AE l

www.FreeLibros.me

658 S o l u c io n e s pa r c ia les y r e s pu e st a s a l o s p r o b l e m a s f u n d a m e n t a l e s

Elem ento n(lcN) N (kN ) L(m) nNL (kN 2-m )

AB 0.5 50 2 50.00
DE 0.5 50 2 50.00
BC 0.5 50 2 50.00
CD 0.5 50 2 50.00
AH -0.707! -70.71 2VÍ 141.42
EF -0.7071 -70.71 2V2 141.42
BU 0 30 2
DF 0 30 2 0
CU 0.7071 28.28 2V § 0
CF 0.7071 28.28 2V2 56.57
CG 0 2 56.57
GH -1 0 2 0
FC, -1 -7 0 2 140.00
-7 0 140.00

2 878.98

^ n N L 875.98 kN2 -m Resp.
. 876 k N -m ,
A c< = -----— — 1

19-12. N (kN) 8N N { P = 40 kN) Mm) N ^L O cM -m )
6P
Elem ento 0.5/* + 30 50 2 50.00
0.5 P + 30 0.5 50 2 50.00
AB 0.5 P + 30 0.5 50 2 50.00
DE 0.5/* + 30 0.5 50 2 50.00
BC -(0.7071 P + 42.43) 0.5 -70.71 2V2 141.42
CD -0.7071
AH -(0.7071 P + 42.43) -70.71 2SÍ2 141.42
EF 30 -0.7071 30 2 0
BH 30 0 30 2 0
DF 0 28.28
CH 0.7071/» 0.7071 28.28 8S 56.57
CF 0.7071 P 0.7071 0 56.57
CG 0 2
GH 0 -7 0 2 0
FG - ( P + 30) -1 -70 2 140.00
-(/» + 30) -1 140.00

X 875.98

875.98 k N -

876 kN-m.

www.FreeLibros.me

S o l u c io n e s pa r c ia l e s y r e s pu e st a s a l o s pr o b l e m a s fu n d a m e n t a l e s 659

» - 1 3 . Para la pendiente.

1... - / W / , / 3" ( - l ) ( - 3 a * ) , 135 kN2 • m3
E l dX = — , —
Resp.
135 k N - m2
eA = ------ — --------7

El

Para el desplazamiento.

270 kN -m 5 , Resp.
V = ------ — -------1

r e - 14. Para la p e n d ie n te , M = - 30x — A /'. P o r lo ta n to , 0*1 = - 1 . S e a M ’ = 0. E n to n c e s, Ai = ( ~ 3 0 r ) k N . m.

ft j9 M \d x f i m ( - 3 0 x ) ( - l ) d x 135 k N - m 2 —

9* - i - i 17 " — 7

Para e l d esplazam ien to , Af •» — P x . P o r lo ta n to , = - x .
dP

Sea P = 30 kN . E nto n ces, A# = ( - 3 0 r ) kN . m.

(-3 0 x )(-x )rfx 270 k N -m 3 .
El El

r e - i s . Para la p end ien te. m e = 1 kN . m y M = 4 k N • m.

... „ m gM f 3m( l ) ( 4 ) d x 12 k N 2-m 3
,kN— ^ = 2 T T dx = J £/ = Ti

12 k N - m 2 Resp.
•-— B — ^ Resp-

Para e l d esplazam ien to , m x kn . m y Ai ^ 4 k N . m.

3“ x(4)rfx 18 k N 2- m3
El El

18 k N - m 3
= — Y¡— T

r e - i 6 . Para la p en d ie n te , M = A f. P o r lo ta n to , ~ = 1.

oM

Sea M ‘ = 4 k N • m. E n to nces, M = 4 k N . m.

rLj B M \ d x [ i m 4 ( l ) d x 12 k N - m 2

Para e l desplazam iento. A/ = (P x + 4) kN . m P o r lo tanto. = x.

oP

Sea P = 0. E n to n ces. M = 4 k N . m.

r ‘\ . ( d M \ d x f 3m4 ( x ) d x 18 k N • m 34

^ ’A ■ JÍ “ 5 ----------i í — 1

www.FreeLibros.me

660 S o lu c io n e s p arciales y re sp u estas a lo s p ro b lem a s fu n d a m e n ta le s

W -17. Para la p en d ien te . m g = — 1 k N • m y Ai = ( —x3) k N • m.

1 kN -m -0, Jo E l Jo 20.25 kN 2-m 3
El
El

20.25 k N -m 2 Resp
E/ ^ p

Para el desplazam iento,m = ( - x ) kN • m y M = (-¿® )kN • m.

mM J f 3m( - x ) ( - x i ) 48.6 kN2 -m 3
= — É í—
,k N - W o ^ = /o — ^7—

48.6 k N -m 3 ,
*• = — T i — *

W -18. Para la p en d ien te , M = (A i' + x3) k N . m. R>r lo tan to , oM = - 1.

S e a M ' ■ Q E nto nces, Ai ■ ( —x3) k N • m. **

í L . . ( d M \ d x [im ( - ¿ ) ( - \ ) d x 3).25kN -m 2 ^ r ""

= oj " l i F j i ? - J 1 ¡— - Él ^
-

Para el d esplazam iento. Ai = — ( P x + x3) k N . m.

ft>r lo tan to . ~ = - x . S e a P = 0. E n to n ces. W = ( - x 3) k N -m .
dr

f Lj 8 M \ d x f im ( - x i) ( - x ) d x 48.6 k N -m 3 ,

a »- - y . \ i p f k ¡ - y — » — - — e t — 1

W -19. Para la p en d ien te , m g = (1 - 0.125x) k N . m y Ai = (32x - 4x*) kN . m.

[' . [ * ” ( ' " ® '1 2 5 x )(3 2 x - 4X2 ) 170.67 k N 2- m 3
Ik M -m . 0A = J — d x = l d x = ---------- --- --------

171 k N -m 2 _ Resp.
0A = ------ — -----\ R esp

Para el desplazam iento, m = (0.5x) k N . m y M = (32x - 4x2) k N . m.

0.5x(32x - 4 x 2) 426.67 kN2 • m3
-----------------------d x ------------------------
j f dx = 2l ‘ El El

427 k N -m 3 ,

Ac , Y ¡ *

F9-20. Para la pend ien te. Ai = A i - 0.125AÍ'x + 32x - 4x*. Por lo tanto. ^ = 1 - 0.125x.

o Si

S e a A i' - 0. en to n c e s. Ai - (3 2 t - 4 t 2) k N . m.

_r U( 9 M \ dx _ j(32x - 4x2) ( l - 0.12 5 x )
VaWV E l i
4i E l dX

170.67 k N • m 2 171 kN • m2

Ti = £7

www.FreeLibros.me

S o l u c io n e s pa r c ia l e s y r e s pu e st a s a l o s pr o b l e m a s fu n d a m e n t a l e s 661

Para el desplazamiento, M = 0.5P x + 32* - 4*7. ftir lo tanto. ^ = 0.5*. Sea P = O.cntonces, M = (32* - 4 r ?) kN • m.
aP

(32* - 4 * 7)(0 .5 x ) d x
El

426.67 k N -m ' 427 k N -m ' Resp.
i

E l El

» - 2 1 . Para la p e n d ie n te (m fl), = 0 ;( m #)2 = - 1 kN . m , A f, = ( - 12*,) k N . m

y M2 - - I2 (i2 + 2 ) k N . m. 0 (-l2 « i) r 2m { - 1 ) [ - 1 2 ( * 2 + 2 )]

. . . . [ L m ,M T i----------------- T i---------i :

,kN m^ = l -E T dx = L

1 kN -m -ec = 72k^ / ' m Resp
P
72 k N - m 7 _
gc = — Y i — 7

Para e l d esp la z a m ie n to .m , = 0 ,m 2 = - x Jt Af, — ( - 1 2 * , ) k N • m

y M j = - 12(Xj + 2 ) kN . m.

, t " <H -I2 * 0 /-J” 12(x 2 + 2 ) ]

,kN' ic = l T T dx = l — T - d x + l T, *

, , kt . 80 kN7 -m '
l k N - A c. = £ /-

80 kN • m ' ,
d c. = — y í — A

W -22. Para la p en d ie n te . M , = ( - 1 2 * , ) k N . m y A#2 - - 12(*, + 2 ) - A f'.
ft>r lo tan to , ^ = 0 y ^ 7 = - 1 . Sea Af' = 0 , A/ 2 = - 12(*2 + 2).

72 k N - m -

" Ti 7

Para e l desplazam iento. A/, = (- 1 2 * ,) k N . m y W , = - 12(x? + 2) - Pxr

l\>r lo ta n to , —^ = 0 y —^ = - x 2. S e a P = 0, A/, = — 12(x, + 2 ) kN • m.
di * dr

80 kN -m 3 ,
£/

www.FreeLibros.me

662 S o l u c io n e s pa r c ia les y r e s pu e st a s a l o s p r o b l e m a s f u n d a m e n t a l e s

M x = 0 .5 x ,. M7 = 0.5x2, M , = ^ 2 4 x , - kN -m

y M 7 = f 4Kx2 “ 6 x | + kN' • m.

fL . 6m ( 0 . 5 x , ) f 2 4 x , - ¿ x ? ) ^ (0.5x2)Í 4 8 x 2 - 6 x | + J x |)

I k N - A C. = / ^ f d x = l \ - — L ± dXx + £ --------- F7--------- ^

1620 kN? • m 3 P
FJ

1620kN -m 3 ,
c*= El

HJ-24. M x = 0.5 P x t + 24x, - M j = O.SPxj + 4Sx2 “ 6x? +
o 6

dMx n r dM7 n r
E n to n ces,— = 0.5x,t — = 0.5x2.

Sea P = 0. A/, = ^ 2 4 x , - g x ^ kN • m y V/2 = ^48x2 - 6x3 + ^ x $ j k N • m

P .jm \ix ! * ' ( 2411 - H ,0 -5 i , ) . / . - ( « * » - « 4 + ! < ) « « « dx2

^ - y. M u -í +T , d " J 17

1620 k N • m J , ^
= — Yi— 1

F10-1. Superposición

(£/2)> L3 43 2.667 m 3 ,
,HB 3£7 2AEI 24£7 £7

A « = A 'fl +

( + t ) 0 . . 2 S S ^ £ + Jip « a í )

= 100 kN /tesp.

E q u ilib rio >1, = 0 A , = 60 kN Resp.
¿ X F , = 0; 100 - 40 - A , = 0 Resp.
+ T = 0; M Á = 4 0 kN •m Resp.
100(2) - 4 0 ( 4 ) - M Á = Q
1+ 2 M a = 0;

www.FreeLibros.me

S o l u c io n e s pa r c ia l e s y r e s pu e st a s a l o s pr o b l e m a s fu n d a m e n t a l e s 663

F10-2. Superposición

8 J0 E l J, El 30 F.I

f L mm ( L <-*>(-*) O,

l ~ E Í = Ja — E r - d x = 3 E I [

= A'fl + B y f n

(.+ii). 0„ =»wo£l *í+“„'(( mE3í\) „s’''n rWqL =i5-.f Rwp-

E q u ilib rio -4, = 0 2tV fíL *"P
^ 2 F , = 0, ^*5
1 H V iL £esp.
+ Í Z £ , = 0; ^ “ 2 ^ + “j j = 0
Resp.
(,+ 2 3 ^ = 0; + ^ (¿ ) - = 0 A#* = ^ Resp
tfesp.
F10-3. Superposición Resp

v - wL4 - ,0(64) - «BOIcN-n»3 1620(103) N , a i3
[200(104) N/m2][300(10-6 ) m4]
8 8 £ / 8E l ' El “

/f l8 ^ 3 É 7 ^ 3Y r ~ É F = [200(1 (#*)N /m 2][300( 10- 6 ) m 4] = 1,2(10
A,, = A',, + B /flfl
( + i ) 5 (1 0 ” 3) m = 0 .0 2 7 m + f l ^ - 1 . 2 ( 1 0 '6)m /N ]
B y = 18J 3 ( 103) N = 18.33 k N = 18.3 k N

E q u ilib rio A, = 0 A y = 41.67 kN = 41.7 kN
X ZF, =0; + 18.33 - 60 = 0 = X>.0 kN •m
+ 1 2 /% = O. M Á + 18.33(6) - 60(3) = 0
t + 2 3 / ^ = 0;

F10-4. Superposición

“ • - 6 £ /L ac - * !) - 6rF£T/ (T2TLr)rK 2' - )' ’ - *■’ J] - 4 £ / 1

£ 3ac ( ^ ) 3 ¿ 3 .
788 4 8 £ / 4 8 £ / 6 £ /

A * = A'fl + f l , / flfl

(•

www.FreeLibros.me

664 S o l u c io n e s pa r c ia les y r e s pu e st a s a l o s p r o b l e m a s f u n d a m e n t a l e s

E quilibrio -4, = 0 r _ Mo R esp .
X I . F , = 0, R esp .
t+ 2 W /4= 0 ¡ - C y(2 L ) + - ^ ( L ) - M 0 = 0 4L R esp .
+ Í Z £ r = 0; 3M0 M 0
~2L " A L ‘ A ’ ' ° A =^
F 10-5. S uperposición A ' 4L

A’« = 6£ / ( 8) (82 £/
6 E IL m

tic 8 10-667 m 1
f BB ~ 4 8 £ / El
4SE I
A „ = A 'fl +

366.67 k N - m 3 , /1 0 .6 6 7 m R esp .
(+t) o = -
R esp.
El V El R esp .
R esp .
B y = 34.375 k N = 2 4 .4 kN

E quilibrio 34.375(4) - 50 (2 ) - C ,(8 ) = 0 C y = 4.6875 kN = 4 6 9 kN
L+XAf4 = 0; 4 y + 34.375 - 5 0 - 4.6875 = 0 A y = 20.3125 k N = 20.3 kN
+ T X £r = 0;
± 2 F , = 0; A, = 0

5 w L \- 5(10)(124) 2700 kN - m 3 2 7 0 0 (1 0 3) N - m 1
F 1 0 -6 . A's = 384E l
El = 0.045 m i
384E l (2 0 0 (1 0 9) N /m 2 ][3 0 0 (1 0 -6 ) m 4]

L \c 123 36 m3 36 m 3 = 0.6(10-6) m /N t
48E I El
fB B = (2 0 0 (1 0 9) N /m 2](3 0 0 ( 1 0 '6) m 4]

48£7

A « = A'h + B y f BB

( + 1 ) 5 ( 1 0 " ’) m = 0.045 m + B y [ - 0 .6 ( 10-6 ) m /N j t í , = 6 6 .6 7 (1 0 3) N = 6 6 .7 kN R esp.

E quilibrio C 7(1 2 ) + 6 6 .6 7 (6 ) - 1 2 0 (6 ) = 0 C y = 26.67 k N = 26.7 k N R esp .
\,+ 1 M a = 0; A , + 26.67 + 66.67 - 120 = 0 A y = 26.67 k N = 26.7 k N
+ 1 'L F y = 0; A, = 0 Resp.
X Z F , = 0;

www.FreeLibros.me

Respuestas a problemas seleccionados

Capítulo 1 2-10. Sobre B E 2 2 0 k/pie. sobre F E D fuciza de 13.2 k
2-11. a. Indeterm inada de 2o
1-1. F = 48.3 k b. Inestable
1-2. F = 24.6 k 2-13. c. Estáticam ente determ inada
1-3. w - 521 lb/pie 2-14. d. Estáticam ente determ inada
1-5. F = 173 kN 2-15. e. Inestable
1-6. ve = 468 lb/pie 2-17. a. Estáticam ente determ inada
1-7. 6 2 0 kN/m b. Estáticam ente indeterm inada de Io
1-9. w = 240 lb/pie 2-18. c. Estáticam ente indeterm inada de Io
1-10. C arga m u erta to ta l = 106 lb/pie7 2-19. a. Inestable
1-11. F , = 94.5 k 2-2L b. Estable y estáticam ente determ inada
1-13. L = 1.70 kN /m 2 2-22. c. Estable y estáticam ente indeterm inada
1-14. L = 302 kN /m 2
1-15. Pt>-\s = 27.8 p sf 2-23. de segundo grado
a. Inestable
P20 = 29.1 p sf b. Estable y estáticam ente indeterm inada
= 30.1 psf
de prim er grado
pw = 31.1 p sf c. Inestable
1-17. Barlovento: a. Inestable
b. Estable y estáticam ente indeterm inada
p> u = 2).9 psf
p i„ = 21.8 psf de sexto grado
Sotavento: c. Estable y estáticam ente determ inada
p = -15.4 psf d. Inestable
1-18. p - - 18.6 psf B , = 48.0 kN
1-19. F = 81.3 kN A y = 16.0 kN
1-21. p , = 0.816 kN/m7 A , = 10.0 kN
1-22. p f = 36 lb/pie2
F b = 110 k
Capítulo 2 A , = 95.3 k
A y = 5.00 k
2 - L S o b re B E - 14.2 kN /m ; so b re F E D , N A = 12 kN
F.y = 35.6 kN B, = 0

2 -2 . Sobre B E carga trapezoidal, pico 21.4 kN/m By = 30 kN
so b re F E D cargas triangulares, picos 10.7 M R = 84 kN • m
N F = 4.00 k
kN/m, con fuerza concentrada de 26.7 kN e n E. N n = 6.00 k

2 -3 . Sobre EF,0.9 k/pie;sobre A B C D E 3 fuerzas N „ = 15.0 k

d e 13.5 k A y = 7.00 k
A, = 0
2 -5 . Sobre B F = 0.675 k/pie. so b re A B C D E 3 N a = 9.59 k
fuerzas d e 6.75 k C , = 9.20 k

2 -6 . Sobre B G = 230 lb/pie, sobre A B C D E 2 N„ = &54 k
Cy = 293 k
2-7. fuerzas d e 1725 Ib
S o b re B G = 368 lb/pie p ico trian g u lar

S o b re A B C D con 2 fuerzas de 736 Ib, 184 lb/pie

pico triangular

2 -9 . Sobre B E carga trapezoidal, pico 4.125 k/pie,

sobre FED cargas triangulares, picos 2.06 k/pie
y £ - 12.9 k

665

www.FreeLibros.me

666 R espu esta s a pr o b l e m a s se l e c c io n a d o s

2 -2 5 . C = *4.8 Ib 2-42. C , = 678 Ib
2-26. A y = 47.4 Ib 2-43. C y = 1.97 k
2-27. Ay = 398 Ib C , = 45.0 kN
fíy = 5.12 kN D , = 45.0 kN
2-29. Ay = 14.7 kN Cy = 7.00 kN
2-30. B , = 20.0 kN A y = 83.0 kN
2-31. C, = 0 A , = 45.0 kN
By = 750 kN Dy = 7.00 kN
2-33. MÁ = 45.0 k N -m B , = 24.8 k
2-34. A y = 7.50 kN By = 22.1 k
2-35. A, = 0 C , = 8.16 k
2-37. A y = 4.00 kN Cy = 31.9 k
2-38. M„ = 63.0 kN -m
By = 17.0 kN C a p ítu lo 3
2-39. £ -L a . Inestable
2 -4 1 . B, = 0 b . Estáticam ente indeterm inada de I o
Ay = 2.00 kN c. Estáticam ente determ inada
B , = IZO kN d . Estáticam ente determ inada
B, = 0 3-2. a . Estáticam ente determ inada
M b = 32.0 k N -m b . Estáticam ente determ inada
c. Inestable
2P 3 -3 . a . Interna y ex te rn a m e n te e sta b le (d e 2o)
W' ~ T b . Interna y ex te rn a m e n te e sta b le (d e I o)
c. Interna y ex te rn a m e n te e sta b le (d e I o)
4P 3 -5 . Fcd = 780 Ib (C)
W7 = T
iv, = 83.3 Ib/pic Fcb = 720 Ib (T)
iv? = 167 Ib/pie
A , = 30.0 kN 3-6. F„h = 0
A y = 6.67 kN F de = 780 Ib (C)
C , = 10.0 kN F be = 791 Ib (T)
Cy = 667 kN
N a = 11.2 k Fb a = 7221b (T)
B , = 9.70 k F ah = 4.47 k (C )
By = 4.10 k Fab = 400 k (T)
B y = 16.6 k F«c = 400 k(T)
A , = 29.0 k
A , = 17.0 k Fbh = 0
A , = 300 N Fhc = Z 24k(C )
A , = 300 N
C , = 300 N F„c = 224k(C )
Cy - 300 N
T = 3501b F fc = 0
Ay = 700 Ib
A , = 1.88 k Fpg = L 5 k ( C )
D , = 1.70 k
D , = 1.70 k Fge = Z 2 4 k (C )

= 1.53 k 3-7. Foc = 0
Fc n = 350 Ib Fec = Z24 k (T )
A , = 522 Ib Feo = 3.5 k (C)
A y = 1.47 k Foc = 0
F qc = 9.24 kN (T )

F de = 4.62 kN (C)
FeE = * 2 4 kN (C)
Fcb = 9.24 kN (T )
F be = 9.24 k N (C)

www.FreeLibros.me

R espu esta s a p r o b l e m a s se l e c c io n a d o s 667

3 -9 . F b a = 9.24 k N (T ) 3-15. F bj = 7.94 kN ( D
F e a = 4-62 k N (C ) F bc = 34.3 kN (T)
3-10. Fa f = 3.33 k (T) 3-17. F „ = 35.7 kN (C)
FAB = Z 6 7 k ( C ) Fjc = 6 0 0 kN (C)
3-1L F bf = 9.00 k (C) 3-18. FCI = 9.11 k N (T )
3-13. F hc = 2 6 7 k (C) 3-19. FCfí = 77.4 kN (T)
F FC = 5.00 k (T ) 3-21. F ih = 35.7 kN (C)
3 -1 4 . F fe = 1.33 k (C ) 3-22. F HD = 6.00 k N (C)
F ce = 3.00 k (C ) 3-23. F h e = 7-94 kN (T)
Fc o = L33 k (T) 3-25. F „ c = 42.9 kN (C)
F d e = 1.67 k ( C ) F eD = 34.3 kN (T)
F e f s 11*7 k (C ) F ,D = 9.11 kN (T)
F eo = 8.875 k (T) F fg = 42.9 kN (C)
F Df = 0 Fc e = 400 kN (C)
F p c = 8l8 7 5 k (T) F f e = 41.1 kN (T)
F ah = Ffe = 25 kN ( Q
= 215 k (Q F ah = F de = 20 kN (T)
= L375k(T) F bc = Fcd = 20 kN (T)
F bh = F o f = 10 kN (T)
F BH = 0 F hg = Fc f = 16.7 kN (C)
ffle = L375 k (T) F hc = F c r = 8.33 kN (C)
F fC = 4 0 4 k (C ) Fec = 20 kN (T)
f> c = 7.67k(C ) F a g = F oe = 4.00 kN (T)
F ab = Foe = 3 4 6 kN (C)
^ c c = 3.00 k (C ) Fcf = F ef = 4.00 kN (T)
FGh = 7.67 k ( C )
Fcw = 5 .86k(T ) Fcr = Fec = 0
F £D = 8.33 k N (T ) Fbf = Fcf = 231 kN (C)
Fc o = 667 kN (C) F BC = 231 k N (C)
F bc = 667 kN (C) F o c = 11.7 k ( T )
F es = 5 kN (T) F f g = 16.6 k (C )
Fcf = 20 kN (T ) F fc = 4.86 k (T)
Fc a = 15 k N (T ) FCo = 2 0 0 k (T )
Fjn = 250 k (T)
= 18.0 kN (C) F ik = 403 k (C)
= 10.0 kN (C) Los elem entos KN, N L , MB, BL, CL, IO , OH,
F bb = 4.17 kN (C) GF., EH, H D son elem entos d e fuerza cero.
Ffb = 7 i0 kN (T) Feo = 667 kN (T)
F ff = 12.5 kN (T) FCf = 12.5 kN (C)
F de = 16.3 k N (C ) Fcc = 0
F pc = H40 kN (T) Fbc = 800 kN (T)
F h c = 10.1 k N (C)
F e a = 8-85 kN (C )
Fec = 6 2 0 kN (C) F bc = 1.80 kN (T)
Fcf = &77 kN (T) FGf = 1.78 kN (T)
FCb = 2 2 0 k N (T ) F eo = 223 kN (C)
Fba = 311 kN (T)
Fbf = 620 kN (C) FCf = 0
Ffa = 620 kN (T) F „, = 600 kN (T)
F ak = 42.9 kN (C) Fm = 4.24 kN ('O
F ab — 41.1 k N (T )
Fkb = 4.00 kN (C) F e o = 10.1 kN (C)
F k j = 42.9 kN (C)

www.FreeLibros.me

668 R espu esta s a pr o b l e m a s se l e c c io n a d o s

3-26. F „ = 9.00 kN (T ) Fb c = 1-80 k N (T )
3-27. Fb e = 1.80 kN (T)
3-29. F,c = 6.00 kN (C) 3-35. Ffe = o
Fcd = 10.1 k N (C) 3-37.
3-30. F kj = 115 k N (C ) Fed = 0
3-31. Fc, = 27.0 kN (T) Fab = 40 0 kN (T)
F be = 5.66 kN (T)
3-33. FCp = 97.5 k N (T ) F bd = 2.00 kN (C )

3 -3 4 . Fab = Ü II Fc e = 0
F a C = 1.50 k ( C )
II
3

ii

Füb = 0.707 k (T) 3-38. F bc = L15 kN (C )
F ol = 0.500 k (C ) 3-39. F df = 4.16 kN (C )
Fbe = 4.16 kN (T)
Fo'/ = 0.707 k (C) Fcf = 0
FL, = 0.707 k (T) Feo = 231 kN (T)
F ed = 3.46 kN (T)
F rK = 0.500 k (C )

F /Jf = 0.707 k (C)

F/ f = 0.707 k (T)

Fbf = 2.12 k (T ) Capítulo 4
F b c = 1.00 k ( C )
4-1. Nc = 0
Ffc = Q707 k (T) V c = 0.667 kN
f> „ = 2.12k(T ) Mc = 0.667 kN • m
Nn = 0
F kh = 0.707 k (T) VD = -5 3 3 kN
F * ,= L50 k (C) M d = - 9 3 3 kN -m

F ,w = Z 12k(T ) 4-2. Nc = 0
V c = 3.33 k
FCD = 0 Mc = 58.3 k - pie
N„ = 0
F/>£ = 0.500 k (C ) V p = -6.67 k
FC£ = 0.707 k (C ) M o = 91.7 k -p ie

F he = 0.707 k (T) 4 -3 . N /AI = 0
V A = 450 Ib
Fj e = 1.50 k (C ) M a = -1.125 k -p ie

Fad = Fbe = 0 Nb = 0
F a f = F bc- = 4.00 k N (C ) V B = 850 Ib
M a = -6 3 2 5 k -pie
Ff d = FCe = kN (T) Vc = 0
Nc = -1 .2 0 kip
F fe = F Cd = 11.3 k N (C) A/c = -8 .1 2 5 k - p ie
4-5. w = 100 N/m
F ed = 16.0 kN (C) 4-6. Nc = 0
Vc = -Q 75 kN
Fe f = 1.15 k N (T ) Mc = -0.375 kN -m
Feo = 3.46 kN (C) ND = 0
V o = 1-25 kN
Fba = L 1 5 k N (T ) M p = 1.875 k N -m
Fbc = 1-15 k N (T ) 4-7. Nc = 0
Fao = 424 kN (T) V c = 1.75 kN
F af = L58 kN (T) Mc = 8.50 kN •m
F cf = L41 kN (C )
www.FreeLibros.me
Fc o = 473 kN (C)

Fbf = 1.15 kN (T)
Fab = 646kN (T )
F'a c = F a d = L 5 0 k N ( O

Fbc = F bd = 3.70 kN (C )
Fbe = 4.80 kN (T)
F b c = F b d = 134 kN (C)

FAa = 2 4 k N (C )

F aC = F ae = L01 kN (T )

R e s p u e s t a s a p r o b l e m a s s e l e c c io n a d o s 669

4 -9 . Nc = 0 4-21. V = { - 1 0 a 2 - 8 0 0 } Ib
V c = 1.25 kN 4-22.
4-10. Mc = 3.50 kN •m 4-23. M = { - 3 . 3 3 a j - 8 0 0 a - 1 2 0 0 } Ib - p i e
4-11. Nc = 0 4-25.
Vc = -(1870 k 4-26. V = { 0 .4 4 4 a 2 - 8 a + 3 6 ) kN
4-13. Mc = 11.2 k - p i e 4-27.
ND = 0 4-29. M = |0 .1 4 8 a s - 4 a 2 + 3 6 a - 1 0 8 ) k N - m
V D = Q930 k 4-30.
M „ = 11.0 k -p ie V'mix = - 3 8 6 Ib
Ne = 0 4-31. M m i,= -2100 Ib-pie
V E = 0.450 k
M f = -0.675 k -pie 4-33. - 4 8 9 kN
0 £ a < 1 m . V = 4.50 kN 4-34.
4-35. M mU = - 2 0 kN • m
M = {4 .5 0 a } kN -m 4-37. 10.1 k
4-38.
l m < i < 3 m , V = 0.500 kN 4-39. M na = - 6 0 k - pie
M = {0.5a: + 4} k N - m 4-41. V'mto = - 3 .0 4 k
] m < i < 4 m , l ' - - 5 5 0 kN 4-42. M mu = 11.6 k - pie
M = {-5.5(1» + 22} k N -m 4-43. v m* = - L25 kN
445. WmiX = 0.521 kN
4-14. 0 £ x < 4-46.
447. =V'mto - 5 1 0 Ib
M=— a 4-49.
Mu M „ a ,= 2401 Ib -p ie

a < L.V = 3wL
v«* = 8
M= - l)
9w L 2
4-15. ) S t < 2 m , V = 375 kN Moni, =
M = {3.75a} k N -m
4-17. ?m < i < 4 m , V = -3 2 5 kN 128
4-18. M = {-3.25a + 1 4 | kN -m V'ml, = - 1 8 6 kN
Moni, = 224 k N -m
4 -1 9 . 4m < a < 8 m. V'm*x = ± 1 2 0 0 Ib
M nU , = 6400 Ib -p ie
V = -3 2 5 kN. V'nnix3 - 3 .8 0 k
M = { -3 .2 5 a + 2 6 } k N • m M mÁ% = -5 5 .2 k -p ie
) < i < I m , K - —4 kN v mb = 24.5 kN
M = {-4 a } k N - m Mn** = 34.5 k N -m
1 m < a < 2 m . V = - 1 2 kN V mta = 83 kN
M = {-1 2 a + 8} k N - m M mix = - 1 8 0 kN • m
2m < a s 3 m . V = - 2 0 kN Vm* = -11.8 k
M = { - 2 0 a + 2 4 } kN -m Mn*> = -8 7 .6 k - pie
3 s a < 6 pie. V = {3 0 - 2 a ) k V míx = 12 k
M = { - a 2 + 30a - 216} k -p ie
5 p ie < A S 10 pies. V = 8.00 k = - 9 0 k - pie
M = { 8 a - 1 2 0 } k -pie 20.0 k
) £ a < 4 p ie . V = - 2 5 0 Ib
M = { - 2 5 0 a } Ib-pie M nU, = - 1 4 4 k -p ie
4 p ie s < a < 1 0 pies, V = { 1 0 5 0 - 1 5 0 a } Ib
M = { - 7 5 a 2 + 1 0 5 0 a - 4 0 0 0 } Ib-pie V'nni, = - 3 6 k
1 0 p ie s < a s 1 4 p ie s . V = 2 5 0 Ib
M = { 2 5 0 a - 3 5 0 0 } Ib-pie =M n i, 162 k - pie

Vm* = 13.3 kN
Mn** = 26.7 k N -m
V mto = -1 4 .5 kN
Moni, = 52.5 k N -m
V'nni, = 2 2 2 k
M m i, = 15.5 k - pie
V'nni, = 12 k
M oa, = - 9 0 k - pie

www.FreeLibros.me

'0 Respuestas a problem as selecc io n a d o s

apítulo 5 F CD = 88.1 Ib 5-27. By = 0116 k .f l , = 172 k
5-29. A , = 1 7 2 k, A y = 3.78 k
5-1. Fbc = 46.7 Ib F ba = 83.0 Ib
1 = 70.2 pies C , = 0.276 k. C y = Q216k
A, = 3k
5-2. /'n a , = 6.41 kN D *f = 8.06 k
y„ = 2.43 m A y = 1.94 k
T ad = 4.08 k
5-3. T a c = 1.60 kN
T c ¡> = 3.72 kN Capítulo 6
T áb = 2.99 kN
y„ = 110 m 6-15. (M e)m í, = 142 k N -m

5-5. P = 71.4 Ib (V'c)m4, = 2 0 k N
5-6. /», = 2.50 kN
6-17. ( * , W ) = 12.4 k
P2 = 6.25 kN
F ^ = 115 kN = -3 7 .5 k -pie
5-7. y = 0.0356*2 6-18. <MCW ) = H 2.5 k - p ic
T0 = 7.03 k
T b = 10.3 k ( ByW ) = 24.75 k
5 -9 . T min = 4(K> kN
T mit = 431 kN 6-19. M /Ím í*») = 20.1 k
5-10. w = 51.9 Ib/pie (M e )mí**» = 151 k - p ie
5-11. T m i t = 14.4 k
T mía = 13.0 k 6-21. ( V v W ) = 40.1 k
5-13. T mix = 10.9 k 6-22. ( Mo)ma« = - 4 k • pie
5-14. r mío = ioo k (M ^ )^ , = -86.4 k-pie
T m i t = 117 k (V, o)mtt = 5.40k
Tgmcbo = 10 k
5-15. Vmla= ± S h 6-23. ( f l , W (+) = 87.6kN
A/mi, = 6.25 k -pie
5-17. 7 mln = 6.25 MN (M c ),„4rt.) = 7 1 0 k N - m
T'mi, = 6.93 MN
5-18. y = (38.5x2 * 577^)(10 3) m ( V c U « - ) = -23.6 kN
T mit = 5.20 kN 6-25. M , W ) = 20.5k
5-19. T , = 7.0 kN
T e = T d = 8.75 kN (M £ )„ w *) = 51.25 k -p ie
Tp^ = t 31 kN
5-21. - 4 ,= 0 (V 'c-)mto( , ) = 3 3 .0 k
Cy = 9.55 kN
A y = 15.5 kN 6-26. ( V 'a c W ) = 7.15 kN
T = 4.32 kN
5-22. Fb = 6.77 k 6-27. (Me)má»(- , = -9.81 k N -m
FÁ = 10.8 k < V « : W > « 17.8 kN
Fc = 11.7 k (M c )m fa(t)= 46.7 k N -m
5-23. M „ = 10.8 k N -m
5-25. fl, = 46.7 k . f l , = 5.00 k 6-30. (V'Afl)¡n4, = 2 .7 3 k
A , = 46.7 k . A y = 95.0 k
C , = 46.7 k ,C f = 85 k 6-31. (M/»)m4, = 61.25 k • pie
5-26. 6 , = 43.75 pies (^flc)mái = 7 k
h2 = 75.00 pies (M c ) m4, = 105 k - p ie
hy = 93.75 pies
6-33. ( V /> ir W ) = -5 2 .9 k

6-34. (Mc)mM-> = -1 1 8 k -p ie
(V'm W * ) = 5.07 k
( M „ ) ^ t ) = 19.2 k - p i e

6-35. 0 'c /> W - , = - 6 k

6-37. (V'bcU - - , = -8 -2 1 kN
(M fl) m^ . ) = 113 k N - m

6-57. <^cd W ) = 12.0 k ( T )

6-58. ( * C f W > = 7.54k(T )
6-59. (M c ) n4, = 44.1 k N - m
6-61. (V'fl)m*x = 1 .4 6 k

6-62. ( M c U ^ ,) = 20.0 k N -m

6-63. (M c )mix<.> = 16.8 k - p ie

www.FreeLibros.me

R espu esta s a p r o b l e m a s se l e c c io n a d o s 671

6-65. (M c )« á * +) = 34.0 kN • m 7-5. F ed = 15.8 k (C )
6-66. (W c)m i« .) = 4 3 7 5 k -p ie F f e = 0.833 k (C )
6-67. (f a c U « = 237 k(T) F fc = 50 k (C)
6-69. W M , = 67.8 k N -m F a g = 12.1 k ( C )
6-70. Mmáx = 64.5 kN • m F bh = 1Z1 k (T )
6-71. V míx = 10 kN F ab = 7.67 k (T)
M mi, = - » kN • m F Gh = 9.67 k (C )
6-73. F b f == 0.417 k (C)
6-74. = 555 k -p ie F CC == 0.417 k (T)
6-75. V&i = 67.5 kN
6-77. F f g -- 19.7 k (C)
6-78. M mi% = 164 k N -m F bc == 17.7 k (T )
fr-79. A/,,,*, = 97.2 k • pie
6-81. Fdf = 11.25 k (C)
- 130k-pie
V * = 12.5 k F Ce = 11.25 k (T )
F e f =- 11.0 k ( C )
= 10.5 k -p ie F Cd == 9.00 k (T )
F a h = 14.25 k (C)
Capítulo 7

7-1. F a e = Fb f = 14.1 kN (C ) F bg = 7.00 k (C )
= 10.0 kN (C) F d e = 13.75 k (C )

F a b = 10.0 kN (T) 7-6. F ag = F b f = F d f = 0
F c b = F bd = 14.1 kN (C) F ce = 22.5 k (T)
F D E ~= 10.0 k N (C) F de = 20.5 k (C )
F BC == 10.0 kN (T ) F bh = 24.2 k (T)
F AF =- 60.0 k N (C) F g h = 19.3 k (C )
F b e == 20.0 k N (C) F a b == 2 0 0 k (C)

7-2. F c d =- 30.0 kN (C) F e a =- 0 8 3 3 k (T)
F a e == F e s = 0
F f c == 20.0 k (C)
F b f == 28.3 kN (T)
Fbc = 17.3 k ( T )
F e f =- 20.0 k N (C)
F e f =- 20.0 kN (C)
F AH == 0
F c d == 0
F b d == 28.3 kN (T ) F a h = 21.5 k (C )
F of. ~= 20.0 kN (C ) F bg = 14.5 k (C )
F b c == 0 F c f = 14.0 k (C)
F Af = TO.O kN (C) F de = 20.5 k (C )

F be = 40.0 kN ( Q 7-7. F ec = 3.33 kN (T)
F bd = 3.33 kN (C )
F cd 40.0 kN (C) F ed = 267 kN (T)
F bc - 267 kN (C)
7-3. F hb = 5.89 k (T) F cd = 200 kN (T)
F ac = 5.89 k (C) F f b - 10.0 kN (T )
F ab = 9.17 k (T )

F a h = 14.2 k (C)

F hc - 417 k (C)

F gc = 1.18 k (C) F a e = 10.0 kN (C )
F f e = 13.3 kN (T)
F bf - 1.18 k (T) F ab - 13.3 kN (C)
F b e = 4.00 kN (T)
F gf : 7.5 k (C) F af = 600 kN (T)
7 -9 . F dg = 248 k (C)
FGb = 5 .0 k (C) F c f - 248 k (T)
F BC - 12.5 k (T )

F ec = 8.25 k (T)
F df = 8.25 k (C)

F cd = 5.83 k (T) F f c - 3.25 k (C )

www.FreeLibros.me

672 R espu esta s a pr o b l e m a s se l e c c io n a d o s

7-10. Fcd = 325 k (T) 7-21. A , = 18.0 kN
F ac = 389 k (C) 7-22. fí, = 6.00 kN
7-11. Fflc = 3.89 k (T ) 7-23. By = 18.0 kN
Fbc = 7.75 k (T ) Fijos:
7-13. F*g = 7.75 k (C) 7-25. A , = 6 0 0 kN
7-14. F ef = 2.12 k (C) 7-26. A y = 9.00 kN
7-15. FDE = 1.50 k ( T ) 7-27. M a = 18.0 k N -m
7-17. F„f = 0 250 k (C) B , = 6.00 kN
7-18. By = 9.00 kN
7-19. Feo = 100 k (C) M„ = 18.0 k N -m
Fa b = 275 k (T ) Fc f = 1.77 k (T )

Fnc = F ac = 0 Fc e = 1-06 k ( T )
Fcf = 4.95 k (T) A , = 1.50 k
Fc o = L50 k (T) A y = 1.875 k
F fc = 5.00 k (C )
M a = 9.00 k -p ie
Fue = 7.78 k (T) B , = 1.50 k
Fbc = 300 k (T) By = 1.875 k
F aG = 10.5 k (C)
F ef = 2.12 k (C) M b = 9.00 k -p ie
F o t = 1.50 k ( T ) F p c = 3.125 k (C)
F o f = 2.00 k (C ) Fc n = 2 0 0 k (T)
Fea = 5.50 k (C) F fg = 100 k (C)
f ab = o F nF = 3.125 k (T)
Fd f = 6.67 kN (T )
Fcf. = 6.67 kN (C) F df. = 3.00 k (C)
Fcd = 5.33 kN (C) F f.g = 27.5 k N (T )
F a c = 15.0 k N ( T ) F ff = 24.0 kN (C )

F Bf = 15.0 k N (C ) F eo = 4-00 kN (C)
Fef = 5.33 kN (T) Fce = 27.5 kN (C)
F ac = 22.7kN (C) Fde = 20.0 kN (T)
F EG = 15.0 k N (T )
F af = 22.7 kN (T)
Fde = 4.00 kN (C) F e o = 4.00 kN (C)
Fcf = 300 kN (C) Fpp = 14.0 kN (C)
Fa b = 9 0 0 kN (T )
M Á = 4.86 k N -m FCe = 15.0 k N (C)
M„ = 3.78 k N -m F oe = 10.0 k N (T)
Mf = 4.05 k -pie A , = 10.0 kN
M „ = 7.20 k -p ie A y = 14.0 kN
Ma = 40.3 k N -m M a = 30.0 k N -m
M , = 9.00 k - pie B , = 10.0 kN
Ml = 20.25 k •pie Byy = 14.0 kN
M „ = 27.0 k - pie M b = 30.0 k N -m
A, = 0 ;B ,= 0 ;C , = 0 F f h = 17.5 k N (C )
A y = 12 k; ñ y = 16 k; C y = 4 k F ef = 16.5 k N (C )
M a = 16.2 k - p ie; Aio = 9 k -p ie ; Fgh = 17.0 kN (T )
M c = 7.2 k -pie F e h - 17.5 kN (T)
A rticu lado s: Fhi = 400 kN (C)
A , = 600 kN
F p , = 17.5 k N (C)

www.FreeLibros.me

R espu esta s a p r o b l e m a s se l e c c io n a d o s 673

Fde = 4.50 kN (T) ~6El
F'di := 17.5 k N (T ) wa*
FC,== 25.0 k N (C )
7 -2 9 . A , = ZOO k 8- 6. WL*
8-7.
7-30. 1.125 k 18V 3E l
8-9. 5wol?
7-31. M Á = 12.0 k -p ie
7-33. B x = ZOO k 192E l
7-34. B , = 1.125 k WqX
M „ *= 12.0 k -p ie V = (4 0 L 7x 7 - I6x* - 25L A)
960E lL
Fgk = 1.875 k (C )
F'c e = 0 w0l *
F jk = (1500 k (C) Pmí» = 120E l
A , = ZOO k
A , = 1.875 k Iwa3
6E l
B , =ZOO k waxi
B , = 1.875 k v, = (2x\ - 9a»,)
F g k = 3.125 k (C ) 12FJ
Fgf = 0 7h’oj
F jk = (1500 k (T) Vc 12E l
F fg = 0
F e h = 0.500 k (T) Vi = Ú i ( ~ x í + 8<u’- " + 4 ,3 x 3 " “4)
F f h = 3.125 k (C ) 8- 10. 0B = 0.00268 ra d \
F hc = 4.02 kN (C)
F k l = 5.29 kN (T) A **, = 0.322 pulg i
F hl = 5.43 kN (C)
f hg = 2.52 kN (C) 8 - 11. e B = 0.00268 rad
F k l = 1.86 kN (T)
F hl = Z 99 kN (C) 8-13. AnUa = 0.322 pulg i

Capítulo 8 8-14. 3937.5 k •pie2 _
8-15. Bc =
8-17.
El
Fo(o ~ L) 50.625 k • pie3
Ac =

El
a = 0.153L
a = 0.153 L

L
“°3

8 - 1* 0A 2FJ

Pxx 8-18. «cc = —4 E l X
V' ^ 6 E Ífl* i +
~ L )\

Fa 8-19.

** = Ü f i x* Xi ~ L) +

8- 2. 3P L 2 8- 21. ACc = 4—E l 't
*-*• 0C = 0.00171 ra d ^
B 8- 22. Ac = 3.86 mm i
a = 0.152 L
A SE/ 8-23. a = 0.152/.
8-25.
- r i? 18 k N -m 2
0B =
Vc ~ ~ 6 e T
£/
„ _ ■■p L ' 90 kN • m3
*» - 48É/ AC =

»I = + 4o' f - « A » El

•» = S S < 4 ,) * a - 4 ¿ )

www.FreeLibros.me

674 R espu esta s a pr o b l e m a s se l e c c io n a d o s

8-26. 6a = 7 /V A 9-6. A E' = 2.95 m m i
8-27. 9-7. 199 k N • m ,
8-29. 4Fl 9-9.
8-30. 9-10. Ad- A E 1
8-31. Ac = 9P a3 9-11. A , t = 0.0392 pulg i
8-33. Af = 00392 pulg i
8-34. AE! 1 9-13.
A Aw = 0 0 5 8 2 p u lg i
0S = IPa7 7 9-14. 170 k • pie
9-15.
4E l 9-17. A“- A E '
9-18. 170 k -p ie
Ac = 9/V 1 9-19.
A°‘ AE
AEI Ac, = 4.91 m m l
A x> = 0.0341 p u lg l
P
A Av = 0.0341 p u lg l
F=
A ^ = 0.507p ulgt
A

0» = SPa7 7

12E l

Ac = 3 Per' 1

AEI

0« = SPa7 7

12E l

AC = 3 Pa* 1 9-21. \ P° i
Ac 4SEÍ*
AEI 9-22.

MpL 9-23. PÜ
9-25. A
0A = 9-26.
2AEI 16E l

0.00802 M nL 2 , Ac = PL3
A -,, -
AHEI 1
El

0C = 3Po* PLl

El A
16F .I

25 Pa3 ■ 2 Pa*
Ac = Ac = 1
3E l
6£ /

8-35. 0C = SP a7
8-37. £/
8-38. 0C =
»-39. 6E l

25 Po3 ■ SP a7
AC =
0c =
6E l 6E l

75 kN -m * 9-27. e
0/> = 9-29.
9-30. A 6EI
FJ 9-31.
9-33. 0C = 0.00156 ra d ^
169 k N • m3
9-34.
Ac ~ El Ac = Q145 pulg 1
9-35.
1008 k - pie* 0C = 0.00156 ra d \
0O =
Ac = 0145 pulg i
El

A„ = 10368 k -p ie 3 Bc = 0.00670 'x

El i

Ac = 0282 pulg i

1008 k • pie* , 3 1 5 0 N - m 2 T_
0O = 0« =

El El

10368 k -p ie 3 6637.5 N -m 3
An =
A» = El i
El

Capítulo 9 3150 N -m 2
0fl =
9 -1 . \ Ai = ü 536 m m i
9 - 2 . A ,, = (1536 m m 1 El
9 - 3 . A fl. = 3.38 m m l
9 - 5 . A Ef = 2.95 mm i 6637.5 N -m 3 .

Ah = El 1

08 = 0.00448 rad A

A fl = 0.455 pulg

www.FreeLibros.me

R espu esta s a p r o b l e m a s se l e c c io n a d o s 675

9-37. 0„ = 0.00*48 rad ¿ 10-3. 4, = 0
10-5. 51wL
9-38. AB = 0.469 p u lg l
9-39. _A ' 128
9-41 .
H - 1WL
9-42. Ac 120£7 B ’ 128
9-43.
9-45. w0L* . w 9wL}
9-46. Ac 120£7 M a 128
9-47.
9-49. 9 kN -m 2 _ 1/*
9-50. :h o á
9-51. = El 7 I II
9-53. 22.95 k N -m 3 ,
9-54. El 1
9-55. 1397 k - p ic 3
9-57.
9-58. Ad E l 1
9-59.
9-61. 1397 k - p ie 3 . 10-6. B , = 37.7 k
A° E l 1 10-7. *4, = 0
A f = 17.1 k
440 k •pie3 . C , = 17.1 k
= El 1 A,, = 1.50 mm
5wL4
Ac . - ~
C* S E I

wL* 10-9. Ac = 2640 k -p ie3

' _ 4E? ¿,

1148 k - p i e 3 10-10. B , = 75 Ib

^ El - *4, = 0
1148 k - p ic 3
A y = 75 Ib
Ac* E l
(Ac )t = 2.81 mm 1 M a = 200 Ib-pie
10-11. By = 7.20 k
(Ac ) , = 2.81 mm i

0A = 0.414(10~3) rad A , = 0.900 k

0A = 0.414(10"3) rad -4, = 0
(Ac )a = 0.0*01 p u lg — Cy = 0900 k
10-13. C x = 3.75 k
79.1 k - pie3 A , = 21.75 k
Cy = 42.4 k
(A c)* El

79.1 k - p ic 3

(Ac)‘ = - E l A , = 29.6 k

417 k -p ic3, 10-14. C y = 1.875 k

(Ac ) . - £/ i

Capítulo 10 A , = 3.00 k
A y = 3.125 k
10-1. * 4 , - 0 M a = 6.25 k • pie
10-15. A y = 4.35 k
2wqL
A> ~ - —

y 10 C, = 0
, . *v0L 2 C r = 5.65 k
Mc = 10.4 k • pie
10-2. c, = o 10-17. Cy = » . 0 kN
A , = 33.0 kN
C , = 14.625 k
A , = 24.0 kN
B , = 30.75 k M a = 45.0 k N -m
A y = 2.625 k

www.FreeLibros.me

676 R espu esta s a pr o b l e m a s se l e c c io n a d o s

10-18. A y = -15.0 k 1 0 -3 3 . F 0b = 19.2 kN
FCB = 53.4 kN
D , = 2 1c
Dy = 15.0 k 10-34. F « o = 22.8 k (C )
F a b = 18.4 k (T )
M „ = 19.5 k - p ie
10-19. D, = -2 2 7 k F ac = 16.3 k ( T )
1 0 -3 5 . F bc = 28.1 k (T )
Dy = 22.5 k 10-37. C , = 0

A y = 22.5 k c mt
A, = 227 k C' " 3
10- 2 1 . D , = 5.41 k 1 0 -3 8 . FCo = 7.48 k ip
A , = 259 k 10-39. F ac = 28.0 k
Dy = 4.65 k 10-15. C y = 0241 k
A y = 4.65 k
10- 2 2 . fí, = 2.65 kN C apítulo 11
A, = 265 kN
fl, = 0 1 1 -1 . M a = - 4.62 k -p ie

Ay = 0 M b = -& 7 6 k -pie
1 0 -2 3 . fí, = 1.53 kN Mc = - 10.6 k - pie

A , = 1.53 kN 1 1 -2 M a B = -102 k-pie
By = 750 kN
M ba = 84 k • pie

M bc = -8 4 k -pie

A y = 15.0 kN Mca = 48 k-pie

1 0 -2 5 . F a b = 0.667 k (C) 11-3. M ab = -18.5 kN -m
Fb d = 0.667 k (T)
Mcb = 20.4 k N -m

Fbc = 0 M ba = 1925 kN • m
10-26. Fc b = 3.06 k (C ) Mac = -19.25 kN -m

F4C= & 23k(C) 11-5. M ab = 4.09 k N -m
Mba = 8.18 k N -m
F oc = 658k(T )
F Ofl = 5 .1 0 k (T ) Mac = -8.18 k N -m

F ^ = 10.1 k (C) Mc b = 8.18 k N -m
F D„ = 4 9 4 k ( T ) Mco = -8 1 8 kN -m
M I)C = - 4 0 9 k N • m
1 0 -2 7 . F a c = 7.91 k N (C )

10-29. = 8.54 kN (C) 11-6. M ab = -49.5 k -pie
M ba = 13.5 k - pie
= 6-0* ^N (T)
F ab = 6.04 kN (T) M a c = -1 3 .5 k - pie
F e a = >4.1 k N (T )
Fc o = 10.0 k N (C) Mea = 9 k -p ic
F BE = 5.61 k N (T )
F bd = 14.0 kN (C) M eo = - 9 k • pie
F o e = 3.96 kN (C) M o c = 40.5 k -pie
1 0 -3 0 . F a c = 1.41 k (T )
F'd c = F c b = 0.414 k (T ) 1 1 -7 . M Ba = 4 1 2 5 k N - m

= 0.414 k (T ) M ac = -41.25 k N -m

1 1 -9 . M ab = -1 6 7 k - pie

M Ba = 6 6.0 k - pie
Mae = -66.0 k-pie

Foa = 0 586 k (C) Mch = 261 k -pie
1 0 -3 1 . Fc o = 4.63 kN (T)
M Co = - 2 6 1 k - pie

www.FreeLibros.me

R espu esta s a p r o b l e m a s se l e c c io n a d o s 677

11-10. M a B = - 10.5 k - p ie 12-7. A , = 0
M ba = 24 k-pie A y = 33 kN
B j = 33 kN
11-11. M a b = -2 4 .5 k • pie M a = 30 kN -m
M Ba = -Q 9 2 3 k - pie Cy = 6kN
M ac = 0.923 k -p ie
Mc b = 77.2 k - pie 12-14. M a b = - Z 30 k -p ie
M Cd = -2 7 .2 k - p ie M ba = 19.4 k • pie
M bc = -1 9 .4 k -p ie
11-13. M AB = - 1 2 6 k • pie Mca = 0
M ^ = 72k-pie
M a c = - 7 2 k • pie 12-15. A , = 29.3 k
Mc b = - 3 6 k • pie A y = 96.0 k

11-14. M a b = - 42.9 k -p ie M a = 146 k -p ie
M Cb = 16.7 k - pie D , = 29.3 k
Dy = % .0 k
11-15. M a b = - 1.98 k N - m M d = 146 k - pie
M ba = 0.540 kN • m 12-19. M a = 20.6 kN -m
Mac = -0.540 kN -m M b = -41.1 kN -m
Mc = -41.1 kN -m
11-17. M a B = - Z llk - p ie M d = 20.6 k N -m
M b a = 40.8 k -pie 12-22. M a b = 128 k - pie
M bc = -4 0 .8 k • pie M ba = 218 k -p ie
M bc = - 2 1 8 k - pie
11-18. M BA = <fí.8 k N -m M Cb = 175 k -p ie
m bc = - M 9 kN • m Mcd = -175 k-pie
M bd = -34.9 kN • m M dc = -5 5 .7 k -p ie
12-23. M ba = ~ 104 k • pie
11-19. M p c = ~ 13.4 k • pie M bc = 104 k-pie
M Cd = 13.4 k - p ie Mc b = 196 k -p ie
M da = 13.4 k - pie Mcd = -1 9 6 k •pie
Mcb = -13.4 k-pie M ab = M d c = 0
12-25. M ba = 24.0 k -p ie
11-21. M dc = 64.0k N -m M bc = “ 24.0 k • pie
M Cd = 80.0 k N -m M Cb = “ 24.0 k • pie
M da = -6 4 .0 kN -m Mcd = 24.0 k - pie
M Cb = -8 0 .0 k N -m 12-26. M d a = 14.2 k - pie
M dc = -1 4 .2 k -p ie
11-22. M Mi = -25.9 kN •m Mcd = -7.54 k-pie
M da = -3 3 2 kN •m Mc b = 7.54 k - pie
M dc = 3.32 k N -m
M Cd = 6 3 2 k N - m C apítulo 13
M bc = -9.43 k N -m
Mcb = “ 632 kN • m 1 3 -L M ab = -3 4 8 k • pie
M ba = 301 k -p ie
11-23. M a b = 25.4 k - pie M bc = -301 k -p ie
M dc = -5 6 .7 k - pie M Cb = 348 k - p ie

Capítulo 12 www.FreeLibros.me

12-1. M b = M c = -8 4 .0 k -p ie
12-2. M a = -2 3 0 k-pie

M b = - 1 8 7 k - pie
Mc = -1 2 2 k - pie

678 R espu esta s a pr o b l e m a s se l e c c io n a d o s

1 3 - 2 . M ab = -3 4 8 k - pie M d c = “ 28.3 k -p ie
M a b = M Cd = 0
Mba = 301 k -p ie 1 3 -1 1 . M c o = M BA = 180k - p ie
M k = -301 k-pie M cf = M Be = 94.6 k - p ie
Mcb = 348 k -pie M cb = M bc = -2 7 4 k -p ie
M p c = M Eb = 47.3 k - pie
1 3 -3 . M ac = 37.6 k •pie

Mca = 75.1 k - pie

M c b = “ 75.1 k -p ie C a p ítu lo 14
Mgc = 369 k-pie 14-1.

13-5. M ab = 0
M Ba = ft>4 k • pie
510.72 0 -2 0 1 J9 0 -154.67 -1 1 6 -1 54.67 116
0 0 -116 -8 7 .0 116 -8 7 .0
Mgc = -610 k-pie 0 174 00 0
M b f = 5.53 k • pie 201.39 00 0 0 0
KV —- -2 01.39 0 0 0 154.67 0 0 0
0 0 0 0 116 116 0 0
M fb = 2.77 k • pie -1 1 6 0 00 87.0 0
Mcb = 610 k-pie -1 5 4 .6 7 -8 7 .0 0 0 154.67 -1 1 6
116 0 00 0 -1 1 6 8 7 .0
-1 1 6 -8 7 .0
-1 5 4 .6 7

116

M eo = -604 k •pie

Mce = -5.53 k-pie 14-2. D , = 0
D j = -0.0230 pulg
M F. c = "2 -7 7 k -p ie
1 4 - 3 . <7, = 33.3 k (C )
Mac = 0 q2= 0
q 2 = 3.33 k (T)
13-6. Mab = 0
M b a = 604 k -p ie 14-5. /), = -0.00172 pulg
q 2 = 12.7 Ib (C )
M Bc ~ - 6 1 0 k - pie
1 4 -6 . q 7 = 6.57 k (C )
M hf = 5.53 k -pie 14-7. k =
M fb = 2.77 k -p ie
Mcb = 610 k -pie

Mcd = -604 k-pie

Mce = “ 5.53 k • pie
Me c = -2 .7 7 k • pie

Mdc = 0 703.033 -53.033 -53.033 53.033 -150 0 0 0 0
-S .ID 3 53033 53.033 -53.033 0 0 0 0 0
13-7. M a b = 1-75 k - p ie -S.CB3 53033 256066 0 0 0 -53033 -53033 -150
M Ba = 3.51 k - pie 53.033 -S .Q 3 3 0 256.066 0 -150 -53033 -53033 0
-150 0 -150 0 0
Mac = -3.51 k -p ie 000 300 ISO 0 0 0
0 0 0 -150 0 0 203033 53.033 0
M c b = 3.51 k -pie 0 0 -53.033 -53.033 -150 0 53.033 53.033 0
Mcd = -3.51 k -p ie 0 0 -53.033 -530 33 0 0 0 0 150
0 0 -150 0 0 0 0 0 0
0 00 0 0

M nc = -1.75 k-pie

13-9. M ba = 28.3 k -p ie 14-9. k -

Mbd = -28.3 k -p ie U 3 4 28.8 - 7 5 0 -3 8 .4 -2 8 .8 0 0 0 0
M db = 28.3 k -p ie
Mdc = -28.3 k -p ie 28? 21.6 0 0 -28.8 -2 1.6 0 0 0 0

- 7 5 0 150 0 0 0 0 0 - 7 5 0

0 0 0 100 0 -10 0 0 0 0 0

M ab = M cd = 0 -3S.4 -3B.8 0 0 1518 0 0 - 7 5 -38 .4 28.8

1 3 - 1 0 . M ba = 28.3 k -p ie -28.8 - 2 1 .6 0 -1 0 0 0 143.2 0 0 28* -21.6

0 0 0 0 0 0 100 0 0 -10 0

M bd = -28.3 k -pie 0 0 0 0 -75 0 0 75 0 0
Mdb = 283 k-pie
0 0 - 7 5 0 - 3 8 4 28.8 0 0 113.4 - a *

0 0 0 0 28J* -2 1 .6 - 1 0 0 0 - 2 8 * 121.6.

www.FreeLibros.me