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SoLUTIONS MANUAL ENGINEERING MECHANICS
of So�J]2T�
EGOR P. POPOV
SOLUTIONS MANUAL ENGINEERING . MECHANICS
of So1JJ2T�
EGoR
P. Porov
PRENTICE HALL, Upper Saddle River, NJ 07458
Acquisitions Editor: Eric Svendsen Special Projects Manager: Barbara A. Murray Production Editor: Michele Wells Supplement Cover Manager: Paul Gourhan Supplement Cover Designer: PM Workshop Inc. Manufacturing Buyer: Pat Brown
© 1999 by Prentice-Hall, Inc. A Pearson Education Company Upper Saddle River, NJ 07458
All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher
Printed in the United States of America 10 9 8 7 6 5 4
ISBN
D-13-080431-2
Prentice-Hall International (UK) Limited.London Prentice-Hall of Australia Pty. Limited, Sydney Prentice-Hall Canada Inc., Toronto Prentice-Hall Hispanoamericana, S.A., Mexico Prentice-Hall of India Prívate Limited, New Delhi Prentice-Hall of Japan, Inc., Tokyo Pearson Education Asia Pte. Ltd., Singapore Editora Prentice-Hall do Brasil, Ltda., Rio de Janeiro
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rool
Po."
-f"4o-f xsp
= - 64�N
V o. _-
(4+8)K./-5"
.z
Vo. = ix40 - / «so
4
- 5 Te -==. -J.41 �¡.¡
=- 2 �N
'1-11
Te
Te
=
JI.
RA
-=
:z.s
kN
3 Pc� -- s Tc ::: 6. 7S k N ( -l:U1.S1M )
T2
= 3,.f;í
,
T,
= �rs
.Ltv1A =o
Vs = 6 l/0
}: p =o
pi,.
I. V=o
Vo.=-3
¿ f,/tG\=O
jvfo. ::::
V°' ==
¡-, ..... -
Ma::::
)( sº « 3 x 2 + 4 Te. X 3::t.3 kN-m :J. :l. S
'i
=
HF
=-3 (K)
¿ MF
b k-f t
i .,.., ->
-=-3.0k.N
Pi,. == 6. ?S l
:.(>
7-20
V.__ ! +____.! __
1
M�
1 Te.= Re,
-pL
7-21 R&
3P
.
Z..H =o
Te.= 4-0/.3 = 13. 3 J{N HA == 3/s Te. = s 1
2:.v==o
VA= 12-t8-"';fTc=7·31
!V
1
+
:2.P
vi
-p
-p
p
i .-M �
- .2.J>L
66
P
P
cb>
Te
f
VF = e¡ kN t
L V=o
1-18
XM1i =o
,._
]
1-22! y
1
-!..
;� -
..3
7-261
+
-
1
--p
::E 3
.3
M '' l )( ) M
1
:f.
= -
(:<)=
1
N'cx)
3
e,=
�
M �PL er
RA
4 ;;t;
X13
-?.X"'tC,
z:
e�
'
= � ( 1"t3Y12x4) =
X�
3
X >3
12
C:i"' 12- �,\�Xl2= -{;
when X=o . Klo)::0
1-Z 1 1-24
l
I
R A=
t l � ·di)( 6
Mtx)-: 4.x -1<
v'==-J<í'<
M
1
4 �N
z:
�3
..::i
V=-� +C :z.
x= L, v=o � e /Vf
-:<
,e L)
= 2-,r� i" 2
e:{: L�
_1$.... L:: a ;2.
?(3 __1S_ L?( T e, = -� + b 2.
X=L, M=o=?
e,=
-l
N IX'-= _!f x - � -X 2. +
3
_!._ X 2
2
2
' 1
· 2X · � 3
x�3
3 ==&x-3/· +..!..x 2 3
M l:O = � x
= q-
M�
- +i3>"bU-q X '>3
3
2)(
-�Kl.
1�1.sl
p
V1
+1-
L.e.z
.2. L-____.
1-301 M = RA "X -
L----' .
K � �
2 'X •
M '== RA -1
Rs
67
= - +' l
3
'?C
Rs
==
RA - l
_L
+
'- K�
2.
'..<' x: i<.::C 3.z..
=1\1.4,.f�?(-� K
2
L .----.(
1-32
2
M (()) =- /000
Xº· j
'P ( 8) � /coo -"
:S,>, I) :::
3
+ K;< .3
2CO
Si'.,,
Prob. 7-24 •--�---------------1 7-31
M ( lt )
v e e) = p ( &) =
e {,bS B
-t
s,-,, · EJ J
.E: ( �s ()
-
s» 6 )
-P ::z
2
'7-34
A
.A
F
_.§..
.1
=-J'
V= - � -x.3 + e, .3
V=-o
so
,x"'- + ./.le e';{ -A v /2.
M=
( Sin B + f - C.Os fl )
.2
I
Ot
-x= L,,
Sll><:R..
S,"/1 � ( -f:ensic,, )
= - PR
V
&
V ( f)) == /ooo Cos &
'1 - 3 3
('
see soluÜCll
�=
.Sin<:!l
L . M
i kL-:a
=o
-t'
so
c.,=; �L� c2 e2
= -: {
= -p J-.C:.cl.
p == r' ,-p. o( siA. ( 9-,o
¿.,V= -7°1'-Ar;).
e,. M =
C.-0(
9-c{)
'f t- � ol. si"' e � -ol. }
1-38
J. V==-�?<, I
.,Z
sin�
-x= o
,
-k
L ...3
P" j,9-pr-.$;"-cG-oOd.r).
p = ? r- (
1- �
G)
C, :::
-So
v= ��?r-�rB-�>kl.
L.M=o
/�
V == - '(Jt- .s_,;, 8
Cs: =-o
V o
::: "f>l'-Si/1. (-{))
H = j\,,....,s;11.c&- . 0J..� o
l,a.r AS:
V::; -t
1-3�
F
M::: -FCL-"l:)
T� Fo.
bL\r 8C : V = ;- F M:::
-F(a.-�,
T�o
68
VI:::
I< S,)i. .::Z.1L X L . .
V= -
t<.t. � � � L. .27t
-+ e,
Kl� -· · 2"11 + e, x-r C2 s,-,._ --'X M = -L 47tª
4
.si,tt.A.
L
"X=O'
.so e, = o ,
v=::z.p
M=t>
e..
o
=
M1 M2
v=P
=
:i
=
p -x + e,
p-x
'X=t,\-tV
M:sO:> C:a=-CA+1')p
-x= ().., /
O. � 1e � 4'.:tb
C:a
-t
M1 =M.2 � C,z:-(.:,o.-t-b)P
L-
1
, p _+____1
o.
o
t1 M=M,-
V=O.
v-----
MI 7-411
¡K
t
-M, M= -'X L
y:::_ L.
M
7-441 V=-p
-M•
V
M= C.1
M= -p-x+c� ')(:: o
,-------.¡ ]ji_ L
M=
4'C=
l-t",
M=D
,
C.:
M
I
1
o. t
M
�t
1..'f'A
1--..,--1 "wt
1-451
-;?"' -11,
o
.
1
C.2::
PC�1'1>)
�
a+b
l -
1
;
+�
V=2, M= :2?C+C..1.
v= -2
..
0$'X�3
3-!:'JC�b t'l= :-2x+ca , 6 � ,e� e¡
M==to-:t�ca.
v-=10,
1
¡_
M==o,
fl>
tvf::-M, � C�=-M, ·
,.,,
V
V
e, ?C -te� . v=- e,
-X=o.
M= Ph:; C,
-x= �+b,
-.::::::::::::: -11' 7-421
Cl+l>
•
V= -10. M=-Jo?C+C,., e¡
69
�':t'�
12
?(::.O •
M=o
C.1 :s O
-:x:::. 3
M=b M=3b
e»
=24
C.3
:r:4g
M=30
C+= 110
-?C=6 -x:: q 'X -=12
M :: - :;- P"' � e, J
P1' .,. e� = 3 ..3 M = -3 P?C + e�
M
I
o .«
M=o
�=o,
M
¡o�N
V
2r..N
�
f
1
1
-�kf.l
i
c.,==o
M=O,
-E; .
=
= - po.
e :i
M= � • C.3=
- 1
M
...3
= o
p()..
o. I<.
.-10 )(..f.J
·3�
M o
3"1
6"'
'im
119'1
M
1-4-G j Vt�)= -30,< + 180 V(.()
= - 3O X + 3O
1-481
v= 10.
v= z .
v=-a.
"= 4.
o , �=+.
-X.:::
-42.l'H� -150lcN
.
· 34;. 6 k#-111 �
'J-4'1
I
«r __ , V -
V::
V=
.!S
_ap
-�
-Jp 70
7 :!: «e u:
= 4?C+C.s- ,.�"1(�22 c_,,;:O· M=o .
M=-8-x+C.4
/()�-X�,,
M
Jv1
= -1:1.
M; 18.
"X•/{).
M.::::a-4.
"'X=lb. ..:,c:=;12,
M= -2.4, M =o.
Jote.
Jkl -� ,c.
4�'X�7
M =1t>?C-r� M:r 2-x-r(:.J
,,c=1.
V
p
o �"' �4
V =-.3 • M:11-3-x+ e,
e�== -52
C.3•
4
C4
a /t,4"
Cs-
�8'8
o.
=
I<.
41<.
-
L,:
j
\/0 = � "q"l'2o
1-4-9
=
V(x)= (-soo)l.lbH5330 +200 l X-lb)
54-0 l
=
Mo=- - '�°C3xz.t6x5) = . .:.2160 kN-t11
V ex) ::
2oox- s�10
-'2 O X "2-+ 5 40
H (x ) = - �o 'X 3 + 540 )( -'21 bO
0$. X � 3 3330 lb
V o -2�?olb
M� - 21bO 1'-N·"'
7-50
�o=
-fl-1"x3,:¡5,..4-)
vtx)= -Is� .s .x
1'1 co::
-15�-t
-151<1\J
7-52
VU.)=--5X-+IOO
-. -f x2
{x� -
! J.'
Vli',) = O
10� X� 6Ci
Vt�J= -5x-+3oO
bO 5. X
f �O
HC;() = - 2.s"Ji=-+100-x
/,'l�
V
=
V
H D< J =
4.'í3"'
�
I
ooo
-151::AJ
- IS!vJ
V �
-iotN
'7-!il
Vlx)=
4-iox'20= soo111i
io = &3'2.5 x
l
o�x�4
Vtt.):. l83"2,5)(4-)-SOoLx-4-) = -SOOX-+5330 71
2omir\
'T-53
V
R
=
+t1xtSxbx5) = 7.5 kN 4Sl:N
+
4.5�N
+
�-J
V
..._____� -3 �N
31., lb-in
-60 lb
-?slb
M¿+�
+
1-51 R t =
1
1 6 r.bX&- 2x6x&x3-
= -7 �
-2�N-rí1
Rr = z:
1
1
-
2 }:.
1
2x 3x�i2)
t
( � 2Y3lC�X�-2thxt�3- (,J< 2)
V V
-,�· M
�V -24k.-
1-5�
�t
-IE,k-H
�k
/ t ;\
V�
H� 72
�20
-3CH.-n
7-5�
�-n
1-63\
1-GO
I
V
1-64]
V
'º l
+
.
V(kN)
�
�b/,lfl.
M '7-6b
V
'lO ICIV-m
r:::::=::::::::
73
o
4m
I
.1111
�ókN
?.-!��� ....,.. 2..., -
O
.. JO kN
1-51
3k ltt
1-70
.3ofl.
e:!Illi1lt� S'
IO'
VO:} o
t.--:-; :-� ¡_I_{+-;.-o_wo tJ.:__,n-�1.fo.0,1
n
'"-_ I
'º'
S'
JSo
ID
10
1ookN/"'
:
2•1
./'! l c-+>::::::::::, ./'<+) /�
V C l.:N)
1 (-)/
o
-1.01./'
-.eso
100
MC<-F:l�
.
<+>
o � o
-.coo
'7-1!
Pon V(N)
> --,--_ ---�-e o---�
M
MCk-k)
0,-.::::-�-:--7�--+---+-�--__.��=-"º 2'. } - _s:.
0 = 7rR3 =
R=
90
4
(+)
10000
111. 11
Oc,JI
1r---.... 2� V(t}
M _
.S= --- -- = 111• 11
,
mm
s-. 21
a
mm
use 11 mm ol<.� �J.. sAA-ft
-IS'·...,_
4-V Lmd\x = --
dA
..... ,r
74
4:,1.St> = -----
= O. 7o MPA
<
lA/1 .·.o.k.
m•
1-'721
,<, "7' m• � ...�kzzzzzzzz=q( ,� l.� l�/¡:e
8'
p
-100o
�15
V (Jb)
o
<
-----==--º
o
(16)
\ 2
:
�
� o
1 e�> �
1 �(-)
3.7,;'
J
•
r
�
703
'7-75"1
--i2S
e
f
R= 414/o.4= 4o
KN/rfl
á
200
(o.)
MU,-lh)�
o�
, --,-o -� -200
7-,3
I
bOkN
----(4C
l
e
8
(e)
40:'f A. A
-
8
-
1
- 68 l
:Z.4 f(.t,/
1
4 X 412 = � !,(N � \(t,.J
1
V
I�
�
6o'IJ.I
p
R
+ 1
-
V
e 1
-4D�N
�
l-.24-tN
75
oo.1m
4.11114,Jfll
2·1�
1-7 b
1
(O.)
R = I o X ( /2
= 5 kN
(b)
+
1
V
· 5 l
\
4m
?_.5tr)
o
l,5tri
�
-SKN
-
1-1�
1
1
H8 = '220 kN (c )
Vs= qo lcN
"210�N
+
V
'
__,,
p
-Sl
·1
t
1
A.
13
V
') - 7:
..._
+--11 �---,I
I
_-t
1
-P
7-801
3
tv,.
M '7-78
V
\/A.=- � (40xf.at30x0.6)::30
¡:�
R1= � (-4P� +
1
1
+ 1
�
-')p
4P.K30.1"' 2p
-
HA :: 3 O � N
4l\ 1
76
o
p
l
, Va = 40 - VA "' / O � N 1.2. n,
3 t¡,
p
V
o
C?oo m..,
u�00,n111
.._________.l
1
-15kN
-70�A/
'J.l �N-l'Yl
V
��
M
1 ?,5�
-t
__,J 20kf\/
.----+- ·
l-
1
-35�N
V _q�N-11\
4Nlrttm
VA
=
, HA::
11"-
o
o
k
fQitl
:-
p -40 �
V
d
50''
30in
1
-SOi<.
121<.
t
-11(.
p
70�-il\
M
� + · -'·
.__
t..
o
-..1. l 'l'fo,,J �Om,...
IOJc-iY'I
160N
-=:¿j
-101'.-in
·
V
1-'82
�
1.4N-m
M Vr,.. = -35 �N
, H" �
7o �r.J
- 2.4r(-m
77
'1- .84
V (L) = o M íL) = o
V(X)
= %-oL �
<X-o';>º-
�oLl
B
(x-o)' - i. <..1<-l:.>' � 1 2 �ol.
+
V
�
o
L/1
M H l4)=0
M
-
1 (,O= IS <'f..-0'>
V lX) =
V
78
-
3 �o <X-1)
IS<X-0>º- �o <X-1;>2
1sf'.N
'7-81
C,::: IS"
H ex) = -.1:�
<)(.-O>\ �'i <.)(.-3. b
Vt�.l)=O
-c1:4o5
>' + c
1
t + c. 1.
lv\10J=o -C1=0
M \o.s):. o
M(�.IJ::O - C1= -157qs o
I
M t)(.): 405 <)(-O) -157'?.5(;(-())-1
1 1 t-Hx) = -75 «-O> + 100 <X-o'> -200<.x-o.1..s·/tc1x � C2
125
17 ,15
V(X)-= 4c,5<'.'.X-O>º-IS�.50-0)¡¡-'f
15" r 3 <�·3.o> «-»3t T
r, 1S <.1. -J• 6>1 <�,.-\Y-+
M (i) =-J8.7s<�-o>-7S<..X-0>2-tlOO Ox-0>3- 200 ('f.-o.2s·/' y lX J = ,�. 75 <x-O>º- is-o <.t-0'>'+3oo <x-0/-600
:2
405"1<.N
V
+ �
V
� O J.6m -
- e, = 18. 7s-
O,Sl'f1
o.��
o
-1i:15 i.1rri
6.'25 W-rr'\
-�
1-93
/M
--
dx
H(X): -
Hlx) =
-
1
J:i_ 240..
-
2
Áí\
-r"'
<X-0)3-t
1 C1 o'.-o>'�C,<'k:30.)
1
1
<J<-o� 2.-+ ;i,o.<.<-o>ºt ttt\.
V
-'
-1
d X�= -2(:i-O>. �y<X-8>* - <x- &>º 4 O'- 24) o .+ C-1..(X-24 i>,-1 4- "2 <x-32.>t-
�' <X-e> , + C,< x-o>¡f-1 -+ c <x.-3CJ,-1,.
°'<(-o'>\� i, a_('(-.AA} - 2.!.. (X-o)3; �� 24� 't V-• 8 - �
e;\ ::i..t-4
M tx): -2<X-o�,c,«-&>
<X-i>�-
1- �
+ { ú-2P1t C1 <.�·24.?'i2.<x-3n'
HllC) = -2(X-O) t 12<(-� >.:.. 2�-'3> �
1
1
+; <.1<-247
1.
1
-,,.
i 4<.X-L-+)
1
r
'l
+ '2.<.x-32)
I
y l�) = -"2 <'(-o>º 4 1<.x-i>º - o:-&>' ;. <x-24,1-+ 4('(-24,º -t2
o
V
79
�-1
,-
"2 ao
A: ,145 x /Q,(J -1-
-1
IS'IJ
�
,Jt
SO �
r
"jt)D,lc51)
= 32 000 /?"ll'YJ
�
J = 1(o. 003 H 0.01&)3 12
x
2
+2'<4.51 10·10
50
'
-4
32tJOO
()
�
¡,
i 200/C 50 J<:25)
'
" H= �
E= 15"(). 4 mm = o. ,5 m I = ¡� )( 145 x()./'$-t (),t4Sxt1,/xt1, ¡2 �
C
D,
_ )C ,
/2
(),05 J<.0,153.+, 0,15' x(),05°1C
"l.
;: 2.q1x10-i 11l4
2 so�50,c1SrP.12s
/,f5 -�
-1
+ '2(/.ooS.x.to Jlf.l�,;/Q )
-� =_L_ (t4S1t/DO�
o,ozs.:+
(lb5x1ob)(2.q1:
== �:...:..:...:...:_:___:�-_.,_
(O.Otb)
8-4
=
�DON· rn
T
-
2..¡-0,0S°XO,-Z X 0,12 - xc>.215 ' 57. /:Z.
::. 3.
3,4 i(/0�4
rn +
111111,
- �N"J: - /óSx/o3x'3.34-X/f)�-== 367
fv1 -
-
C
O,
15
KJ./·rtl
l---�---------_.__--1
3-'2
í�k 2
Í-t'tnn
t1j
Afp�a';x: _ t:
r
=
2
7C
0
("C.
=
=4.�6,/l)-ll ,,,-,
�·,·
I
m4
2(4.6Í,,<1r>-6-1-1.!)6"-I0-41(().o�4)=�.73J(t"if
e
8- 3 - �
r
I. =
0.11
=
tfllll�
3
/&S�IP x3,75"�/0 o, 1125
4(0.00�) t O-Off, 3Jl z -··
-5
=SS'l
ó"x4 ""' Y:2
f�=;¡,�----r-:,c.'
• 411,j�
r ;(.-.
• oif3}1z
X
Ín
"x;"
. . � I�=-4(6.27+4.7sx21.01)
+.!.."2--".-.� r3 12 � · - .... :;;,
= /O 984 ;n 4 M _ Q°'.vl _ 24-JC/DJ84 _ ,
=- /. f4X ,o-1.. rn
R+-= o.11 lo.008)<\= 4-.s1x10-1º
::¡==ZZ-o.9!37-::::;¡1.0/
h1
..;
12xl>.01>125>
1 �4(±,�12)t4J
�-5
.
t
A :: ?! !?ova t =J.!)6,ttt>
M=
12i
=· o. 09a m
. -* ,.
·
¡q421
i(, lb)(
-:z
3
I:'2JL
*ug.¿l{¡)(.2�ft
o.,-:z.s
"E T
I0�0. o95'7C R ... "J
-1
I=
IYl
80
- C
-
'2 2
= /Or:,c, K-ft:
X /:l.
Ac = 3q30 rn111-:t �-� Ic= l.b{A/Qómm4-
C310x31
X= W460 í74
17.7
f
Aw = 9460 mmz I...¡ :: 333Jt 106 1!!)114
(3'130 + 1?460 )
171- 7
==
1 �
( ft0rr'\
rniri
(O
24000
@ 44-�0
IGo
'716800
® 4000
310
1240000
0
4 .5(\
l
@
j)
I I e == 60- 7So.4 = 13. s-o.?
q o.
)
A� lrn1113J
CD '2400
�-=
(8.'2�)
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rn m
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7¡. 6"
=
11-:z.6 .
So �So ::::: roo
=
ST>-SD ::
.U, + 0.:1.
:e ,�
o
=-
() ,,.�-1(2fL)::: 4-0
01(+/J'y
o :«.
e J,}
�t.
()
=
6.a. =
= 11· "
(T, +
40 - ICJ's
6z.
= 8o =
8 = iAn_, (
1,2. 4
6x � Oy
_(b)
11-28
= 11>,/s
(l, ::- 40 + lt>/J=
/<.
:zb. b o
(�)
r().13iu.s - < /o" �::z.o� J =,
o.
(j>(-+ (Jy
J:;t··
p (CD,.20)
...l.
J+-
psi
Lma.r = .Jt> psi
'ºº
, a>
e-
/(s.:.
I K.st.
o-;
'1j
/+ S ::: 6 l<s¿ ,
� = 1-S = -4. J, )
p llo,q.¿,)
�cr¡
8
=
.....
'40
{),:: tan-'�:: :2.t,.i/ (j,
-�
(20,40
MP-..
!1PA. o :«,
'º�20-10) = 31. 7•
(b)
ca.>
r = < ::z.o"+
•
2.0ª) �
== :u,�
(1, ,:: · -,o+ �ofi :.: (f::.
=
6; �
-Jo -
.2.D./:z
a; - -.zo =
,e. 3
·= · -31/. :5
6,c+6;1
lJ = �-, ( :z.o!i-JO .zo ) :::' 117
:Z.l_.
Ks
�.x. So
= � (
{l:>)
Gm"'-.X.
::::
/5"):: 11.3º
b.S
V=
Jv{fp,... ,
/0 Hft?,..
1/-11
//-t'f
{O.)
r
I
=
CJ02-+ 1s2 J :i"
Ú, = Co.)
r=
.:.
( s ".-t- :z.S )
U-,
= -r:
= ..2S.
S-
Mf"'
-3.s-::zS.$ = -60.S
MftA
2S. S
0:2. ;:: - Je, =
(J� + 67
8=.:t-wn.._, ( 3.c.r :1 S'
/1-Jo
- -·
:20
=
ks¿_
= .::z. o = (;" -+ 6°_y
o. K.
= -s.s
ÍJ>< + 67
l:t·.
,� • rt
= c,10>+ 10"' )2 = 14.J
=
-10
+
14
.t =
4.,
0-. ... 0-z = - .:z o J::s¿ ::
e:
LD)
MP�
118
_t-'-'""' ( •. y.. f 10
=
/4. I
ks¿.,
K.sZ
(;x _. 67 o .1:.
) : Z2... J
q>: �'"" ( :;'): CmlAX
o, K ·
!<'si
� = -10 - 14. I � - ..24 . J
6s 0;..
r
(j'",
t1')� �-
=
/<51.-
= -�. o
-10
10�
02.
.
.:Z3°, o
o. IC
/ J;,�·
(j, +
Óz·
Ú, -+
fo..)
MfA •
=
8
1
)= So.7º
r
{f, = 7s
/
(J� = /t> - 18
MPo..
= - ¡· S
O, = - 3S -r
U.:z
I
::¡-
/0 �
=
º
.2.2.�º
u=
-/o /::s¿
11--lJ
r
-;:IJ
o-�:: 21;+ x o , ó:? 't: :::::. - 20. 6 2
h ere, gl,(,�
�.;.'<•>
5,n ex ==
- S. o o M Pa
• 20 = 7'>. � Ó • t.a11 5 o(.: �80 - {75,96+45)] - 4,S
f•lo
/
= 45 M Pct
::A:?>c<
=
,4.04.
�'>
Y.
(Je= =/o - ro- � �. =. -IS Ksi ?:9
=
-10 5¡,.., 6�'
=
8-6b
(D >O)
so
J]J
Ks<-
cr- . (o,->o)
r= a o
r=
(
Is:
�
Jl-38
I
� ;;:
+ /.:L )
== 19·
:l
2p .,
� = .)'ta,1t,
Ob == S+
_, (
/:2
,s
/<j.2 �
)
=- -38-.
7
•.
º'" ·- 38· 7"-U)
p
o
·P
Ksi.
L9 =.
-19.2 si>i..úao·- 33. ?._ '°•;
- - ''·º. J:si
r=- (.4�-.;ªJ�= s s-J>f'-� = - ¡;:¡ =-9&.13'
T
x:
�o 8•
Ji'�-.J
: 14.78 •
.
119
�"-'"'
chctck � w�e ,ne:thod · ,as""'e A...• .. , ,A.,.c s:.. 8,Jt11cC0•8 N: c.z �e-3;:,.eJCo,9
8 = 1
1,)
Ox =- 3s-r:,e, + �>VO
=
$: (.z�;n8+ict>S9)Co,.8-t (-l:.:.B+6CM8);}.it6 z: 1 . .lÍ -t '·�1 ª �.ri
a-.,.• #/,.o• O rv-é'�/,.o :.·�re
k
(Ju- :::
�
Z'
¡ 1-.i12
¿o.$
KÑ/m.a
3 S"l7I' -
�.$UD u,,;,
= - 33/,o
�·-�-
.·
J:3.8 •
1<.A//m ...
6� �2i �·�. ·2 p cu.;48 . 7T ti
.
6y = 6,. Sin B ,,,:- ;:
sin:r(l cos:z&
2
-¡:)()'; �rsintl cosp
0-. = � -t-6.SD = 9#"0
-.4W
8r =
= 33.7•
f-.an-1 tro 'ftn,
=2P
11 et
�p :s��cos
3{)
=-
_
>;,," e cos3EJ f
f$i
0-a..:; �-!>SO=
7�. 9 •
kÑ/m.a.
= - 3� .$;,..
T,r= -
7�- a·
448D
� .2s:z.o
�-,
1e,; o-e.
J.3.fr
Jfrr>-.2(s3.J):::
¡d.
�+·�
b) 'T = 651> psi
rr·= as» ,s'-
&.:,, = taJJ _,
»s»
= ��- 7()
,,-�,
11-43
'
•t
-[�]� l �,:�
a («» f Sin:1«)
�-·
,nA ;,.S�O �
(4.)
Ü¡
s: =- ti ( r
6� = E�3·$·
,-�=.3.s?n>
= 7 /10'0
o/ :i:· /IJº
'1N<
<3.500, � seo)_
6.) �i&IS =
·¿Jt= ¿;,u;s:il) =-í'¿'1$fJ cosr r.{e( ti Sin'«) 6.JC :: · - f,tJS'f)
KN/M•
6x
ó,c- ==
lif s-«
120
r
za.t«11/Q'
= -e
�.��=2tt·
< b) e<-= .::tG" p¡A>f
{J�c O
-
P
l,flt ""-S-1·�41) - - P.�b4.
-r
= . . :. p
_
-e
_ · -e
K( ·7$7-t-,f>) - .
/.�S-:¡4..
.2A Tl!lfl4S• .. · 2,a ••• '",¡"
•••
11-4t
I t-44
�
�- (JJ-·23)
6n
(-< -
n '!)
} V
4r �/11 IJ cos_B .==-
-C� =
(
- lt()Sl 6 ,;; n !} r t«> t�ir111:<)
2
')
:z n. O)
ncrm""llze
-,
"'''' l =t>
, ..
,
o(
-C>
�=3
{}j=,,
u,:::6, L,.
On) - 4 = O
)(S--
,
Ie"t,J.
,
n ,,, ;z. =
n.�C'IJ =o , n:3CI) = z ' �) 19 n or ; ( o , is· ,Js -f 2
n "'.: � n o.». o) n "�· .,.,-o., Let. n
.L.
(:a)
J"'r
(.%):::
(3)
(J)
v'I (.�, -
1�>'
t
c
�
:z
1:
I
= VQ
(Z-1) ne�)
?X '1
H y -::: -
Ó)(. -==
·
1
/1-46
�-:: 31Jq
!{
E/e,,
S'.,/n
1:X == -
'SinW: P.Pj
6-">"'""' = - 3.6 /
0n -
/
_
Ó.)r,ll'IAJ( - -
-3fxc
z e�
f
,;xt
=-4.5
<"-> 115
�
f (e== xiM3J') ¡;:(,cJ
J!,J
�
n
-
o.
= ¡
-1 n3 =z (1)
..
l3)::
� -=1. (»'R•fi)
f�'""' -e¡. ( 1/-::i.3) 3
6.x =- - //./ ,Fs-in¿I)
E/a,;:f. !:u/r,. .6x,0=6o" =
0(-
�
¿
2/1.B)_
-t-
llDYJn#../i�e. �
-Pfl.
::a
18
s-: -
18 ,
.
/.20
:Ilcr
u, = 19. 164-6 , u:1 = -10. 43:,.7
=
611
+ ,,.12 = º
-/.2e>,
Illo = -¡372
�='l. 3/?/
2 (C) (¡o- 19.1641.) n,.;..4/l. -t,n3 =o
tli�Cte-p. -:::
411, -
< 6-+ ,9. t64t. J n.; + �n.3
:.
o
n, = -tJ.s-s- n.� ., ns= "·2.3n� n, .....:. lk... -+ n,.a = , , n3 = o . 91, y
121
I
//-1¡ �
(;, =
so/u/;im,,
62. 4 ,
"Í
l!.r,r ()1 > "· T ' UH""'fei.11-�'>:> ,t 1 =s+.
fn,l,. l/-.21>
� = I?. /,
( Í)c
� =O
o,» J_ I
0.,, .R,
"?::
-t
[.r'j /'rl¡:: O .
o, M 1
T
-r
e o - o, ) n , == o
J 1 � ..,. m, � ..,. n, .:i. =
• '. J, l,2.4
� ().2
Yrs-.
=
h-1, = -
7rs-.
YI,
)�;:a..,. T1t'1 M:,.=
. (�¡(-o
',
I
=o o
T,c'J 2:,.. ..,. l 15"� - o> 1t1� == o
.f?m,
IY¡.
e 15".c-
�) ;? � t... � rll? = o
O« �J -r 0,, y111 ...
;�=as. "'�
< 0_ t>�) n1 = o
...v r .2'"1' n1¡ � T n, .:. = J =
Yrs--.
e:8" :=,St;rol/1. 111,.
-�
1- d�ti61v 8"!!'- stn,.¡11, /'1,
;¡-; r c tc]� � ��+,,;---+ l(\-t��d� .
/t-4'/
AB';' =
( 1+
E-o) d.s
( AB ,,, ) ª= [ ( /+ to )ds
=
n3=0
. )(-di,ed117'-
r
(A:rJ::a-t-(JB)
::a
:: l . < i+ e3 )dj + et+ 6x) dxJ .. + [ (I+ e3-, cJ1 J
�
:i.
= [ ( !+ €e J ds ] ( /-1-
€.)�=- [ (l+é.·w:) � --t
2/
cls :a
(J+€if)
tl]::a
d Jz + [ ( /+ é ¡>.;]
a>< -_ bu-f dS
= 122
G.fXJ
� =fi and -;:Js
.sña
9
éK t:.�sªO + '?sm. ªb+ .. siAPa4_
)1 (:3)
=
(.C.1
a,
I )
IJ-.S..
• •• /S::::
-Gx�in{;c.o-c6+o/mP"'°B+tr3á{_8
.:: -cé�-�·).s,ñ6ao�+o1(1 �:as
r= l1re +-- .
,{a,n
lí 2 VI
trO = --.;t4()
,
11
C, I .::a
-
4 • S°8'-
-
-r . / ,
/1.:lC> +/�O)+ :>
�( =
5VO
f:..2 =-
j,:7l;;> - /,::z.8
-+
::Ztn)
�;z.8 = //.::,B
-:-
2
==e,
M111/m
= - /::1� Mm/,n
JJ-91 ;;>,..
:::::
60 -t
.2
o
z.., == � Mm/,,, z�,,,. dP M,n/m far e, , Le-é 17. <;) :: J -,o -J§] f < : : : o [ -J"E
n�·> =
� ntt
-30
-�
r = r- s-trt> + [
.n
�r�/,'ze
(I}
.
I --:z '
E, ==
z. -
z.
(J)
n 3 =O.,
fo r E.:;,, , n ,�, = - ..,,rz:3 n. (.;.,.) /'"�e n �,)�.,, . e n c:.a) n':'=t> ., , a , 1
:l.
123
J a+ 4 tfT) z]::a.:::: sr:ro
-sv» + S1JT> =
o
M"'/,,,
= +so» _ SDt> .:: - /otro Hm/,,,
- .z-_
.2
I
j.C"r)
2. ()
::.
r !1
r = 2(.01Jo12)-(-.opo:z2.+.l)()0.Z:1.) = . �
oco::z4
/,2 -
2
T
¡r-· ººº22; -�022)� ( -�o;:z4-)7.
: : : .± • 000:::zs !
a; =
.3ox /� 1-,3
6[.
ODÓ2S/-.
3 (.ouo.2Sf)l
{L_ = -s. ?6
8 ,::::�I
é¿ = .
0¡
=
OOUD
l 7-.
17UO
6
rr= - • tJlTO /,,tro
r_ vU7>7-J4
?crt;Tñ;,
,-. :zs:a <.-
-. :zs(. ��>]
43,ó HP"'-.
o;,_ ==
'j
.? "1n:n:> r·-.V(Jf)/.IJ't) +. :zS (:lm) 734-J]
,-.��
·
::: -3hl H Pa
11-S,
/CSt-
t�-1 .�4. ..
-.2(:z2)
V�'Mj- Ei. I ,->"�. -4 p�;,.,.. tJ.
"'· 7 o -- 7.'.,_
s. 7¿.
. o-rn,7::J4
E:,=. 07Zt>67-f. 0Pl>ó77 =
=
S- 71, kSL.
::
jc. t7Cad.O-. 0�067 f+. l)'pr;J:7')""
::;; • (T(}7)677
-.OD022-,..()0022
_
Yl:M:Íitl.5:::
os-
o
� ... Í'f_ r-<'1 z,,.o= z l:n 2 Z
k$<.
. '. r
1(
'1 = i"
-r
�ro·,
llSt"-J Zo•,
i '1 - :z i ,» •
1.#-,· To C..C1>+-p«fc...
rx., "2
ll-f8
Gl
-.:200
"
éx
= ;
=-
€�
(.z€6o.
=. 00-040 +__ ;ze/�·--
U>m'j.
-�b·)
�
5{é6o·-6P<>.);.
(-, . 'J =
ce,,,.i:er =
.2
�o
T Z-'7Dº - 2.
0:JHf"ºfL_
tos:
= (- /�0-f' //�C t -2 ,< é¡;o "'·¿00�'%,
.2
.§(.O<J04.0+.�lcJ
.'. �51$t�.
::: .• 00//SS-
é X+
),lt>;/;n
zo•, 'i.r0•. t,$S-' to
= ; (.ooo8D- .00/:20-. o=,de>): -. HtJ�7 ,r "r:
(-/::r.Or/1:>0)
=} ( i"..,. t'1
C.e,.�
E:, -= , 00040-. ()oo:z.67 z
)=
fooP1¡/,.,
.
rJ(lf
- :: -/00. 2
.r:z
r�u�=
124
!
l-/:ztJ-.}1>0):,,.+l-/00);;, .,._
6'-8-
í,;:
z
z.
>ºº � 6:z8
:: ¡¡:,g
)l'Yrri
= too - 6�g "' -¡�g ,q%
I>,:: 70,,""' ( /1;¿8-0.��,�aJ lo" , / 11 1-0."5""2
,'.
D"2 =
7º,"ºº
1-0.°7'>
2-
y;
[-p,8--ro. '>'S°" 1•�8J
10(,
•
= /l-4-1HP. . .
11-60 1 '
' '
\
'
' ''
125
12-1
-.
CT' =
(�
4 -{:,
8
=
-b
3
)
8
( '==
14-
(¡ o ) + (- (, ) t ({4 ) =
b
.3
sheqr s-t ress
"<J(,\ti m um
=15oHF"'
ºrr = .3oo HPo..
(
b o o ) 4 4 -b o G o + 4 -12 8 o o G -b '& 8
� ml\�imun1 shea.r sh-ess theor Control! le.]
�"' ISO , ()�
= l�o
l:x� "". O
dev,o:tor,c 12 - 3
cr = a,+ o::i.té1 3
(.so
-30
-3o
·? o
U
- 2O
-:o '=(boO } 6o
o
=
Sot70+60 =.3
mo,xrmu h1 norm0t 1 shes-s üyp = 1 M HP(\
Ji'rtod ron - ener8¡
60
:o � \ tl:;� -:i _; J
G. b o D - "20 o ��
=r
mo..xirnuW\ norrr1e1I stress
L-----------------11-_ 1 _ 2' _5 - _cr,t""
The three trr+erro, ho.ve -the s0tme °rr
-,so
t�eo7 wn-lrol �
HP"',
1he -three criten� h""e the
/2-4
lb)
slre5s
Sheo. r
IY1ll\)( 1 mu n1
dev,cdort'c
sphenw.\
Uoi° +\l�C/-t (150{.: 2 6y�
=
o� =O
.
MP� , Txi = 7s Hfl\ � <S, e 110·7� Mf'11.
. Ti�= -150 HPa.
�
m o-x, rYl\.ln\
lb) o-)1 -o
5�rne Oyp
norrYU l
O-, = -150
stress
d,sforHon - ener�y
u
1 �
_____....,..___es;= -so.1i
Hfo..
6yp/�3
z:
=
O
iso HPC\
is-o HPo.
Cfyp '°" ".25�. & MR
126
Hfo.
Hp�
<:í'{p
= 11 O. 7� Hfo.
1'2-'1 1
'Tresco: �
1
l,)'nAX. ( 16!. 5b/ -t U 10. 478/t (S0.'7'&/°::: 2
=
07 p 2
=
.... . [ ( (t, ; ) + ?::xy
:ZJ
I
:z
cry;
143 . 1 H Po..
(fíP "'
I
sheo-r 5iress
Di = �O.
r:
or o »
=
Üx [ fk>�]� 2 f ( :z. ) + Z><;y
7� HP"'
a. ,o
r.%-.
le) 0-11 :=!)
(f.
=
= '75 �p°' . ª-a=
,s
m �x; i rY11.rm
Hf� .
o. 40
-100 HPQ,, , Tx� = o
. u;
:drf5s
=
== 1
loo�p°'
o o H fo.
o.oo
L_.----��----'
o.oo
0.20
o.•o
o.,a
0.10
1.ao
a;;/a-.
�Ts-\odtoi\ - .ener�y l.J'1Sl°-+t75)�(100J� 2ó",.;._
7
G,r • 152. 01 Hf"
�
/
-'2
l
--1
J.,,. pare: she=
ó> zo , C,.�o.
'2
( boti.-·s-oex )-+ l500( - 7o�)t l'TO(;(.- óoc() ""? e 2soJ
seo ex -i
,t.
�
= 1 '2 so o o
Z,,.,.:uc -- � 6i --
127
r»:
LO
r.
� U¡:2.
7
(..O
/h · 7�
P= 11.541
.
G. :: 1
Üyp
¡-'?)
128
13- /
�-Z
u::.= =
==
/ 3-2
),1,,.r
-r
.I..
/Q-o,c .20
smro
16::un:> x:zo
+
7T-".
-= �
:i.
Jt
=
US)lSo) 2 l4)
R= J L(1�.75-�.38)/2]'ltl35.q2) v1r1o.x
=
12.?S+q.38
011 i\'1
=
1�·75�9·38 -36.'22
2
+ 36.'22
=- � 38 HPi . o.
U3 � o U¡3 = o (
= 36.22HP�
2
p.st.-
VA= o)
·.·
= so.2q �Pq. _ = -2'2,IGMPe>..
¡�,
o;_
13-3
¡¡¡i¡¡¡¡¡¡¡¡¡ A 1tjl)o
1 1
1
1
----1,.
-
V-4 =o
=
'l"º,. .6 - ;}_ x
/6200
lb -
:: /C'D
.
x '/ ) .x /.2
/4
V e, = :3crr, lb
H s = ( 9(11) ,. 3 - ..L :z
=
/03177>
x ra» x
¿ "'J x /�
Ú¡
= .E.!.. t:
//7r)JC .20
62..
= ...E[_ + .:J."{;
Ms · o
o,
.:=::::- ()
Ut:z.
==
o. 2.
., x
Vs · Gis
:r. · .2t_
/i, - ,..._
=
V
o;,
�
=
Ia7l70
47,
p.rL
ps e,
J-t;Pt> f>.l L-
V.e --2tr� _ Vs 1l � .2t 1rrt
1>r 7f. • << � deo.d we,3ht · has
x-:« :
· .: th�
�Ú::,
1 l 1
47. 74
1Tx10 xe,.:z.
Vs Gls
1
' cr �'' o;
lb
J1 lt =- {
2t) ;¡ X O • .Z
-t-64.4t-
== >"vt4. 46
e:
n
pr :2t
psi t: �CT>
•
fH·
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EGOR P. POPOV
SOLUTIONS MANUAL ENGINEERING . MECHANICS
of So1JJ2T�
EGoR
P. Porov
PRENTICE HALL, Upper Saddle River, NJ 07458
Acquisitions Editor: Eric Svendsen Special Projects Manager: Barbara A. Murray Production Editor: Michele Wells Supplement Cover Manager: Paul Gourhan Supplement Cover Designer: PM Workshop Inc. Manufacturing Buyer: Pat Brown
© 1999 by Prentice-Hall, Inc. A Pearson Education Company Upper Saddle River, NJ 07458
All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher
Printed in the United States of America 10 9 8 7 6 5 4
ISBN
D-13-080431-2
Prentice-Hall International (UK) Limited.London Prentice-Hall of Australia Pty. Limited, Sydney Prentice-Hall Canada Inc., Toronto Prentice-Hall Hispanoamericana, S.A., Mexico Prentice-Hall of India Prívate Limited, New Delhi Prentice-Hall of Japan, Inc., Tokyo Pearson Education Asia Pte. Ltd., Singapore Editora Prentice-Hall do Brasil, Ltda., Rio de Janeiro
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0,-f.J
p::
p(.2-)= 7.2 I< (-)
V :::
12 (�
5
M= se.céioh . ,�I(
t
.J,
== 13 k.
J = 9.t, k (+)
12(::z.J=
24 k (-)
h- b
P=
/3(
..J_)
,J"ñ
k (-)
::: 3. IS
4
V== 13 ( - )
Po.=- �t�x+l,4-A,a) .;2H6 z:
fü
:= /2. 61
& 7. 68 �N
M = 12 cq J- 13((,)
Vo.. =- � �IA·A,( -A�)" 31 "N
::: 3c
.¡2.%
M� �
0.1 A-,. - 0.5" A'1
=
2(,. 61
J< (-)
1'-N
65
k-f-1: <+)
n-«
rool
Po."
-f"4o-f xsp
= - 64�N
V o. _-
(4+8)K./-5"
.z
Vo. = ix40 - / «so
4
- 5 Te -==. -J.41 �¡.¡
=- 2 �N
'1-11
Te
Te
=
JI.
RA
-=
:z.s
kN
3 Pc� -- s Tc ::: 6. 7S k N ( -l:U1.S1M )
T2
= 3,.f;í
,
T,
= �rs
.Ltv1A =o
Vs = 6 l/0
}: p =o
pi,.
I. V=o
Vo.=-3
¿ f,/tG\=O
jvfo. ::::
V°' ==
¡-, ..... -
Ma::::
)( sº « 3 x 2 + 4 Te. X 3::t.3 kN-m :J. :l. S
'i
=
HF
=-3 (K)
¿ MF
b k-f t
i .,.., ->
-=-3.0k.N
Pi,. == 6. ?S l
:.(>
7-20
V.__ ! +____.! __
1
M�
1 Te.= Re,
-pL
7-21 R&
3P
.
Z..H =o
Te.= 4-0/.3 = 13. 3 J{N HA == 3/s Te. = s 1
2:.v==o
VA= 12-t8-"';fTc=7·31
!V
1
+
:2.P
vi
-p
-p
p
i .-M �
- .2.J>L
66
P
P
cb>
Te
f
VF = e¡ kN t
L V=o
1-18
XM1i =o
,._
]
1-22! y
1
-!..
;� -
..3
7-261
+
-
1
--p
::E 3
.3
M '' l )( ) M
1
:f.
= -
(:<)=
1
N'cx)
3
e,=
�
M �PL er
RA
4 ;;t;
X13
-?.X"'tC,
z:
e�
'
= � ( 1"t3Y12x4) =
X�
3
X >3
12
C:i"' 12- �,\�Xl2= -{;
when X=o . Klo)::0
1-Z 1 1-24
l
I
R A=
t l � ·di)( 6
Mtx)-: 4.x -1<
v'==-J<í'<
M
1
4 �N
z:
�3
..::i
V=-� +C :z.
x= L, v=o � e /Vf
-:<
,e L)
= 2-,r� i" 2
e:{: L�
_1$.... L:: a ;2.
?(3 __1S_ L?( T e, = -� + b 2.
X=L, M=o=?
e,=
-l
N IX'-= _!f x - � -X 2. +
3
_!._ X 2
2
2
' 1
· 2X · � 3
x�3
3 ==&x-3/· +..!..x 2 3
M l:O = � x
= q-
M�
- +i3>"bU-q X '>3
3
2)(
-�Kl.
1�1.sl
p
V1
+1-
L.e.z
.2. L-____.
1-301 M = RA "X -
L----' .
K � �
2 'X •
M '== RA -1
Rs
67
= - +' l
3
'?C
Rs
==
RA - l
_L
+
'- K�
2.
'..<' x: i<.::C 3.z..
=1\1.4,.f�?(-� K
2
L .----.(
1-32
2
M (()) =- /000
Xº· j
'P ( 8) � /coo -"
:S,>, I) :::
3
+ K;< .3
2CO
Si'.,,
Prob. 7-24 •--�---------------1 7-31
M ( lt )
v e e) = p ( &) =
e {,bS B
-t
s,-,, · EJ J
.E: ( �s ()
-
s» 6 )
-P ::z
2
'7-34
A
.A
F
_.§..
.1
=-J'
V= - � -x.3 + e, .3
V=-o
so
,x"'- + ./.le e';{ -A v /2.
M=
( Sin B + f - C.Os fl )
.2
I
Ot
-x= L,,
Sll><:R..
S,"/1 � ( -f:ensic,, )
= - PR
V
&
V ( f)) == /ooo Cos &
'1 - 3 3
('
see soluÜCll
�=
.Sin<:!l
L . M
i kL-:a
=o
-t'
so
c.,=; �L� c2 e2
= -: {
= -p J-.C:.cl.
p == r' ,-p. o( siA. ( 9-,o
¿.,V= -7°1'-Ar;).
e,. M =
C.-0(
9-c{)
'f t- � ol. si"' e � -ol. }
1-38
J. V==-�?<, I
.,Z
sin�
-x= o
,
-k
L ...3
P" j,9-pr-.$;"-cG-oOd.r).
p = ? r- (
1- �
G)
C, :::
-So
v= ��?r-�rB-�>kl.
L.M=o
/�
V == - '(Jt- .s_,;, 8
Cs: =-o
V o
::: "f>l'-Si/1. (-{))
H = j\,,....,s;11.c&- . 0J..� o
l,a.r AS:
V::; -t
1-3�
F
M::: -FCL-"l:)
T� Fo.
bL\r 8C : V = ;- F M:::
-F(a.-�,
T�o
68
VI:::
I< S,)i. .::Z.1L X L . .
V= -
t<.t. � � � L. .27t
-+ e,
Kl� -· · 2"11 + e, x-r C2 s,-,._ --'X M = -L 47tª
4
.si,tt.A.
L
"X=O'
.so e, = o ,
v=::z.p
M=t>
e..
o
=
M1 M2
v=P
=
:i
=
p -x + e,
p-x
'X=t,\-tV
M:sO:> C:a=-CA+1')p
-x= ().., /
O. � 1e � 4'.:tb
C:a
-t
M1 =M.2 � C,z:-(.:,o.-t-b)P
L-
1
, p _+____1
o.
o
t1 M=M,-
V=O.
v-----
MI 7-411
¡K
t
-M, M= -'X L
y:::_ L.
M
7-441 V=-p
-M•
V
M= C.1
M= -p-x+c� ')(:: o
,-------.¡ ]ji_ L
M=
4'C=
l-t",
M=D
,
C.:
M
I
1
o. t
M
�t
1..'f'A
1--..,--1 "wt
1-451
-;?"' -11,
o
.
1
C.2::
PC�1'1>)
�
a+b
l -
1
;
+�
V=2, M= :2?C+C..1.
v= -2
..
0$'X�3
3-!:'JC�b t'l= :-2x+ca , 6 � ,e� e¡
M==to-:t�ca.
v-=10,
1
¡_
M==o,
fl>
tvf::-M, � C�=-M, ·
,.,,
V
V
e, ?C -te� . v=- e,
-X=o.
M= Ph:; C,
-x= �+b,
-.::::::::::::: -11' 7-421
Cl+l>
•
V= -10. M=-Jo?C+C,., e¡
69
�':t'�
12
?(::.O •
M=o
C.1 :s O
-:x:::. 3
M=b M=3b
e»
=24
C.3
:r:4g
M=30
C+= 110
-?C=6 -x:: q 'X -=12
M :: - :;- P"' � e, J
P1' .,. e� = 3 ..3 M = -3 P?C + e�
M
I
o .«
M=o
�=o,
M
¡o�N
V
2r..N
�
f
1
1
-�kf.l
i
c.,==o
M=O,
-E; .
=
= - po.
e :i
M= � • C.3=
- 1
M
...3
= o
p()..
o. I<.
.-10 )(..f.J
·3�
M o
3"1
6"'
'im
119'1
M
1-4-G j Vt�)= -30,< + 180 V(.()
= - 3O X + 3O
1-481
v= 10.
v= z .
v=-a.
"= 4.
o , �=+.
-X.:::
-42.l'H� -150lcN
.
· 34;. 6 k#-111 �
'J-4'1
I
«r __ , V -
V::
V=
.!S
_ap
-�
-Jp 70
7 :!: «e u:
= 4?C+C.s- ,.�"1(�22 c_,,;:O· M=o .
M=-8-x+C.4
/()�-X�,,
M
Jv1
= -1:1.
M; 18.
"X•/{).
M.::::a-4.
"'X=lb. ..:,c:=;12,
M= -2.4, M =o.
Jote.
Jkl -� ,c.
4�'X�7
M =1t>?C-r� M:r 2-x-r(:.J
,,c=1.
V
p
o �"' �4
V =-.3 • M:11-3-x+ e,
e�== -52
C.3•
4
C4
a /t,4"
Cs-
�8'8
o.
=
I<.
41<.
-
L,:
j
\/0 = � "q"l'2o
1-4-9
=
V(x)= (-soo)l.lbH5330 +200 l X-lb)
54-0 l
=
Mo=- - '�°C3xz.t6x5) = . .:.2160 kN-t11
V ex) ::
2oox- s�10
-'2 O X "2-+ 5 40
H (x ) = - �o 'X 3 + 540 )( -'21 bO
0$. X � 3 3330 lb
V o -2�?olb
M� - 21bO 1'-N·"'
7-50
�o=
-fl-1"x3,:¡5,..4-)
vtx)= -Is� .s .x
1'1 co::
-15�-t
-151<1\J
7-52
VU.)=--5X-+IOO
-. -f x2
{x� -
! J.'
Vli',) = O
10� X� 6Ci
Vt�J= -5x-+3oO
bO 5. X
f �O
HC;() = - 2.s"Ji=-+100-x
/,'l�
V
=
V
H D< J =
4.'í3"'
�
I
ooo
-151::AJ
- IS!vJ
V �
-iotN
'7-!il
Vlx)=
4-iox'20= soo111i
io = &3'2.5 x
l
o�x�4
Vtt.):. l83"2,5)(4-)-SOoLx-4-) = -SOOX-+5330 71
2omir\
'T-53
V
R
=
+t1xtSxbx5) = 7.5 kN 4Sl:N
+
4.5�N
+
�-J
V
..._____� -3 �N
31., lb-in
-60 lb
-?slb
M¿+�
+
1-51 R t =
1
1 6 r.bX&- 2x6x&x3-
= -7 �
-2�N-rí1
Rr = z:
1
1
-
2 }:.
1
2x 3x�i2)
t
( � 2Y3lC�X�-2thxt�3- (,J< 2)
V V
-,�· M
�V -24k.-
1-5�
�t
-IE,k-H
�k
/ t ;\
V�
H� 72
�20
-3CH.-n
7-5�
�-n
1-63\
1-GO
I
V
1-64]
V
'º l
+
.
V(kN)
�
�b/,lfl.
M '7-6b
V
'lO ICIV-m
r:::::=::::::::
73
o
4m
I
.1111
�ókN
?.-!��� ....,.. 2..., -
O
.. JO kN
1-51
3k ltt
1-70
.3ofl.
e:!Illi1lt� S'
IO'
VO:} o
t.--:-; :-� ¡_I_{+-;.-o_wo tJ.:__,n-�1.fo.0,1
n
'"-_ I
'º'
S'
JSo
ID
10
1ookN/"'
:
2•1
./'! l c-+>::::::::::, ./'<+) /�
V C l.:N)
1 (-)/
o
-1.01./'
-.eso
100
MC<-F:l�
.
<+>
o � o
-.coo
'7-1!
Pon V(N)
> --,--_ ---�-e o---�
M
MCk-k)
0,-.::::-�-:--7�--+---+-�--__.��=-"º 2'. } - _s:.
0 = 7rR3 =
R=
90
4
(+)
10000
111. 11
Oc,JI
1r---.... 2� V(t}
M _
.S= --- -- = 111• 11
,
mm
s-. 21
a
mm
use 11 mm ol<.� �J.. sAA-ft
-IS'·...,_
4-V Lmd\x = --
dA
..... ,r
74
4:,1.St> = -----
= O. 7o MPA
<
lA/1 .·.o.k.
m•
1-'721
,<, "7' m• � ...�kzzzzzzzz=q( ,� l.� l�/¡:e
8'
p
-100o
�15
V (Jb)
o
<
-----==--º
o
(16)
\ 2
:
�
� o
1 e�> �
1 �(-)
3.7,;'
J
•
r
�
703
'7-75"1
--i2S
e
f
R= 414/o.4= 4o
KN/rfl
á
200
(o.)
MU,-lh)�
o�
, --,-o -� -200
7-,3
I
bOkN
----(4C
l
e
8
(e)
40:'f A. A
-
8
-
1
- 68 l
:Z.4 f(.t,/
1
4 X 412 = � !,(N � \(t,.J
1
V
I�
�
6o'IJ.I
p
R
+ 1
-
V
e 1
-4D�N
�
l-.24-tN
75
oo.1m
4.11114,Jfll
2·1�
1-7 b
1
(O.)
R = I o X ( /2
= 5 kN
(b)
+
1
V
· 5 l
\
4m
?_.5tr)
o
l,5tri
�
-SKN
-
1-1�
1
1
H8 = '220 kN (c )
Vs= qo lcN
"210�N
+
V
'
__,,
p
-Sl
·1
t
1
A.
13
V
') - 7:
..._
+--11 �---,I
I
_-t
1
-P
7-801
3
tv,.
M '7-78
V
\/A.=- � (40xf.at30x0.6)::30
¡:�
R1= � (-4P� +
1
1
+ 1
�
-')p
4P.K30.1"' 2p
-
HA :: 3 O � N
4l\ 1
76
o
p
l
, Va = 40 - VA "' / O � N 1.2. n,
3 t¡,
p
V
o
C?oo m..,
u�00,n111
.._________.l
1
-15kN
-70�A/
'J.l �N-l'Yl
V
��
M
1 ?,5�
-t
__,J 20kf\/
.----+- ·
l-
1
-35�N
V _q�N-11\
4Nlrttm
VA
=
, HA::
11"-
o
o
k
fQitl
:-
p -40 �
V
d
50''
30in
1
-SOi<.
121<.
t
-11(.
p
70�-il\
M
� + · -'·
.__
t..
o
-..1. l 'l'fo,,J �Om,...
IOJc-iY'I
160N
-=:¿j
-101'.-in
·
V
1-'82
�
1.4N-m
M Vr,.. = -35 �N
, H" �
7o �r.J
- 2.4r(-m
77
'1- .84
V (L) = o M íL) = o
V(X)
= %-oL �
<X-o';>º-
�oLl
B
(x-o)' - i. <..1<-l:.>' � 1 2 �ol.
+
V
�
o
L/1
M H l4)=0
M
-
1 (,O= IS <'f..-0'>
V lX) =
V
78
-
3 �o <X-1)
IS<X-0>º- �o <X-1;>2
1sf'.N
'7-81
C,::: IS"
H ex) = -.1:�
<)(.-O>\ �'i <.)(.-3. b
Vt�.l)=O
-c1:4o5
>' + c
1
t + c. 1.
lv\10J=o -C1=0
M \o.s):. o
M(�.IJ::O - C1= -157qs o
I
M t)(.): 405 <)(-O) -157'?.5(;(-())-1
1 1 t-Hx) = -75 «-O> + 100 <X-o'> -200<.x-o.1..s·/tc1x � C2
125
17 ,15
V(X)-= 4c,5<'.'.X-O>º-IS�.50-0)¡¡-'f
15" r 3 <�·3.o> «-»3t T
r, 1S <.1. -J• 6>1 <�,.-\Y-+
M (i) =-J8.7s<�-o>-7S<..X-0>2-tlOO Ox-0>3- 200 ('f.-o.2s·/' y lX J = ,�. 75 <x-O>º- is-o <.t-0'>'+3oo <x-0/-600
:2
405"1<.N
V
+ �
V
� O J.6m -
- e, = 18. 7s-
O,Sl'f1
o.��
o
-1i:15 i.1rri
6.'25 W-rr'\
-�
1-93
/M
--
dx
H(X): -
Hlx) =
-
1
J:i_ 240..
-
2
Áí\
-r"'
<X-0)3-t
1 C1 o'.-o>'�C,<'k:30.)
1
1
<J<-o� 2.-+ ;i,o.<.<-o>ºt ttt\.
V
-'
-1
d X�= -2(:i-O>. �y<X-8>* - <x- &>º 4 O'- 24) o .+ C-1..(X-24 i>,-1 4- "2 <x-32.>t-
�' <X-e> , + C,< x-o>¡f-1 -+ c <x.-3CJ,-1,.
°'<(-o'>\� i, a_('(-.AA} - 2.!.. (X-o)3; �� 24� 't V-• 8 - �
e;\ ::i..t-4
M tx): -2<X-o�,c,«-&>
<X-i>�-
1- �
+ { ú-2P1t C1 <.�·24.?'i2.<x-3n'
HllC) = -2(X-O) t 12<(-� >.:.. 2�-'3> �
1
1
+; <.1<-247
1.
1
-,,.
i 4<.X-L-+)
1
r
'l
+ '2.<.x-32)
I
y l�) = -"2 <'(-o>º 4 1<.x-i>º - o:-&>' ;. <x-24,1-+ 4('(-24,º -t2
o
V
79
�-1
,-
"2 ao
A: ,145 x /Q,(J -1-
-1
IS'IJ
�
,Jt
SO �
r
"jt)D,lc51)
= 32 000 /?"ll'YJ
�
J = 1(o. 003 H 0.01&)3 12
x
2
+2'<4.51 10·10
50
'
-4
32tJOO
()
�
¡,
i 200/C 50 J<:25)
'
" H= �
E= 15"(). 4 mm = o. ,5 m I = ¡� )( 145 x()./'$-t (),t4Sxt1,/xt1, ¡2 �
C
D,
_ )C ,
/2
(),05 J<.0,153.+, 0,15' x(),05°1C
"l.
;: 2.q1x10-i 11l4
2 so�50,c1SrP.12s
/,f5 -�
-1
+ '2(/.ooS.x.to Jlf.l�,;/Q )
-� =_L_ (t4S1t/DO�
o,ozs.:+
(lb5x1ob)(2.q1:
== �:...:..:...:...:_:___:�-_.,_
(O.Otb)
8-4
=
�DON· rn
T
-
2..¡-0,0S°XO,-Z X 0,12 - xc>.21
::. 3.
3,4 i(/0�4
rn +
111111,
- �N"J: - /óSx/o3x'3.34-X/f)�-== 367
fv1 -
-
C
O,
15
KJ./·rtl
l---�---------_.__--1
3-'2
í�k 2
Í-t'tnn
t1j
Afp�a';x: _ t:
r
=
2
7C
0
("C.
=
=4.�6,/l)-ll ,,,-,
�·,·
I
m4
2(4.6Í,,<1r>-6-1-1.!)6"-I0-41(().o�4)=�.73J(t"if
e
8- 3 - �
r
I. =
0.11
=
tfllll�
3
/&S�IP x3,75"�/0 o, 1125
4(0.00�) t O-Off, 3Jl z -··
-5
=SS'l
ó"x4 ""' Y:2
f�=;¡,�----r-:,c.'
• 411,j�
r ;(.-.
• oif3}1z
X
Ín
"x;"
. . � I�=-4(6.27+4.7sx21.01)
+.!.."2--".-.� r3 12 � · - .... :;;,
= /O 984 ;n 4 M _ Q°'.vl _ 24-JC/DJ84 _ ,
=- /. f4X ,o-1.. rn
R+-= o.11 lo.008)<\= 4-.s1x10-1º
::¡==ZZ-o.9!37-::::;¡1.0/
h1
..;
12xl>.01>125>
1 �4(±,�12)t4J
�-5
.
t
A :: ?! !?ova t =J.!)6,ttt>
M=
12i
=· o. 09a m
. -* ,.
·
¡q421
i(, lb)(
-:z
3
I:'2JL
*ug.¿l{¡)(.2�ft
o.,-:z.s
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::::
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10-34 J
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r C>.t:Fl>o
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=
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= 14-.Sb MR
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rn m
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=
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4
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t-o b e-:1 m¡
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242 l<Ñ/;,,,..""'
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z
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o../NZAtÍ-f
•
t"�í
.T
$h_eev,,.
116
z
10-2. -
a-
�,¿
1or6'
4 t,s;_
= -1>
= �"-" _, : = «s :
Z> 8 11-2>
17'&
't
-"T"-.(11.0) (j
(l¡S)
z
11-27
=s
z::::: s K$i. Bi = iio» -, -2-:: I
(Fa
+ Ü.z.
=
z
' ( 30:,,. + 40:._) � =SO
ca) r= V, ==
U..z.
7¡. 6"
=
11-:z.6 .
So �So ::::: roo
=
ST>-SD ::
.U, + 0.:1.
:e ,�
o
=-
() ,,.�-1(2fL)::: 4-0
01(+/J'y
o :«.
e J,}
�t.
()
=
6.a. =
= 11· "
(T, +
40 - ICJ's
6z.
= 8o =
8 = iAn_, (
1,2. 4
6x � Oy
_(b)
11-28
= 11>,/s
(l, ::- 40 + lt>/J=
/<.
:zb. b o
(�)
r().13iu.s - < /o" �::z.o� J =,
o.
(j>(-+ (Jy
J:;t··
p (CD,.20)
...l.
J+-
psi
Lma.r = .Jt> psi
'ºº
, a>
e-
/(s.:.
I K.st.
o-;
'1j
/+ S ::: 6 l<s¿ ,
� = 1-S = -4. J, )
p llo,q.¿,)
�cr¡
8
=
.....
'40
{),:: tan-'�:: :2.t,.i/ (j,
-�
(20,40
MP-..
!1PA. o :«,
'º�20-10) = 31. 7•
(b)
ca.>
r = < ::z.o"+
•
2.0ª) �
== :u,�
(1, ,:: · -,o+ �ofi :.: (f::.
=
6; �
-Jo -
.2.D./:z
a; - -.zo =
,e. 3
·= · -31/. :5
6,c+6;1
lJ = �-, ( :z.o!i-JO .zo ) :::' 117
:Z.l_.
Ks
�.x. So
= � (
{l:>)
Gm"'-.X.
::::
/5"):: 11.3º
b.S
V=
Jv{fp,... ,
/0 Hft?,..
1/-11
//-t'f
{O.)
r
I
=
CJ02-+ 1s2 J :i"
Ú, = Co.)
r=
.:.
( s ".-t- :z.S )
U-,
= -r:
= ..2S.
S-
Mf"'
-3.s-::zS.$ = -60.S
MftA
2S. S
0:2. ;:: - Je, =
(J� + 67
8=.:t-wn.._, ( 3.c.r :1 S'
/1-Jo
- -·
:20
=
ks¿_
= .::z. o = (;" -+ 6°_y
o. K.
= -s.s
ÍJ>< + 67
l:t·.
,� • rt
= c,10>+ 10"' )2 = 14.J
=
-10
+
14
.t =
4.,
0-. ... 0-z = - .:z o J::s¿ ::
e:
LD)
MP�
118
_t-'-'""' ( •. y.. f 10
=
/4. I
ks¿.,
K.sZ
(;x _. 67 o .1:.
) : Z2... J
q>: �'"" ( :;'): CmlAX
o, K ·
!<'si
� = -10 - 14. I � - ..24 . J
6s 0;..
r
(j'",
t1')� �-
=
/<51.-
= -�. o
-10
10�
02.
.
.:Z3°, o
o. IC
/ J;,�·
(j, +
Óz·
Ú, -+
fo..)
MfA •
=
8
1
)= So.7º
r
{f, = 7s
/
(J� = /t> - 18
MPo..
= - ¡· S
O, = - 3S -r
U.:z
I
::¡-
/0 �
=
º
.2.2.�º
u=
-/o /::s¿
11--lJ
r
-;:IJ
o-�:: 21;+ x o , ó:? 't: :::::. - 20. 6 2
h ere, gl,(,�
�.;.'<•>
5,n ex ==
- S. o o M Pa
• 20 = 7'>. � Ó • t.a11 5 o(.: �80 - {75,96+45)] - 4,S
f•lo
/
= 45 M Pct
::A:?>c<
=
,4.04.
�'>
Y.
(Je= =/o - ro- � �. =. -IS Ksi ?:9
=
-10 5¡,.., 6�'
=
8-6b
(D >O)
so
J]J
Ks<-
cr- . (o,->o)
r= a o
r=
(
Is:
�
Jl-38
I
� ;;:
+ /.:L )
== 19·
:l
2p .,
� = .)'ta,1t,
Ob == S+
_, (
/:2
,s
/<j.2 �
)
=- -38-.
7
•.
º'" ·- 38· 7"-U)
p
o
·P
Ksi.
L9 =.
-19.2 si>i..úao·- 33. ?._ '°•;
- - ''·º. J:si
r=- (.4�-.;ªJ�= s s-J>f'-� = - ¡;:¡ =-9&.13'
T
x:
�o 8•
Ji'�-.J
: 14.78 •
.
119
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chctck � w�e ,ne:thod · ,as""'e A...• .. , ,A.,.c s:.. 8,Jt11cC0•8 N: c.z �e-3;:,.eJCo,9
8 = 1
1,)
Ox =- 3s-r:,e, + �>VO
=
$: (.z�;n8+ict>S9)Co,.8-t (-l:.:.B+6CM8);}.it6 z: 1 . .lÍ -t '·�1 ª �.ri
a-.,.• #/,.o• O rv-é'�/,.o :.·�re
k
(Ju- :::
�
Z'
¡ 1-.i12
¿o.$
KÑ/m.a
3 S"l7I' -
�.$UD u,,;,
= - 33/,o
�·-�-
.·
J:3.8 •
1<.A//m ...
6� �2i �·�. ·2 p cu.;48 . 7T ti
.
6y = 6,. Sin B ,,,:- ;:
sin:r(l cos:z&
2
-¡:)()'; �rsintl cosp
0-. = � -t-6.SD = 9#"0
-.4W
8r =
= 33.7•
f-.an-1 tro 'ftn,
=2P
11 et
�p :s��cos
3{)
=-
_
>;,," e cos3EJ f
f$i
0-a..:; �-!>SO=
7�. 9 •
kÑ/m.a.
= - 3� .$;,..
T,r= -
7�- a·
448D
� .2s:z.o
�-,
1e,; o-e.
J.3.fr
Jfrr>-.2(s3.J):::
¡d.
�+·�
b) 'T = 651> psi
rr·= as» ,s'-
&.:,, = taJJ _,
»s»
= ��- 7()
,,-�,
11-43
'
•t
-[�]� l �,:�
a («» f Sin:1«)
�-·
,nA ;,.S�O �
(4.)
Ü¡
s: =- ti ( r
6� = E�3·$·
,-�=.3.s?n>
= 7 /10'0
o/ :i:· /IJº
'1N<
<3.500, � seo)_
6.) �i&IS =
·¿Jt= ¿;,u;s:il) =-í'¿'1$fJ cosr r.{e( ti Sin'«) 6.JC :: · - f,tJS'f)
KN/M•
6x
ó,c- ==
lif s-«
120
r
za.t«11/Q'
= -e
�.��=2tt·
< b) e<-= .::tG" p¡A>f
{J�c O
-
P
l,flt ""-S-1·�41) - - P.�b4.
-r
= . . :. p
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-e
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11-4t
I t-44
�
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6n
(-< -
n '!)
} V
4r �/11 IJ cos_B .==-
-C� =
(
- lt()Sl 6 ,;; n !} r t«> t�ir111:<)
2
')
:z n. O)
ncrm""llze
-,
"'''' l =t>
, ..
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o(
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{}j=,,
u,:::6, L,.
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)(S--
,
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,
n ,,, ;z. =
n.�C'IJ =o , n:3CI) = z ' �) 19 n or ; ( o , is· ,Js -f 2
n "'.: � n o.». o) n "�· .,.,-o., Let. n
.L.
(:a)
J"'r
(.%):::
(3)
(J)
v'I (.�, -
1�>'
t
c
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:z
1:
I
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H y -::: -
Ó)(. -==
·
1
/1-46
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!{
E/e,,
S'.,/n
1:X == -
'SinW: P.Pj
6-">"'""' = - 3.6 /
0n -
/
_
Ó.)r,ll'IAJ( - -
-3fxc
z e�
f
,;xt
=-4.5
<"-> 115
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f (e== xiM3J') ¡;:(,cJ
J!,J
�
n
-
o.
= ¡
-1 n3 =z (1)
..
l3)::
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f�'""' -e¡. ( 1/-::i.3) 3
6.x =- - //./ ,Fs-in¿I)
E/a,;:f. !:u/r,. .6x,0=6o" =
0(-
�
¿
2/1.B)_
-t-
llDYJn#../i�e. �
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::a
18
s-: -
18 ,
.
/.20
:Ilcr
u, = 19. 164-6 , u:1 = -10. 43:,.7
=
611
+ ,,.12 = º
-/.2e>,
Illo = -¡372
�='l. 3/?/
2 (C) (¡o- 19.1641.) n,.;..4/l. -t,n3 =o
tli�Cte-p. -:::
411, -
< 6-+ ,9. t64t. J n.; + �n.3
:.
o
n, = -tJ.s-s- n.� ., ns= "·2.3n� n, .....:. lk... -+ n,.a = , , n3 = o . 91, y
121
I
//-1¡ �
(;, =
so/u/;im,,
62. 4 ,
"Í
l!.r,r ()1 > "· T ' UH""'fei.11-�'>:> ,t 1 =s+.
fn,l,. l/-.21>
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( Í)c
� =O
o,» J_ I
0.,, .R,
"?::
-t
[.r'j /'rl¡:: O .
o, M 1
T
-r
e o - o, ) n , == o
J 1 � ..,. m, � ..,. n, .:i. =
• '. J, l,2.4
� ().2
Yrs-.
=
h-1, = -
7rs-.
YI,
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. (�¡(-o
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I
=o o
T,c'J 2:,.. ..,. l 15"� - o> 1t1� == o
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e 15".c-
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O« �J -r 0,, y111 ...
;�=as. "'�
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...v r .2'"1' n1¡ � T n, .:. = J =
Yrs--.
e:8" :=,St;rol/1. 111,.
-�
1- d�ti61v 8"!!'- stn,.¡11, /'1,
;¡-; r c tc]� � ��+,,;---+ l(\-t��d� .
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AB';' =
( 1+
E-o) d.s
( AB ,,, ) ª= [ ( /+ to )ds
=
n3=0
. )(-di,ed117'-
r
(A:rJ::a-t-(JB)
::a
:: l . < i+ e3 )dj + et+ 6x) dxJ .. + [ (I+ e3-, cJ1 J
�
:i.
= [ ( !+ €e J ds ] ( /-1-
€.)�=- [ (l+é.·w:) � --t
2/
cls :a
(J+€if)
tl]::a
d Jz + [ ( /+ é ¡>.;]
a>< -_ bu-f dS
= 122
G.fXJ
� =fi and -;:Js
.sña
9
éK t:.�sªO + '?sm. ªb+ .. siAPa4_
)1 (:3)
=
(.C.1
a,
I )
IJ-.S..
• •• /S::::
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.:: -cé�-�·).s,ñ6ao�+o1(1 �:as
r= l1re +-- .
,{a,n
lí 2 VI
trO = --.;t4()
,
11
C, I .::a
-
4 • S°8'-
-
-r . / ,
/1.:lC> +/�O)+ :>
�( =
5VO
f:..2 =-
j,:7l;;> - /,::z.8
-+
::Ztn)
�;z.8 = //.::,B
-:-
2
==e,
M111/m
= - /::1� Mm/,n
JJ-91 ;;>,..
:::::
60 -t
.2
o
z.., == � Mm/,,, z�,,,. dP M,n/m far e, , Le-é 17. <;) :: J -,o -J§] f < : : : o [ -J"E
n�·> =
� ntt
-30
-�
r = r- s-trt> + [
.n
�r�/,'ze
(I}
.
I --:z '
E, ==
z. -
z.
(J)
n 3 =O.,
fo r E.:;,, , n ,�, = - ..,,rz:3 n. (.;.,.) /'"�e n �,)�.,, . e n c:.a) n':'=t> ., , a , 1
:l.
123
J a+ 4 tfT) z]::a.:::: sr:ro
-sv» + S1JT> =
o
M"'/,,,
= +so» _ SDt> .:: - /otro Hm/,,,
- .z-_
.2
I
j.C"r)
2. ()
::.
r !1
r = 2(.01Jo12)-(-.opo:z2.+.l)()0.Z:1.) = . �
oco::z4
/,2 -
2
T
¡r-· ººº22; -�022)� ( -�o;:z4-)7.
: : : .± • 000:::zs !
a; =
.3ox /� 1-,3
6[.
ODÓ2S/-.
3 (.ouo.2Sf)l
{L_ = -s. ?6
8 ,::::�I
é¿ = .
0¡
=
OOUD
l 7-.
17UO
6
rr= - • tJlTO /,,tro
r_ vU7>7-J4
?crt;Tñ;,
,-. :zs:a <.-
-. :zs(. ��>]
43,ó HP"'-.
o;,_ ==
'j
.? "1n:n:> r·-.V(Jf)/.IJ't) +. :zS (:lm) 734-J]
,-.��
·
::: -3hl H Pa
11-S,
/CSt-
t�-1 .�4. ..
-.2(:z2)
V�'Mj- Ei. I ,->"�. -4 p�;,.,.. tJ.
"'· 7 o -- 7.'.,_
s. 7¿.
. o-rn,7::J4
E:,=. 07Zt>67-f. 0Pl>ó77 =
=
S- 71, kSL.
::
jc. t7Cad.O-. 0�067 f+. l)'pr;J:7')""
::;; • (T(}7)677
-.OD022-,..()0022
_
Yl:M:Íitl.5:::
os-
o
� ... Í'f_ r-<'1 z,,.o= z l:n 2 Z
k$<.
. '. r
1(
'1 = i"
-r
�ro·,
llSt"-J Zo•,
i '1 - :z i ,» •
1.#-,· To C..C1>+-p«fc...
rx., "2
ll-f8
Gl
-.:200
"
éx
= ;
=-
€�
(.z€6o.
=. 00-040 +__ ;ze/�·--
U>m'j.
-�b·)
�
5{é6o·-6P<>.);.
(-, . 'J =
ce,,,.i:er =
.2
�o
T Z-'7Dº - 2.
0:JHf"ºfL_
tos:
= (- /�0-f' //�C t -2 ,< é¡;o "'·¿00�'%,
.2
.§(.O<J04.0+.�lcJ
.'. �51$t�.
::: .• 00//SS-
é X+
),lt>;/;n
zo•, 'i.r0•. t,$S-' to
= ; (.ooo8D- .00/:20-. o=,de>): -. HtJ�7 ,r "r:
(-/::r.Or/1:>0)
=} ( i"..,. t'1
C.e,.�
E:, -= , 00040-. ()oo:z.67 z
)=
fooP1¡/,.,
.
rJ(lf
- :: -/00. 2
.r:z
r�u�=
124
!
l-/:ztJ-.}1>0):,,.+l-/00);;, .,._
6'-8-
í,;:
z
z.
>ºº � 6:z8
:: ¡¡:,g
)l'Yrri
= too - 6�g "' -¡�g ,q%
I>,:: 70,,""' ( /1;¿8-0.��,�aJ lo" , / 11 1-0."5""2
,'.
D"2 =
7º,"ºº
1-0.°7'>
2-
y;
[-p,8--ro. '>'S°" 1•�8J
10(,
•
= /l-4-1HP. . .
11-60 1 '
' '
\
'
' ''
125
12-1
-.
CT' =
(�
4 -{:,
8
=
-b
3
)
8
( '==
14-
(¡ o ) + (- (, ) t ({4 ) =
b
.3
sheqr s-t ress
"<J(,\ti m um
=15oHF"'
ºrr = .3oo HPo..
(
b o o ) 4 4 -b o G o + 4 -12 8 o o G -b '& 8
� ml\�imun1 shea.r sh-ess theor Control! le.]
�"' ISO , ()�
= l�o
l:x� "". O
dev,o:tor,c 12 - 3
cr = a,+ o::i.té1 3
(.so
-30
-3o
·? o
U
- 2O
-:o '=(boO } 6o
o
=
Sot70+60 =.3
mo,xrmu h1 norm0t 1 shes-s üyp = 1 M HP(\
Ji'rtod ron - ener8¡
60
:o � \ tl:;� -:i _; J
G. b o D - "20 o ��
=r
mo..xirnuW\ norrr1e1I stress
L-----------------11-_ 1 _ 2' _5 - _
The three trr+erro, ho.ve -the s0tme °rr
-,so
t�eo7 wn-lrol �
HP"',
1he -three criten� h""e the
/2-4
lb)
slre5s
Sheo. r
IY1ll\)( 1 mu n1
dev,cdort'c
sphenw.\
Uoi° +\l�C/-t (150{.: 2 6y�
=
o� =O
.
MP� , Txi = 7s Hfl\ � <S, e 110·7� Mf'11.
. Ti�= -150 HPa.
�
m o-x, rYl\.ln\
lb) o-)1 -o
5�rne Oyp
norrYU l
O-, = -150
stress
d,sforHon - ener�y
u
1 �
_____....,..___es;= -so.1i
Hfo..
6yp/�3
z:
=
O
iso HPC\
is-o HPo.
Cfyp '°" ".25�. & MR
126
Hfo.
Hp�
<:í'{p
= 11 O. 7� Hfo.
1'2-'1 1
'Tresco: �
1
l,)'nAX. ( 16!. 5b/ -t U 10. 478/t (S0.'7'&/°::: 2
=
07 p 2
=
.... . [ ( (t, ; ) + ?::xy
:ZJ
I
:z
cry;
143 . 1 H Po..
(fíP "'
I
sheo-r 5iress
Di = �O.
r:
or o »
=
Üx [ fk>�]� 2 f ( :z. ) + Z><;y
7� HP"'
a. ,o
r.%-.
le) 0-11 :=!)
(f.
=
= '75 �p°' . ª-a=
,s
m �x; i rY11.rm
Hf� .
o. 40
-100 HPQ,, , Tx� = o
. u;
:drf5s
=
== 1
loo�p°'
o o H fo.
o.oo
L_.----��----'
o.oo
0.20
o.•o
o.,a
0.10
1.ao
a;;/a-.
�Ts-\odtoi\ - .ener�y l.J'1Sl°-+t75)�(100J� 2ó",.;._
7
G,r • 152. 01 Hf"
�
/
-'2
l
--1
J.,,. pare: she=
ó> zo , C,.�o.
'2
( boti.-·s-oex )-+ l500( - 7o�)t l'TO(;(.- óoc() ""? e 2soJ
seo ex -i
,t.
�
= 1 '2 so o o
Z,,.,.:uc -- � 6i --
127
r»:
LO
r.
� U¡:2.
7
(..O
/h · 7�
P= 11.541
.
G. :: 1
Üyp
¡-'?)
128
13- /
�-Z
u::.= =
==
/ 3-2
),1,,.r
-r
.I..
/Q-o,c .20
smro
16::un:> x:zo
+
7T-".
-= �
:i.
Jt
=
US)lSo) 2 l4)
R= J L(1�.75-�.38)/2]'ltl35.q2) v1r1o.x
=
12.?S+q.38
011 i\'1
=
1�·75�9·38 -36.'22
2
+ 36.'22
=- � 38 HPi . o.
U3 � o U¡3 = o (
= 36.22HP�
2
p.st.-
VA= o)
·.·
= so.2q �Pq. _ = -2'2,IGMPe>..
¡�,
o;_
13-3
¡¡¡i¡¡¡¡¡¡¡¡¡ A 1tjl)o
1 1
1
1
----1,.
-
V-4 =o
=
'l"º,. .6 - ;}_ x
/6200
lb -
:: /C'D
.
x '/ ) .x /.2
/4
V e, = :3crr, lb
H s = ( 9(11) ,. 3 - ..L :z
=
/03177>
x ra» x
¿ "'J x /�
Ú¡
= .E.!.. t:
//7r)JC .20
62..
= ...E[_ + .:J."{;
Ms · o
o,
.:=::::- ()
Ut:z.
==
o. 2.
., x
Vs · Gis
:r. · .2t_
/i, - ,..._
=
V
o;,
�
=
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