PROBLEM 2.10
A
square yellow-brass bar must not stretch more than 2.5 mrn when
it is subjected to a tensile load. Knolvin,s
that E = I05 CPa and that the allowable tensile strength is 1 80 MPa, determine (a) the maximum allowable
length of tlre bar, (&) tlte required dimensions of the cross section if the tensile load is 40 kN.
SOLUTION
O= 180xl06Pa P=40x103N
E_
l05xl0qPa 3 = 2.5x10-3rn
PL oL
(a) a=-=AE I.:
, _ 86 - (105x10eX2.5x10-3) = 1.45833 m
o
180x106
nr
{
a=14.91mm
{
I
= 1.458
P
A
A
P
40x103
o
2
reproduced, or distributed
"
.,ortffllYY
(O
mm2
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All rights
reserved. No part of this Manual rnay be displayed.
in any form or hy any nreans, without the prior rvritten perrnission ol the publisher, or used beyond the limited
10 teachers and educators permitted by
rvilhout pcrntission.
= 222.22
o = JA = Jzzzzz
PROPRIETARY II'IATERIAL.
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McGrarv-Hill lbr tlreir individual course preparation. A student using this manual is using it
PROBLEM 2.19
[
Botlr portions of the rod ABC are made of an aluminuln for lvhiclr = 70 CPa.
Knor,ving that the rnagnitude of P is 4 kN, determine (a) the value of Q so that
tl-re deflection at
is zero. {b) the corresponding deflection of rg.
I
2()nrn cliiulcler
noN
Ar, =
An
=
f
rtlu =[{o.ozo)'= 314.l6x t0-6m]
tdi,,
=
l1o.oooy' = 2.Bli4xl0-3m2
rorce in rnenrber
l,B
is P tension.
llongatiol1:
6rr=PLr,,- (4-x103X0.4) - 8.4r, (70xt0qx3l4.t6xl0
n.1
rorce in tnember BC is
Q
-
=r2.156xI0-6m
P c,ompression.
ihortenins:
=!*=,?-r]!o=.f,
. _, =2.5263xr0-n1p*r,y
t:AR( (70xl0qx:.8274x10r1
6,,,
r)(
:or zero deflection t$ A, 6ur, 6uo
=
2.5263x10-e
(Q- P)=72.756x.1A-6 QQ=28.:x103 +4x103
0.tn
=
6nr'
-
6R
=72.756x10-6
m
P =28.Bx103N
=32.8x103N
g=32.8 kN
4a
= 0.0728 rnrn
J
ETARY ll.4TERlAL. O 2012 The Nlc(iraw-Hill (iompanies, Inc. All rights reserved. No part of this Vlanual nray be displayecl,
d. or distributecl in an1'lbrm or by any means, witltout the prior r.r,ritten pernrission ol'the pr.rblisher. or used beyoncl the lirrrited
m to teachers and eclucators permitted by lvlc(irarv-Hill tirr their individual course preparation. A student using tlris uranual is using it
rrmission.
tls\
t'{
ii
il
I 'inl
iil
ii
il
,sI
PROBLEM 2.25
Each of the links ,48 and cD is made of aruminum
(E = r0.9 x r06psi)
and has a cross-sectionar area of 0.2 in.2. Knorving
tt-,ut ttr*y ,upport the
rigid member BC, detennine the cleflection of poiniE.
rnoN
dl
BC:
*)r,ur,
=o
: - (32)t7,t, + (22)(r xl03; = 6
F"tn = 68"1'5 lb
I
*l:4
=0:687.5-lxl0r * F.n =g
Fco =312'5 lb
trr
'_=
.1ll L tB
(687.s) (l 8)
E_1
(r0.9x106)(0.2)
trI
t i)
Lt.l)
-=E_1
(3 l2.s) (l 8)
(r0.9x106)(0.2)
= 5.6766x10
3
in = d;,
= 2.5803 x I0-3 in =
4
atiorr diaglarn:
Sloped
'
TA'-
- 6, _ 3.0963xr0
- Ln,
32
6n
=96.i59x10
l
6rad
5r. = 5c.+ Lur.0
= 2.5803x 10-3 +(22)(96.759x10-6)
= 4.7090x10-3 in
5t: =
4.7lxl0-3 in J
'ARY nI'ITERIAL' o )1y12 Thc tr'lc(irarv-llill Companies, lnc. All rights reserved. No part of this
Manual may be clisplayed.
or distributed in an'v lbrm or by an1' means, without the prior
r'r'ritten permissi.n or'rhe publisher, or used beyoncl
the limited
lo teachers and educators perrlitted bv Mc(}rarv-Ilill tbr
their individual
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nission.
A student usi,g this manual is r-rsing it
PROBLEM 2.26
The length of the *-in.-diameter steel wire cDhasbeen
adjusted so
with no load applied, a gap of in. exists between the end B
of the
beam ACB and
f
a
r
contact point E. Knowing that E=29x106
determine where a 50Jb block shourd be placed on the beam
in
cause contact between
B
and E.
SOLUTION
Rigid beam,4CB rotates through angle
0
to close gap.
t =t'-'!=
20
3. 125 x l o-3 rad'
Point C moves downward.
6c = 40 = 4(3.125x10-') = 12.5x10*3 in.
6r.1,
= 6c =12.5xl 0-r in.
4u =4d,
d
g^,.
=L(1\'
4G2)
=6.so2sx1o-3 inz
FrnLc,
\'u- 84,,
(2gx106
xrc\ gsozs xr o4
D<,u __ E4o6ro= _Q9
_
--.-__
Lt:n
1
1r
z.s x
r
o{ ;
12.5
= 200.18 lb
Freebody ACB:
fiztt o = g, 4Fcn - $o)(20 -x) =
20
AYI-;
-x=
(4)(Zo-o'1 8)
50
x = 3.9856 in.
Q
=16.0144
x < 3.99 in.
PRoPRIETARY
IIATERIAL' o 2012 The McGraw-Hill Companies, Inc. All rights
reproduced' or distributed
reserved. No parr of this Manual nray be di
in any form or by any means, without the prior rvritten permission
of the publisher, or used beyond the
distribution to teachers and educators permitted by McGrarv-Hill
for their individual course preparation. A student using this manual
is
without permission.