()
2.43
A steel tube ( = 29 X 106 psi) with a I!in. outer diameter and a
kin. thickness is placed in a vise that is adjusted so that its jaws just touch the
ends of the tube without exerting any pressure on them. The two forces shown
are then applied to
Test 2
CE3400 Strengths, Summer 2005
Closed Book, Closed Notes
M on, Jul 18th 2005, 12:10 P.M1:10 P. M
No questions will be allowed once the exam begins. If you need to
make an assumption write it down clearly in the blue book. Show all work and
proper f
Exam 1
CE3400, Strengths, Fall 2008
Closed Book, Closed Notes
Tues.) Sept 30th 2008 1 4:30 P.Nl5:30 P.M
Draw FBDs as required
Clearly state all assumptions mad e towards solving the problem
r
r
1) Links BF&C E are each
wide and
thick and are made of st
Exam No. 1
CE 3400(01 ) and (02)
Formula Sheet
Stresses and Strains
p
(J' =
T =
Anormal
(J'
=
b
p
F
Ashearing
<5
&= 
A
L
bearing
Axial Deformation
J,=

;
l
l
J,.,.,
a,L,AT,
=
J = J, " + J .
Generalized Hooke's law
Torsion
r=p
r
max
= Tp = I
J '
i
Li P =
0
t I ;,_,'.\'
('
/
f'\ 0 Y !'I\ CIJ,;, \i(), (M cfw_!j
'0 [;_,:OV'U111
eAJ e.U\Vo.,
( / l/ 1=)
c
C id )
(
_
I
f
1j
(a)
L g IrtI A I
cfw_;) tA C,h
)
I,[)
ri t
cuif l e
u)
id
cfw_J;lf
cfw_;e., ;J e eJ/L
cJ r7p f.ev 2 d e,f r.
;:.
'
: r
/'
irI
n
C r''
1) Three steel rods AB, CD&E F (E = 200 GPa, a = 17 x 106 /C) are undeformed in the po
sition shown and are attatched to a rigid member BED. The area of crosssection for AB&C D
is 200 mm2 and rod EF is has a crosssectional area of 625 mm 2 . If the tem
0
(_
I
(:;
q tA
J
ex
l
)
e
i\
l
J
'
j
'
i
/
0
L
0
rs
I
L
+
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.  ,
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y') (
()
cfw_)
L
L
J
P;
I

I
b
I
t) G
p L.
10.1 Knowing that the torsional spring at B is of constant K and that the bar AB
is rigid, determine the critical load Per
Fig.
80 MPa
7.68 Forthe state of stress shown
.
.
when (a) uY = ,1 0 iv1.pa, (b) er = ,PdOetermme the 11u1axn
num shearin
and outofplane shearing stres;es.)  MPa. (Hint: . Consider both
in
!Pa
/"
f
Fig. P7.68 and P7.69
O\of.J.1
ri"'(;#
I . a1'l
sNPr
fr :h
7,55 through 7.58 Determine the principal planes and the principal
for the state of plane stress resulting from the superposition of the t\vo
of stress shown.
1 50 \!Pa
'
70 .\!Pa

+
+
Fig. P7.55
fl.J
'
I
)
l :
)
'\
)
cl
= = 
(
, , r L,;UQ1
,r.lI
i
1) Determine the principal shear stresses and associated principal shear directions for the state
of plane stress resulting from the superposition of the two states shown
(25 pts)
+
7
! '
12 
'
\
C>:
1;
S:2'I
f
tc
CJ;_ : 70  4(r . 4: g : 2/.i Ct1
Exam 1
CE3400, Strengths, Spring 2009
Closed Book, Closed Nates
Tues.J Feb. 17th 2009 4 :30 P.M 5:30
P.M
1
Draw FBDs as required
0
Clearly state all assumptions made towards solving the problem
1) Deformable links BD and CE are attached to a rigid link
f1)
1) The pinconnected structure consists of a rigid link AD and two steel links BC and DR
Each steel link has an ultimate normal stress 200MPa and there lengths are 50mm. The area
of crosssection for BC is 20 mm2 and that for DE is 15 mm 2 Assuming th
h d e bevfr\e, 'v,o._ f beo. J' cfw_,5 I . B )
f fo. ,hCA L
'
8r S
lM.[;'b rc.'(/IJ'i1
retA.cJ.'o,n f . cfw_
, '" Ive C Tei J.J.
Tvc:ck_
t:'J f q
l
fav
w
._. ..,.
[
:..
Som e
J
a1
N p (X, )
f;,r
Y'e.a cl,'crns
=
H, h ) t
S cm
k_,10
wVL
l
q ,r 
7.128 through 7.131 For the given state of plane strain, "HltTI'>f
Qf.ec.7"'lO to determine th state of plane strain associated with axes
y' rotated through the given angle e.
y '\
Fig. P7.128 through P7.135
x
Ex
240
+240
+350,
7.128 and 7.132
7.129
I
r o.
L( )
c
!
Ci
('
.b"
e
I ,
\(
/ . '")_
I ,3
('
0
re U lC Gd
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o. l t:1 1'"1
( lA)
/1
LJ,J.
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cfw_.!t
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'('
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r)
r
,r
I
l,
l
L
y
f
h() YlY\0, L,
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II
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rl
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, I
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l)
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6
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s
(
(
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0 7 tfo,(J,fl 'i:1) r
uf'
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t
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cfw_J (),
(
3V\
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eo v rd"
C b)
At
7
u
2.8 An 80mlong wire of 5mm diameter is made of a steel with E =
200 GPa and an ultimate te
4. 12
j & f:tie.
OXl o (
f,<ce
1
tJu C YO C S  s e
uri 1e.Y" r'I' I
Yy'>'\ o. f
v6
c. 'CY)'\
.
J
Mt 'J,
i+
for, c.e
f
Co.YI.
lJ.
t
p Yr> c&.Al
+
'
1
f.,
Loo <i,
p
l :r")
Y"eCA.
0.VL
cfi
,(>"("\.
M 0'1'1 e
t'l
M +Pt o  Fd .: o O'Y'
H = Fd
r c
Exam 3
CE3400, Strengths, Summer 2008
Closed Book, Closed Notes
Thur.) July 23rd 2008) 12:10 P.M_1:10
P.Af
o
Draw FBDs as required
Clearly state al l assumptions mad e towards solving the problem
1) For the state of plane shown in fig. (la), determine
(
(
128
Stress and StrainAxial Loading
36 mm
Fig. P2.128
c
28111111
2.128 A 250rnmlong aluminum tube (E = 70 GPa) of 36mm outer
diameter and 28mm inner diameter may be closed at both ends by means of
singlethreaded screwon covers of 1.5mm pitch. Wit
tr
6
.f'i'a Ls
" Tf(.t,L
@) Pl'euv
:J
m di(
t
I
Yf\
0.lLM.:
Li.y pof<.te he.
Yl
u/
3
C) n
;
d;
1
1r
73.eu./Yts
r
CO/l. t.J.(.1,( j 0/La.1!. .i Da.
P<:.L+, ve fl. cfw_ O i t
a,S e:,ut
, lu.\. t
II
.1. u,' v
CD 1(
c.
cfw_lb <"'1.Cl
;._,J
.;:J' c

C Powe r
,'
oy
p
I
I
I
(

df
C T(fY' i;,t (#'\
J1,u "1 wo. cfw_I e rJ
"o r,
01.N ,rih_ o.
cfw_k .!)
313
Jvi "
./,r l;()V,o J
1'
; ,'
U:,o Jecl
tt
L.:
ftv '., wO'I 11e cl ho flow s ho. fA:
t. = +,
, . 5(.,r.c e ,rh e
Ot!.C u.Me
h +1' e
(
x,'
h
J
.I1 _'_, _
odI cf f
I
, I
Oil
,
h
)
I
C,
)
I
cfw_
I 2.
4.142 The tube shown has a uniform wall thickness of 12 mm. loading
given, determine (a) the stress at points A and B, (b) the point the neutral
axis intersects line ABD.
"\
( ('
.
'f'Ct trV\ J
5.22 and 5.23 Draw the shear and bendingmoment diagrams for the
beam ;111d loadi ng shown and detennine the maximum normal stress due to
bending.
2 in
Fig. P5.23
2 rn
rn
5.9 and 5.10 Draw the shear and bendingmoment diagrams for the
beam and loading sho
1.,
<,., /
:;:.O
')">
ci F
T
(a)
T
"'
/'
l
\)
I
1
1
J
r
I
L()
r
!
l
l, \"
l/
3.5 (a) Determine the torque that can be applied to a solid shaft of 20mm
diameter without exceeding an allowable shearing stress of 80 MPa. (b) Solve
part a, assuming that the

Se
I
)
"

"
I

I =
:;:
i
"
1
,
d,.
I
@rr1.
"'\

;1.,.
" "'
0
t,
,
"
t
),
()4
;.,
jP\
er
,Ii
)
t
l
!
l,
t
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)
)
J
J
fM
'

i
1 ,J
*
l
l
11
t
/;
=
f
I
'"',g.
=
'
/
\,"'
rI
I
I
I
le : 
7. J
y
4
Ivo
l,
;
;
:,
:
l.
I
cfacfw_ S

ve
/
't',\
I
L
)
\
7.i28 through 7.131 For the given state of plane strain, use the method
of Sec. 7.10 to determine the state of plane strain associated with axes x' and
y' rotated through the given angle a.
!J i
!
Fig. P7.128 through
P?.135
e
l"y
7.129 and 7.133
7.130 and
9.65 through 9 68 P .
.
deflection at C' ( b) the slop,eoart tehnedbeAa.m and 1o.,d'n g s h own, determine (a) the
[r )
cfw_ cfw_ ;3,Je 5J
Jt
cl)
Ir
+
P l r
 L


:f L

.
I
2_
C,t3T
cfw_ r
f
; ,
 I
4;
7;< !69 J
PL
'2,.
9.65 through 9.68 For the be
4.41 and 4.42 The 6 x l 2in 1: b b
. bolting to it the steel reinforcement sh ,m ; earn has h:en strengthened by
is i.8 X 106 psi and for steel 29 X
n;si e modlus ot elasticity for wood
11bo11t a horizontal axis by a coup.le f . Knowmg that the beam
.
o
/
. .
/
i
5.1 hrough 5.6 For the beam and loading sho
and b.endingmoment diagrams , (b) determm. e the equawf n, (a) draw the _:,_
ions of the
bendmgmoment curves.
shem.,
.
\
oz:t Z C\ ,
. ' O
L/_:cfw_).
1
V cfw_1)
0 ),.,
V[c,. ) "' W llW
2
/_,>c, U
.1 and 4.2 Knowing that the couple shown acts in a vertical pl
termme the stress at (a) point A, (b) point B.
ane, de
(
I
Cl:Y,
cfw_
(.IA
1,
j
'.?J'fr X Je Ch'OV\.
vfvterr cJ4 le
.
CtH". /y'(!l
4.7 through 4.9
Two vertical forces are applied to a bea