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8/12/2019 Final Soln 99
1/5
12/6/00
ME111 Lecture 9 1
1
Final Exam
ME111 Stress, Strain and Strength
Monday, December 6, 1999
Three hours
Open Notes and Textbook (Only)
A machined shaft is subjected to a fully reversed torque of 8.5 in-klb.
Determine the diameter of the shaft needed to provide a factor of safety
of 2.5 if a life of 105 cycles is required. The material properties are:
)(100,9.0
,67,220
correctedfullykpsiSSS
kpsiSkpsiS
eutm
yut
==
==
Problem 1 (20 points)
SOLUTION
2
( ) ( ) ( )
indd
Sd
S
Now
S
abSbSa
S
S
S
Sb
aNS
SCompute
SNNow
d
dd
d
I
Tc
ff
f
utm
e
ut
e
m
b
f
f
ff
aa
a
14.1;493.157.125
5.298.74
57.125;98.74
;5.2
,
57.125000,1004.392
04.3925933.239.0log3loglog
09889.09.0
log3
1log
3
1
:
5.2
98.7433
129.43
32/
2/5.8
3
3
09889.0
101010
1010
32
34
==
=
===
==
====
=
=
=
=
==
===
=
==
ss
s
tts
pt
8/12/2019 Final Soln 99
2/5
12/6/00
ME111 Lecture 9 2
3
In a machine component subject to a fluctuating multiaxial stress state,
the von Mises effective alternating and mean stress are:
The relevant material properties are:
(a) Determine whether or not the element is safe for infinite life fatigue
(hint: compute the appropriate factor of safety assuming a fixedratio of stresses),
(b) If it is not safe for infinite life, estimate the number of cycles to
failure.
kpsikpsima
40,24 == ssss
)(40,9.0
,67,80
correctedfullykpsiSSS
kpsiSkpsiS
eutm
yut
==
==
Problem 2 (20 points)
05.14024
67::
.909.0
:
=+
=+
=
=+
=
ma
yy
emuta
utef
SNyieldingbyfailurenoNote
fatiguelifeinfiniteforsafenotSS
SSN
fatiguelifeinfiniteFor
ss
ss
Part (a)
4
( ) ( ) ( )
cyclesNNGiving
a
bSbSa
SS
SSb
aNSNow
utm
e
ut
e
m
bf
341,1176.1290.48:
6.129
1126.239.0log3loglog
085.09.0log31log
31
085.0
101010
1010
==
=
===
=
=
=
=
0.481
:
=+
== ffmuta
utf
f SSS
SSN
HCFinfailureFor
ss
Part (b)
8/12/2019 Final Soln 99
3/5
12/6/00
ME111 Lecture 9 3
5
Problem 3 (20 points)
The figure below shows a schematic drawing of an automobile jack
which is subject to a load of W = 10 kN. The opposite-handed threads
on the two ends of the screw are cut to allow the link angle to vary
from 15o to 70o. The links are rectangular in cross-section with
dimensions 25 x 7 mm. They are made from steel with E = 206.8 GPaand S
y= 290 MPa. If the load is to be supported over the full range
of the jack, what is the factor of safety against buckling of the links?
Assume that the axial load in the links is central (i.e. there is no
eccentricity) and that the links can be modeled as pinned-pinned
about both axes.
mm220
007015: toanglelink
kNW 10=
mmthickness 7:
mm25
6
( )
52.1318.19
382.29
382.292
1
6.1182
87.10802.2
220
)(02.212
7
12
12/
318.1915sin2
15sin2
:
2
2/
3
00
===
=
=
==
===
====
=
==
link
crb
crry
ycr
yyr
r
linklink
P
PN
kNPSS
ES
db
P
columnJohnson
S
ES
LS
axisweakusingd
bd
bd
kNW
PWP
staticsfromlinkinloadaxialCompute
p
p
r
r
8/12/2019 Final Soln 99
4/5
12/6/00
ME111 Lecture 9 4
7
A thin-walled cylindrical pressure vessel has an inner radius of r = 10 in.
and a wall thickness of t = 0.8 in. The pressure vessel supports an
internal pressure of p = 5 kpsi and an axial compressive load of
N = 9000 klb.
Consider the following:
(a) The pressure vessel is made of a ductile material with a yield
strength of Sy= 250 kpsi. Determine the factor of safety against
yielding under the applied load using:
(i) The von Mises (i.e. distortion energy) criterion,
(ii) The maximum shear stress criterion.
(b) The material is brittle with an ultimate tensile strength ofS
ut= 180 kpsi. What is the minimum ultimate compressive
stress Suc
that is required of the material to provide a factor of
safety of 1.5 against brittle failure? Use the modified Mohr
theory and assume plane stress conditions.
int 8.0=
inr 10=
kpsip 5=
klbF 000,9=
Problem 4 (20 points)
8
23.14.203
250),,max(
:
39.145.179
250:
45.179
9.1402
0.5
5.62
13133221
13322123
22
21
3
2
1
==
=
=
==
=
=++=
==
==
==
ssssssss
s
ssssssssss
s
s
s
yyy
y
y
SSNTresca
SNMisesvon
A
P
t
pr
p
t
pr
( )
( )kpsiS
S
Sor
SS
SSN
andquadrantfourthSince
uc
uc
uc
utuc
ucutb
5.2455.19.1405.621805.62
180
5.1
,
311
13
==
+==
>
sss
ss
Part (a)
Part (b)
8/12/2019 Final Soln 99
5/5
12/6/00
ME111 Lecture 9 5
9
The beam shown has depth of50mm and a thickness of 20 mm. A
crack through the thickness of the beam is detected in the bottom face
as indicated. The crack is measured to be 10 mm long and it needs
to be determined if the beam can safely support the two point loads
P = 30 kN. The beam is fabricated from AISI 4340 steel with a yield
strength Sy = 800 MPa and a fracture toughness Kc = 185 MPa(m)1/2.
(a) Using LEFM, determine the value of the load P that will cause
the crack to propagate.
(b) Repeat (a) taking plasticity at the crack tip into account.
(c) Can the beam support the design load of P = 30 kN?
Problem 5 (20 points)
kNP 30=kNP 30=
mm10
mm20
mm50
mm200mm200
10
( ) kNPP
Now
P
I
McaKK
d
a
C
5.431000
10
12/5020
252000.1185
12/5020
2/50200;185
0.12.0
3
3
=
=
=====
=
p
spbs
b
Part (a)
Part (b)
( ) kNPP
Now
aKK
d
a
mmaaKK
effC
eff
meters
effC
y
C
S
K
6.151000
27
12/5020
252007.1185
185
7.154.0
0.271000
3
21
=
=
===
=
=+==
p
pbs
b
p
Part (c)
No, fails when plasticity at the crack tip is considered.
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