### Ödev5

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al
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ic
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ess
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to
based on a 0.2% strain offset method.
The rigid
is supportedspecimen
by a pinhas
at the
A and an
F3–11.3–15.
The material
forpipe
the 50-mm-long
3–18. A tension test was performed on an aluminum 2014A-36 guy
wire shown.
BD. If If
thePwire
a diameter
0.25 in.,
stress–strain
diagram
= 150
is applied of
and
T6 alloy specimen. The resulting stress–strain diagram is
determine
P permanent
if the end C
is displaced
0.075 in.
then released,
determine
elongation
of the
3
shown in the figure. Estimate (a) the modulus of resilience;
specimen.
*3–4. downward.
A tension test was performed on a specimen having
and (b) modulus of toughness.
an original diameter of 12.5 mm and a gauge length of
3.8
F
AILURE OF MATERIALS DUE TO CREEP AND FATIGUE
111
50 mm. The data are listed in the table. Plot the stress–strain
3
diagram, and determine approximately the modulus of
s (ksi) ÖDEV NO 5.
elasticity, the ultimate stress,Pand the fracture stress. Use a
mm
20PROBLEMS
mm = 50 MPa and 20 20
mm
= 0.05 mm>mm.
scale ofs (MPa)
70 mm ve uzunluğu 100 mm olan bir
Soru 1. Çapı 15
B region, using the same stress scale
Redraw the linear-elastic
çubuğa 100 kN60eksenel çekme yükü tesir etmektedir.
but a strain
500 scale of 20 mm = 0.001 mm>mm. P
•3–25. The acrylic plastic rod is 200 mm long and 15
mm in
*3–28. The
elastic portionE=200
of the stress–strain
diagram for
Boyundaki
değişimi
hesaplayınız.
GPa.
50
3–5.diameter.
A450
tension
was
performed
a steeltospecimen
If antest
axial
of 300 N ison
applied
it, determine
a steel alloy is shown in the figure. The specimen from
having
original
diameter of 12.5 mm and gauge length
40 it was obtained had an original diameter of 13 mm
the an
change
which
4 ft in its length and the change in its diameter.
P
of 50
Using
the
2. Şekilde
gösterilen
mmIf auzunluğunda
np =data
Ep mm.
= 2.70
GPa,the
0.4. listed in the table, plotSoru
and30a gauge
length of 50
50 mm.
load of P = 20 bir
kN is
stress–strain diagram, and determine approximatelynumunenin
the
applied
to the specimen,
determine ilişkisi
its diameter
and gauge
gerilme-birim
deformasyon
verilmiştir.
modulus of toughness.
20 Take n = 0.4.
A Use a scale of 20Dmm = 50 MPa and
length.
Numuneye
etki eden
P kuvveti 100 kN iken uzamayı
20 mm = 0.05 mm>mm.
C
10
300 N
300 N
hesaplayınız.
Numuneye
150 kN yük uygulanır ve yük
3
3 ft
200 mm
0.03
0.00225
3 ft
P (mm/mm)
kaldırılırsa numunenin
kalıcı 0.04
uzaması
olur.
0
0.02
0.08
0.10
0.002
0.004
0.006
0.008
P (in./in.)
0.010
Probs. 3–14/15
Prob. 3–25
Soru 3. Ölçüm mesafesi 50 mmProbs.
ve orijinal
3–17/18 çapı 12.5 mm
F3–10/11
Elongation (mm)
bir numune çekme
s(MPa)deneyine tabi tutulmuştur. Deney
3–26. The short cylindrical block of 2014-T6 olan
aluminum,
0
0
The stress–strain
diagram for Deformasyon
a bone is shown, and
having an original
diameter of 0.5
in. and a length
of 1.5 in.,tabloda3–19.
verileri
verilmiştir.
Gerilme-Birim
0.0175
11.1
can
be
described
by
the
equation
P = 0.45110-62 s !
400
is
placed
in
the
smooth
jaws
of
a
vise
and
squeezed
until
the
F3–12.*3–16.
If the Determine
elongation
of wire
BC
is of
0.2the
mm
after
the bar
0.0600
31.9
ilişkisini
milimetrik
kağıda
the
elongation
square
hollow
-12
3 (veya Excel gibi bir program
0.36110 2 s , where s is in kPa. Determine the yield
applied
lb.the
Determine
(a) the
decrease
in its
0.1020
37.8is 800to
forceaxial
Pwhen
applied,
determine
wire
it is subjected
the magnitude
axial
forceof
kN . If this beyaz kağıda)
P P.
= The
100
kullanarak
elastisite modülünün,
strength assumingçizerek
a 0.3% offset.
length
and
(b)
its
new
diameter.
0.1650
40.9
is A-36
steel
and
has
a
diameter
of
3
mm.
axial force is increased to P = 360 kN and released, find
0.2490
43.6
maksimum
gerilmenin
ve
göçme
gerilmesinin yaklaşık
the permanent
of the
bar. The bar is made of a
*3–20. The stress–strain diagram for a bone is shown and
1.0160
53.4elongation800
800
lb
lb
değerlerini belirleyiniz.
Çizim için
= 50PMPa
ve 20
-6
metal alloy having
a stress–strain
can be described
by 20
the mm
equation
= 0.45110
2s!
3.0480 diagram which can be
62.3
approximated64.5
as shown.
mm = 0.05 mm/mm
Lineer-elastik
6.3500
is in kPa. Determine
the modulus
0.36110-12ölçeklerini
2 s3, where skullanınız.
8.8900
62.3
of toughness
andve
the20
amount
of elongation
of a 200-mmbölgeyi aynı gerilme
ölçeği
mm=
0.001 mm/mm
C
11.9380
58.8
long
region
just
before
it
fractures
if
failure
occurs at
P
P(mm/mm)
ölçeği ile yeniden
çiziniz.
300 mm
P = 0.12 mm>mm. 0.002
200 mm
Probs. 3–4/5
Prob. 3–28
Soru 4. Şekilde verilen
içi boş kare kesitli
s (MPa)
A
500
P
B
112
C H400
A P mm
TER 3
M E C H A N I C600
AL PROPERTIES OF
mm
Prob. 3–26
3–6. A specimen is originally P
1 ft long, has a diameter of
50 mm
0.5 in.,
and250
is subjected
to F3–12
a force of 500
lb. Whendiagram
the force
3–27.
The
elastic
stress–strain
forisa
3–30.
The
block portion
Ti-6A1-4V and
is increased
from
500
lb
to
1800
lb,
the
specimen
elongates
steel alloytoisashown
in the figure.
specimen
which
subjected
compression
of 0.06The
in. along
the y from
axis, and
its
5the
mm a
0.009
in. Determine
the
modulus diameter
of elasticity for
it was
and
shape
isobtained
given a tilt
ofan
u original
= 89.7°. DetermineofPx13
, Pmm
y, and gxy.
material
remains
elastic.
P (mm/mm)
gaugeif it
length
of linear
50 mm.
When
0.00125 y
P
0.05
çubuğun P=100 kN eksenel yükleme altındaki
uzamasını
belirleyiniz.
P yükü 360 kN değerine
M
AT E R I A L S
s
yükseltildikten sonra kaldırılırsa çubukta
m eyd
a n aThegsupport
e l e c e kconsists
k a l ı of
c ı three
d e fo
r mplates,
a s yowhich
nu
•3–33.
rigid
are
connected
together
using
two
symmetrically
placed
hesaplayınız.
gerilme-birim
•3–29. The Çubuk,
aluminum
block has a deformasyon
rectangular cross
#6 of 5 N is #12
rubber
averilen
vertical
applied
plate
P " 0.45(10
s + 0.36(10
)s3 to
section
and isIfsubjected
toforce
an )axial
compressive
force
of
ilişkisi
şekilde
metal
alaşımdan
imal
A,
determine
the
approximate
vertical
displacement
of
8
kip.
If
the
1.5-in.
side
changed
its
length
to
1.500132
in.,
edilmiştir.
this plate due to shear strains in the rubber.
P Each
50 mm
5Determine
mmof a
is 50 kN,
the diameter
is 12.99265
3–7.specimen
A structural
member
in a nuclear
reactor mm.
determine Poisson’s ratio and the new length of the 2-in.
Poisson’s
ratio
for
the
material.
has
dimensions of 30 mm and 20 mm.
zirconium alloy. If an axial load of 4 kip is to be supported
side.cross-sectional
Eal ! 10(103) ksi.
Prob. 3–16
Probs. 3–19/20
Gr = 0.20 MPa.
by the member, determine its required
cross-sectional area.
s(MPa)
Use a factor of safety of 3 relative to yielding. What is theSoru 5. Çapı 15 mm, uzunluğu 100 mm olan bir
if it is 3 ft long and its elongation is
çubuk 10 kN eksenel çekme kuvvetine maruz kalırsa
4004 in. u 3
0.02 in.? Ezr = 14(10
) ksi, sY = 57.5 ksi. The material has
çapında meydana gelecek değişimi hesaplayınız. E=70
elastic
behavior.
3
x
5 in.
GPa ve ν=0.35 alınız.
1.5 in.
C
Soru 6. Bir çelik alaşımın
gerilme-birim2 Bin.
deformasyon
8 kip
diyagramının
elastik
kısmı
şekilde
gösterilmiştir.
8 kip
3–31. The shear stress–strain diagram for a steel alloy is
shown in the figure. If a bolt having a diameter of 0.75Numunenin
in.
orijinal çapı
133 in.
mm ve ölçüm
40 mm
40 mmmesafesi 50
P(mm/mm)
0.002
and used in the double lap joint,
mm dir. 50 kN yüklendiğinde çap 12.99265 mm
determine the modulus of elasticity E and the force P
oranını hesaplayınız.
Prob. 3–27
Prob. 3–29
required to cause the material
to yield. Take n = 0.3. olmaktadır. Malzemenin Poisson
Prob. 3–30
A
P/2
P/2
P
t(ksi)
60
Soru 7. Şekildeki çelik alaşım için gerilme-birim
deformasyon diyagramı verilmiştir.5 N Bu malzemeden
yapılmış 0.75 in. çapında bir Prob.
bulon3–33
şekildeki birleşimde
kullanılmıştır. Elastisite modülünü belirleyiniz.
Malzemenin akmasına sebep olacak P kuvvetini
0.00545
Prob. 3–31
*3–32. A shear spring is made by bonding the rubber
annulus to a rigid fixed ring and a plug. When an axial load
P is placed on the plug, show that the slope at point y in
3–34. A shear spring is made from two blocks of rubber,
each having a height h, width b, and thickness a. The
blocks are bonded to three plates as shown. If the plates
%41
are rigid and the shear modulus of the rubber is G,
determine the displacement of plate A if a vertical load P is
applied to this plate. Assume that the displacement is small
so that d = a tan g L ag.
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