Stress
Jave=F/A def
E E
T
=
.
Shear stress
acts
the area of the
"cut" surface.
Acirc
use
case
inal
2(
&
Emax=KTc/J
and the
Torsion
.
[max=
"
.........
70
E
%
A
T
c
E= shear strain
E 2 E(l + v)
solid
J
=
Poissen's Ratio
Cylinder
6
force.
=
(co"-cit)
M
Aily
yi(
Qeq
[(y yc)(Ai)
-
axis
& neutral
of
datum
&
for all sections
outside
theas
Max shear
T
=
·
·
I
2
-
Axis
parallel
Ediyetalaxis
is
+
-
from
axis
.
A
MayNormalfrombending
.
max
Shear
not the reaction
from Torsion
& outside surface
.
Non-Mohr's
circle
Stress
v(ux + Tz)
=
(x
+
+y + (x
2
-
2
Ty(os (20) + ExySin (20)
0x + +y
(x Ty(os(20)
Gy'
Tankop) = 2ExyY(*x (g)
=
+
=
8x1
-
-
-
ExySin(20)
-
Theory
Failure
May shear
theory
Tabsmax
both
T
=
2
&
/
principle
Stresses
are
&
S
4
of
Strain
stresses
.
Taxis
Von Mises
452
Ty
Stress
theory
52
+
Normal
Ilor/il
=
Tultimate
=
usually brittle materials
fail under norm stress
asthey
2)
I
&
(
S2
Tx
-
TySin(20)
+
ExyCos (20)
=
Sup
a
&
max
Ex'
=
Ex+ Ey
2
Ey'
=
Ex
+
931
2y
2
tan(20p)
Max distortion
energy
Max
,
2
either side
are to
side
Taxis
-
-
-
j
or12)
principle
one
5
=
Tylz
Emax=
of
[x'yl
tresca
.
or
to
stress
=
+
-
Ex-EyCos (20 +
Sin (2
Ex-EyCos (20
Sin (20
-
Uxy/(Ex-Ey)
cost
2
(5x ,[xy)
j
2
0
&
Tmax
.
Strain Transformation
Same as above but in
Circle Exy = x Exy/2
strain rosettes
Ey (2(Ec + Eb) Ea)
=
for 600 -xEx=Ea
,
Uxy 2(Eb-E)/Es
=
for
D
C
Ex=Ea
Ey= Eb
(
-So
in
Uxy=2Eb
450 -
-
3
E
bending
⑧
①
w
T 29
-
Determine
axial
piece from
Ey E (ty
Er E(t -v(rx ry)
=
[ Ii
+(
of neutral
E)(x v(5y + 52)
-
Determine
Determining
I
-
=
Shear
-
noop
=
(
e
iI
⑦
Exy
circle with
the
for
/Glx/53/Y/52)
pressless Pr
4
same
where
5 Tr/J
My/T VQ/It
:
are
0
=
dist
.
Hook's
3D
Ex
=
you
Xfrom
distance of
max
T
v
Torsion
Bending
Tave
,
P/A
Tube :
-Elat/Elong
Elong is parallel
=
radius
of the
Normal
inertia
.
.
sign
Axial
of
.
51
TX-Tave
e
must evaluate
Txy Abs Max
Stress States
c/J
shear stress
=
T= U G
to
.
Ttorquemoment
-------
* If given axis,
relative to given
v=
T
and In
T,
moment
.
charts
·
T2
remember if both
.
remember the
slope
%
,
=YO outside
problems.
.
stat ind
(Ty -[xy)
5) Remeber ①' in Circle
.
Bending
I determined from
new
angle is 0
always radians.
zA
ton
Stress Concentra
.
angle
orig
-
sectionhe
FBD
one
o for compatability
and S for comp
.
in
,
Plot Tave
3) Calculate E
1) Calculate O
use
Tmax=Jave.K
O in
where
2)
and
Sum
.
torsion/axial
Cry -Exy)
D plot (*x ,Exy) and
·
startWithto
LATL
Mohr's Circle
L/G J
multiple
Torques
section
Thermal
=
.
down the bar
Cutting between each
Just imagine stress
flows
-
T
is
.
Strain
=
the
the
For
When a width's
distance from force.
S
T
=
more
the J = Tave
E=ff-10)/lo
In case of an
empty
ball
U
p
internal Axial load
=
StVenant's
Strain
Shear
S=NL/AE
L= length
Cross-sectional Area
A=
. Elasticity
E= Mod
on
,
Angle of Twist
N
.
ChooksLaw)
Elastic Deformation
,
60
-60
&L
&
a
E] W
b
-45
L
745 a
T
L
-