Vectors
I
Moment of a Force:
:
M
F Exc Fij
F
=
+
Ex =EcoSp
Fy : sing
Fy
moment (m) applied
by force F about pt O
Mo IFd
.
-
SI units
F1)
* IF1 is magnitude of
F /Fi
(Fy)
=
=
.
USCS +t 1b
:
-
moment arm
+
=
N m
:
F
Nd
...
It
8
To find resultant force
do component-wise (t).
O
:
F
P
L
⑧
Y
Supports
:
d
Fixed Support
If object is
equilibrium
⑤
X, y,&M reaction
Stress [+(sigma)]
(
K
:
[Fx
compression
strain
force-per-unit-area
OR y reaction
T
Elastic Plastic Deformation
:
will Shrink Ad transverse strain
·
proportionality constant
=
E() E
=
Work (in
·
YOUNG'S MODULUS .
:
Al
W=
rotational
motion)
small amount of work by
constant F for small do
dW Force x dist.
=
A
=
v
·
X
=
Fds
Frdq
= ds rd
v
r
0
W
=
Fro
>
-
w
=
24
travelled
r-radius of rotation .
roo
:
=A=
units : SI : Watts(w)
N
.
=
m/s
uscs horse power
:
:
V = rw
·
gen transmitted using years.
years transmit speed & torque.
motion
.
regular year sour gear *
:
Rotational Power (P)
P
V=
t
Gears
·
2-moment/torque from F
=
ds-small circumference
:
.
at distance r
ds
of
-
Power (in rotational motions
35
.
60
EA
.
.
vel along the tangent
.
*
Travel do
2π (RPM)
0 25 <V / 0
Point p will have lin.
P
angular vel(59)
dt-time taken to
w
* For most metals ,
T
do
:
=Rdo
=
:
Linear velocity (of angular motion)
rotation .
RPM - w
S
E
W
o
U
:
(c) of point P as
P
M
o
OR
=
[
:
# AKA Elastic Modulus
T= Et
Poisson's ration (nu0)
Define angular velocity
·
stress directly proportional
to strain
=
compression -ve stress
-> Slightly increase
do
:
Etrans Ad
-
=
-XE
cross sectional area
Tension : the stress
7 F
ALOngAndin strate
-
For tension force , diameter
:
=
Slightly Shrink
=
original length
T : Stress (sigma)
Angular velocity (rotational motion)
permanent plastic
Hooke's law (Elastic Def)
:
E
A
=
7)
LtAL
amount of stretch
=
relative to its
=
:
N/m2 Pa
1b/in2 Psi
X
:
S
Diameter will shrink
C)
Strain [E Cepsilon)]
stress is
Roller support
↑
>o
on the rod .
Units :
(
Forces point
-
we are applying stress
Length will increase
K
-
pressing material together
By pulling with F,
A
direction Erotation allowed. :
apart
TOWARDS the center :
=
:
d-Ad-
:·
↳
=
If pull on rod with F
translation along one
Forces pulling
0
=
rotation abt pin allowed:
↑
X , y reaction
:
-
AWAY from each other
:
& Fy 0
CM 10 0
7)
L
Tension
in
zero net moment
·
7 F
C)
↑d
Tension vs. Compression :
net Force
ling the material
zero
·
:
no rotation no translation ·
Pin support
S
Y
Equilibrium
a
ut
N-#teeth on
r-radius of
S-space btwn
gear
geara
w-width of tooth
* assume S w
=
N=
OUTPUT POWER
INPUT POWER
MatingGearsEFCEN =
Normal
push/pull the material
Shear stress (2) applied force 11 to cross-section
-
&
↳ tends to slice the material
z
gear ratio :eth
2
.
V-shear force parallel to cross-section
outpu
of roa
A-cross-sectional area
v
-GUETEBOL
:
Torque of input gear
*
=
z-shear stress
of output gear
speed ratio Angular speed
=
of
Angular speed input gear
of output year- E
Torque ratio Torque
:
requires calculation of shear force
↳
Equations derived for years also apply to
Belt and chain drives
applied force +to cross-section
-
↳ tends to
·
*
shear stress
v.s
Normal Stress (2)
·
(single shear)
F
↓
2,
D
stress-strain curved part failure
ItBOLT
Stress (1)
It
N
"
PLASTIC DEFORMATION
STRAIN
HARDENING
↑
!
NECKING
↑
ULTIMATE
YIELD STRENGTH
SGM(M)
in design, keep normal stress
below yield strength
&y
shear yield strength (2y) *
=
of normal yield strength (Ty)
Zy : Ty
·
keep applied shear stress (2)
below shear yield strength (2)
< Ty
·
strain , E
F
FoS(n) is a ratio between yield strength
& applied stress.
·
N
FAILURE
hear
Factor of Safety CFoS)
For normal stress :
n
ULTIMATE
·
·
"
It
Y
↓
·
=
- applied
normal stress
For shear stress
U
=
z 2- applied
shear stress
* Typically 1 5 <n < 4 0
.
.
Tera (T)
Giga (G)
=
10
=
109
Mega (M)
10
=
double sheer
"
V
=
=
deka (da)
deci (d)
10
=
Centi (c)
10
=
+
10
=
milli (m)
=
nano (n)
=
-
10-3
micro (M) 10
=
-
10
pico(p) 10-12
=
e t
Cylinder A
=+
p
Power is conserved in
an
ideal
-
9
=
n
yield
strength
kilo (k) 183
necto (h) 10
==
Pin Port
Pin
=
Watts
=
year
lesund
Fort Wort
Joces Nim
=
train
=
Kim