statics (met 2214) prof. s. nasseri forces and moments met 2214
TRANSCRIPT
Statics (MET 2214)Prof. S. Nasseri
Forces and Moments MET 2214
Statics (MET 2214)Prof. S. Nasseri
Moments and Forces
Part 4
Statics (MET 2214)Prof. S. Nasseri
Moment of a Couple
A couple is defined as:Two parallel forcesSame MagnitudeOpposite directionSeparated by a perpendicular distance d
-F
d
F
Statics (MET 2214)Prof. S. Nasseri
Couple MomentA moment produced by a couple is called a Couple Moment.
FrM
rr-rBut
Frr-M
FrF-rM
FrF)(rM
AB
BA
BA
BA
So a couple moment is a free vector which can act at any point and depends only on r, not on rA and rB.
Statics (MET 2214)Prof. S. Nasseri
Couple MomentRemember:Scalar Formulation:Magnitude: M = Fd
Direction and sense using right-hand rule
Vector Formulation:
Magnitude: M = r x F
Note: The moment of a couple does not depend on the point one takes the moment about. In other words, a moment of a couple is the same about all points in space.
Statics (MET 2214)Prof. S. Nasseri
Example 1Each person in this figure is exerting a 20N force on the tube. If the distance between the two points is 150mm, what is the moment due to the forces applied.
M = F.d= (20)(0.15) = 3N.m
Statics (MET 2214)Prof. S. Nasseri
Example 2The crossbar wrench is used to remove a lug nut from the automobile wheel. The mechanic applies a moment couple to the wrench such that his hands are a constant distance apart. Is it necessary that a = b in order to produce the most effective turning of the nut? Explain.
Solution:Couple moment: Mc = F(a+b),The couple moment depends on the total distance between grips. a = b is not a necessary condition to produce the most effective turning of the nut.
Also what is the effect of changing the shaft dimension c in this regard? The forces act in the vertical plane.
Changing the dimension c has no effect on turning the nut.
Statics (MET 2214)Prof. S. Nasseri
Example 3Determine the resultant couple moment of the two couples that act on the pipe assembly. The distance from A to B is d = 400 mm. Express the result as a Cartesian vector.
Statics (MET 2214)Prof. S. Nasseri
Example 3
m k0.2j35.0r
m k0)(0.4sin30j0)(-0.4cos30i0.350.35r
)sin30 ,0.40.4cos30- B(0.35,
0) 0, A(0.35,
:VectorPosition
AB
AB
Statics (MET 2214)Prof. S. Nasseri
Example 3
N.m 51710
0050-
0.23500
N.m 2512
3500
0.23500
N }{-50 N; }{35
m 0.2350
:Moments Couple
2
k.j.
kji
M
FrM
i..
kji
M
FrM
iFkF
kj.r
2C
AB2C
1C
1AB1C
21
AB
N.m 517102512
:Moment CoupleResultant
N.m 51710
N.m 2512
N }{-50 N; }{35
m 0.2350
k.ji.MMM
ΣMM
k.jM
i.M
iFkF
kj.r
2C1CR
R
2C
1C
21
AB
Notice this is negative because we are taking moment about A !
Statics (MET 2214)Prof. S. Nasseri
Example 3
Come on!There must
be an easier way!!
Statics (MET 2214)Prof. S. Nasseri
Example 3Lets check three different views and see what
forces are causing moments about x, y and z axes:
y
z
x
z
x
y
35N
35N
50N
50N
50N
50N
0.4cos300.4sin30
0.4cos30
X-viewGives moment about x
Y-viewGives moment about y
Z-viewGives moment about z
-
--
Statics (MET 2214)Prof. S. Nasseri
Example 3
N.m 517102512
:vectorCartesian a as M Express
N.m 517
304050
N.m 10
304050
N.m 2512
304035
axes z and y, about x, moments Summing :AnalysisScalar
R
k.ji.M
.
)cos.(
)sin.(
.
)cos.(
R
zR
zzR
yR
yyR
xR
xxR
M
ΣMM
M
ΣMM
M
ΣMM