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Unformatted text preview: MEEN 221 Summer 2008  Worksheet 6 Dr. A. Palazgolo (l) HW S6 Due at Beginning of Next Class Ch 6 g 35, 37, 43, 60, 62, 8g
(2) Attendance Mandatory for 10:00 am— 12:45 pm , unless excused by instructor. Quizzes may be given at any time during this period.
(3) Subjects: Equilibrium for 2D Models EXAM I NEXT WEDS. 18 JUNE 6:00—8:00 PM ZACH 104B
EXTRA TIME [MAY BE GIVEN (I) Static Equilibrium  Moments .
Suppose that a body is represented by a collection of particles with ‘
internal f‘interaction” and external forces. If the body is rigid and in static equilibrium than each particle must be
in static equilibrium, i.e. Ri+2ﬂj:0 Where R, is the resultant external force on particle i and" is the force
on particle 1‘ due to particle j, and by Newton‘s 3‘d Law sz = 721' Take the cross produCt of F, with Eq. 1, and sum the results over all
particles: —'D 9
Fax j 4‘ X 4 we
in 2+i°°iXi.,.=0 , (3)
2': i=1 j=l
The ﬁrst term is the sum of moments of all external forces acting
on the body:
A20 = i i=1
Terms of the second sum in (3) will appear as:
ﬁxﬁi+EX(—fi)=(j—Fj)xfﬁ=ri/jxZi (5) by Eq. 2.
This term is zero because r (a) 0 for two interacting neighbor” particles and/ or . , W _ a _ _ a 6/u (b) nn => r1,,.=0, (6)
(central force problem) Therefore if the body is in static equilibrium
M0 = resultant moment of all external forces (7)
acting on the body = Z x 1—2.1. = 6
(11) Free Body Diagrams External forces on a body may result from pressure, hydraulic loads,
wind gusts, etc.. They also result from the interaction forces that occur wk
interconnection points between the. body and other bodies and ground.
These latter, forces are called reaction forces and they are summarized in Riley's Tables 61 and 62. A free body diagram displays all force
acting on an isolated body. 5 Mfmé Fig. 63 ~ Wm; I roller, 61' rocker (III) Two Force Member
If a body only has two forces acting on it the lines of actions of the two
forces' are collinear and pass through the points of appliCation of the . forces.
Note: 215:0 :> F]=—F‘2 (8)
U250 => a/ax;=o (9)
3 171mg (10)
=> Ella/abyw) (11)] (IV) 3 Force Members If a body is in static equilibrium with 3 external forces the lines of
action for the 3 forces intersect at a point. Proof:
The moments of F] and F2 abOut b are zero but 1171 f 3 $0. This contradicts the condition 2M0 = 0 therefore a and b must be
coincident, i.e. all 3‘ lines of action meet a single point. Q.E.D. (V) Examples
EXAMPLEI Rile 621 621 Draw a. freebody diagram
got the bent bar show=15: Fig. P6_21 which is
fixed at the wall at A. EXAMPLE 2 Riley 644 (Similar to HW 643) Determine the force exerted 35,0”
——__—_’—— ‘ by the cable at B and I react ion at SUpport "A g lthe curved bar shown in.Fig.
[Pa44. ' 0
ii 4xs=;’.°“'~‘*°: Solution __?he lawn mower Shaun
in Fig. P659 weighs
35 lb. Determine the force F required to
M move the mower at a‘
m constant velocity and
m— the forces exerted on I A the front and reg: wheels by the inclined ‘$ *’ __ .17 in “ﬁrm " V ' WatXVL ‘17 ..  — t ‘ ’ , Iiﬂiiﬂlmﬁﬂggﬂﬂﬂ
A p “ I L p I L
'a‘WL.” EXAMPLE4 Rile 6100 A bracket is loaded and supported as shown in ' Fig. P6100. Determine “— . 'the reactions at
, ——————‘ ' supports A and B. Rile 6—87 The plate shown in Fig. "(‘2‘ng 2" W5 x 
9687 weighs 150 lb and w . v ._ e a. .n
is supported in a dw‘Pdﬂm‘ 4:“, m J horizontal position by 5; 34“~ two hinges and a cable. ”
The hinges have been
properly aligned;
therefore, they exert
only force reactions on
the plate. Assume that
the hinge at B resists
any force along the axis
ofthe hinge pins. Determine the :gggtions at supports A and B and Solution C10) 656* Pulleys 1 and 2 of the rope and Outer ro‘AAu‘t. .. (\
pulley system shown in Fig. P656 \ 0 Inner.
. Y'cnckxxnx
are connected and rotate as a unit. yr,
The radii of the pulleys are 100 mm I"
and 300 mm, respectively. Rope A f“ “17 is fastened to pulley 1 at point A'.
Rope B is fastened to pulley 2 at
point B' . Rope C is continuous
over pulleys 3 and 4. Determine
the tension T in rope C required to
hold body W in equilibrium if the .
mass of body W is 225 kg. [El ...
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 Spring '08
 McVay

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