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245 - Couple in the boxTags:coupleboxequivalent couples

Problem 245

Refer to Fig. 2-24a. A couple consists of two vertical forces of 60 lb each.

One force acts up through A and the other acts down through D.Transform the couple into an equivalent couple having horizontal forces

acting through E and F.

Solution 245

HideClick here to show or hide the solution

answer

- See more at:http://www.mathalino.com/reviewer/engineering-

mechanics/245-couple-box#sthash.IpcJ7APr.dpuf
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246 - System with couples and forces on itTags:couplemomentmoment centermoment effectresultant moment

Problem 246

Determine the resultant moment about point A of the system of forces

shown in Fig. P-246. Each square is 1 ft on a side.

Solution 246


answer


mechanics/246-system-couples-and-forces-it#sthash.I6rTwrgc.dpuf
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247 - Resultant of couples in a 3-step

pulleyTags:pulleycoupleequivalent coupleresultant couplethree-step pulley

Problem 247

The three-step pulley shown in Fig. P-247 is subjected to the given

couples. Compute the value of the resultant couple. Also determine the

forces acting at the rim of the middle pulley that are required to balance

the given system.

Solution 247


Solving for the resultant couple

answer

Solving for equivalent couple acting in the middle pulley

The resultant couple is composed of two 63.3 lb forces. answer


mechanics/resultent-couples-3-step-pulley#sthash.KL8SG8hj.dpuf

248 - Broken handwheel replaced by lever

to close a gate valve

Tags:

torquecoupleleverhandwheelhand wheelgate valve

Problem 248

To close a gate valve it is necessary to exert two forces of 60 lb at

opposite sides of a handwheel 3 ft in diameter. Through an accident the

wheel is broken and the valve must be closed by a thrusting bar through

a slot in the valve stem and exerting a force 4 ft out from the center.

Determine the force required and draw a free-body diagram of the bar.

Solution 248


Required couple to close the gate valve
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Equivalent torque for the lever

answer


mechanics/248-handwheel-replaced-lever-close-gate-

vale#sthash.S0nVwxGO.dpuf

249 - Reactions at the bolts of speed

reducer gear box

Tags:bolttorquecouplespeed reducergear boxbolt reactioncouple reaction

Problem 249

Fig. P-249 represents the top view of a speed reducer which is geared for

a four to one reduction in speed. The torque input at the horizontal shaft

C is 100 lbft. The torque output at the horizontal shaft D, because of the

speed reduction, is 400 lbft. Compute the torque reaction at the

mounting bolts A and B holding the reducer to the floor. Hint: The torque

reaction is caused by the unbalanced torque, which is a couple.

Solution 249


The couple resistance at the bolts is equivalent to the difference of

torques on each shaft
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R = 120 lb up at A and down at B. answer


mechanics/249-reactions-bolts-speed-reducer-gear-

box#sthash.FQQU5k7i.dpuf

250 Reaction at the supports of cantilever

truss

Tags:trusscouplecouple reactioncantilever trusstruss reactionreaction at the supportclockwise couplecounterclockwise couple

Problem 250The cantilever truss shown in Fig. P-250 carries a vertical load of 10.8

kN. The truss is supported by bearing at A and B which exert the forces

Av, Ah, and Bh. The four forces shown constitute two couples which must

have opposite moment effects to prevent movement of the truss.

Determine the magnitude of the supporting forces.

Solution 250


The given load and AVproduce a counterclockwise couple

Since Bh= Ah, the two are clockwise couple.
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Thus,

Summary (answer)


mechanics/250-support-reactions-cantilever-

truss#sthash.WrxXZopu.dpuf

251 Two forces producing a couple and a

force

Tags:coupleresultantcounterclockwise momentresultant couple

Problem 251

A vertical force P at A and another vertical force F at B in Fig. P-251

produce a resultant of 100 lb down at D and a counterclockwise couple C

of 200 lbft. Find the magnitude and direction of forces P and F.

Solution 251


answer

answer

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252 Equivalent single force for a force anda coupleTags:clockwise coupleResolution of a Force into a Force and a Coupleequivalent single force

Problem 252

A force system consists of a clockwise couple of 480 Nm plus a 240 N

force directed up to the right through the origin of X and Y axes at x =

30. Replace the given system by an equivalent single force and compute
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the intercepts its line of action with the X and Y axes.

Solution 252


The figure below shows the given force system

The force system above can be replaced by the following three force

system shown below where the two pair into a couple which is the couple

480 Nm. The effect of these forces would be the same as the original

system.

The two opposing forces above will get canceled, thus, leaving a single

force with the same effect as the three forces above which in turn has the

same effect to the original system.

Thus, the equivalent single force is 240 N parallel to the given one and at

a distance d = 2 m from O. The intercepts of this single force are A(-4, 0)

and B(0, 2.31). answer


mechanics/252-equivalent-single-force-force-and-

couple#sthash.h2Pv8uPv.dpuf
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253-254 Equivalent single force to replace

a force and a coupleTags:clockwise couplecounterclockwise coupleResolution of a Force into a Force and a Couplegraphical solution

Problem 253In Fig. P-253 a system of forces reduces to downward vertical force 400

lb through A plus a counterclockwise couple of 800 lbft. Determine the

single force that will produce an equivalent effect.

HideClick here to read or hide the solution to Problem 523

Problem 254

Rework Prob. 253 if the system reduces to a leftward horizontal force of

300 lb through point A plus a clockwise couple of 750 lbft.

HideClick here to read or hide the solution to Problem 524


mechanics/253-254-equivalent-single-force-replace-force-and-

couple#sthash.NSPO9Xj7.dpuf

255 Equivalent loads to a compression

member with eccentric load

Tags:coupleeccentricityequivalent coupleResolution of a Force into a Force and a Coupleeccentric loadcompression membereccentrically loaded membershort column

Problem 255

A short compression member carries an eccentric load P = 200 lb

situated 2 in. from the axis of the member, as shown in Fig. P-225. In

strength of materials it is learned that the internal stresses are

determined from the equivalent axial load and couple into which P may

be resolved. Determine the equivalent axial load and couple.
http://www.mathalino.com/tag/reviewer/clockwise-couplehttp://www.mathalino.com/tag/reviewer/clockwise-couplehttp://www.mathalino.com/tag/reviewer/counterclockwise-couplehttp://www.mathalino.com/tag/reviewer/counterclockwise-couplehttp://www.mathalino.com/tag/reviewer/resolution-force-force-and-couplehttp://www.mathalino.com/tag/reviewer/resolution-force-force-and-couplehttp://www.mathalino.com/tag/reviewer/graphical-solutionhttp://www.mathalino.com/tag/reviewer/graphical-solutionhttp://www.mathalino.com/reviewer/engineering-mechanics/253-254-equivalent-single-force-replace-force-and-couplehttp://www.mathalino.com/reviewer/engineering-mechanics/253-254-equivalent-single-force-replace-force-and-couplehttp://www.mathalino.com/reviewer/engineering-mechanics/253-254-equivalent-single-force-replace-force-and-couplehttp://www.mathalino.com/reviewer/engineering-mechanics/253-254-equivalent-single-force-replace-force-and-couplehttp://www.mathalino.com/reviewer/engineering-mechanics/253-254-equivalent-single-force-replace-force-and-couple#sthash.NSPO9Xj7.dpufhttp://www.mathalino.com/reviewer/engineering-mechanics/253-254-equivalent-single-force-replace-force-and-couple#sthash.NSPO9Xj7.dpufhttp://www.mathalino.com/reviewer/engineering-mechanics/253-254-equivalent-single-force-replace-force-and-couple#sthash.NSPO9Xj7.dpufhttp://www.mathalino.com/reviewer/engineering-mechanics/253-254-equivalent-single-force-replace-force-and-couple#sthash.NSPO9Xj7.dpufhttp://www.mathalino.com/reviewer/engineering-mechanics/253-254-equivalent-single-force-replace-force-and-couple#sthash.NSPO9Xj7.dpufhttp://www.mathalino.com/tag/reviewer/couplehttp://www.mathalino.com/tag/reviewer/couplehttp://www.mathalino.com/tag/reviewer/eccentricityhttp://www.mathalino.com/tag/reviewer/eccentricityhttp://www.mathalino.com/tag/reviewer/equivalent-couplehttp://www.mathalino.com/tag/reviewer/equivalent-couplehttp://www.mathalino.com/tag/reviewer/resolution-force-force-and-couplehttp://www.mathalino.com/tag/reviewer/resolution-force-force-and-couplehttp://www.mathalino.com/tag/reviewer/eccentric-loadhttp://www.mathalino.com/tag/reviewer/eccentric-loadhttp://www.mathalino.com/tag/reviewer/compression-memberhttp://www.mathalino.com/tag/reviewer/compression-memberhttp://www.mathalino.com/tag/reviewer/eccentrically-loaded-memberhttp://www.mathalino.com/tag/reviewer/eccentrically-loaded-memberhttp://www.mathalino.com/tag/reviewer/short-columnhttp://www.mathalino.com/tag/reviewer/short-columnhttp://www.mathalino.com/tag/reviewer/short-columnhttp://www.mathalino.com/tag/reviewer/eccentrically-loaded-memberhttp://www.mathalino.com/tag/reviewer/compression-memberhttp://www.mathalino.com/tag/reviewer/eccentric-loadhttp://www.mathalino.com/tag/reviewer/resolution-force-force-and-couplehttp://www.mathalino.com/tag/reviewer/equivalent-couplehttp://www.mathalino.com/tag/reviewer/eccentricityhttp://www.mathalino.com/tag/reviewer/couplehttp://www.mathalino.com/reviewer/engineering-mechanics/253-254-equivalent-single-force-replace-force-and-couple#sthash.NSPO9Xj7.dpufhttp://www.mathalino.com/reviewer/engineering-mechanics/253-254-equivalent-single-force-replace-force-and-couple#sthash.NSPO9Xj7.dpufhttp://www.mathalino.com/reviewer/engineering-mechanics/253-254-equivalent-single-force-replace-force-and-couple#sthash.NSPO9Xj7.dpufhttp://www.mathalino.com/reviewer/engineering-mechanics/253-254-equivalent-single-force-replace-force-and-couplehttp://www.mathalino.com/reviewer/engineering-mechanics/253-254-equivalent-single-force-replace-force-and-couplehttp://www.mathalino.com/tag/reviewer/graphical-solutionhttp://www.mathalino.com/tag/reviewer/resolution-force-force-and-couplehttp://www.mathalino.com/tag/reviewer/counterclockwise-couplehttp://www.mathalino.com/tag/reviewer/clockwise-couple

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257 Horizontal couple equivalent to vertical

forcesTags:frameresultantequivalent coupleResolution of a Force into a Force and a Couple

Problem 257Replace the system of forces acting on the frame in Fig. P-257 by a

resultant R at A and a couple acting horizontally through B and C.

Solution 257


Resultant of vertical forces

Moment about point A

Location of R as measured from point A

Magnitude of horizontal couple at B and C
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Thus the given system is equivalent to downward force of 50 kN at point

A and clockwise couple of 220 kNm. The couple is represented by 110

kN horizontal forces at B and C. The force at B is to the right and the

force at C is to the left, producing the clockwise couple. answer


mechanics/257-horizontal-couple-equivalent-vertical-

forces#sthash.ZFHLhZvR.dpuf

258 Equivalent horizontal and vertical

couples

Tags:resultantequivalent coupleResolution of a Force into a Force and a Couplehorizontal couplevertical couple

Problem 258

Replace the system of forces shown in Fig. P-258 by an equivalent force

through O and a couple acting through A and B. Solve if the forces of the

couple are (a) horizontal and (b) vertical.

Solution 258

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Equivalent force through O and couple through A and B are shown in the

figure below:

- See more at: http://www.mathalino.com/reviewer/engineering-

mechanics/258-equivalent-horizontal-and-vertical-

couples#sthash.9my8AY4T.dpuf

es 23 couples

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