ENGINEERING MECHANICS-Solution Equilibrium Prob 308-361
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Transcript of ENGINEERING MECHANICS-Solution Equilibrium Prob 308-361
![Page 1: ENGINEERING MECHANICS-Solution Equilibrium Prob 308-361](https://reader038.fdocuments.us/reader038/viewer/2022102409/544bb189b1af9f74678b4e88/html5/thumbnails/1.jpg)
ENGINEERING MECHANICS-STATICEQUILIBRIUM FORCE SYSTEM PROBLEM SET
PROBLEM 308
The cable and boom shown in Fig. P-308 support a load of 600 lb. Determine the tensile force T in the cable and the compressive for C in the boom.
Solution 308
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answer
answer
Another Solution (By Rotation of Axes)
(ok!)
(ok!)
Another Solution (By Force Polygon)
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(ok!)
(ok!)
PROBLEM 309
A cylinder weighing 400 lb is held against a smooth incline by means of the weightless rod AB inFig. P-309. Determine the forces P and N exerted on the cylinder by the rod and the incline.
Solution 309
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answer
answer
Another Solution (By Rotation of Axes)
(ok!)
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(ok!)
Another Solution (By Force Polygon)
( ok! )
( ok! )
Problem 310
A 300-lb box is held at rest on a smooth plane by a force P inclined at an angle θ with the plane as shown in Fig. P-310. If θ = 45°, determine the value of P and the normal pressure N exerted by the plane.
Solution 310
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answer
answer
Problem 311
If the value of P in Fig. P-310 is 180 lb, determine the angle q at which it must be inclined with the smooth plane to hold 300-lb box in equilibrium.
Solution 311
answer
PROBLEM 315
The 300-lb force and the 400-lb force shown in Fig. P-315 are to be held in equilibrium by a third force F acting at an unknown angle θ with the horizontal. Determine the values of F and θ.
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Solution 315
By Cosine Law
answer
answer
The correct position of F would be as shown below.
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PROBLEM 316
Determine the values of α and θ so that the forces shown in Fig. P-316 will be in equilibrium.
Solution 316
By Cosine Law
answer
answer
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PROBLEM 317
The system of knotted cords shown in Fig. P-317 support the indicated weights. Compute the tensile force in each cord.
Solution 317
From the knot containing 400-lb load
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answer
answer
From the knot containing 300-lb load
answer
answer
PROBLEM 318
Three bars, hinged at A and D and pinned at B and C as shown in Fig. P-318, form a four-link mechanism. Determine the value of P that will prevent motion.
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Solution 318
At joint B
At joint C
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answer
PROBLEM 319
Cords are loop around a small spacer separating two cylinders each weighing 400 lb and pass, as shown in Fig. P-319 over a frictionless pulleys to weights of 200 lb and 400 lb . Determine the angle θ and the normal pressure N between the cylinders and the smooth horizontal surface.
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Solution 319
answer
answer
PROBLEM 322
The Fink truss shown in Fig. P-322 is supported by a roller at A and a hinge at B. The given loads are normal to the inclined member. Determine the reactions at A and B. Hint: Replace the loads by their resultant.
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Solution 322
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answer
Thus,RB = 4618.80 lb at 30° with horizontal answer
Another Solution
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(okay!)
From the Force Polygon
(okay!)
(okay!)
PROBLEM 323The truss shown in Fig. P-323 is supported by a hinge at A and a roller at B. A load of 20 kN is applied at C. Determine the reactions at A and B.
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Solution 323
answer
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Thus,RA = 21.06 kN down to the left at 34.7° with the horizontal. answer Another Solution
(okay!)
(okay!) (okay!)
PROBLEM 324
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A wheel of 10-in radius carries a load of 1000 lb, as shown in Fig. P-324. (a) Determine the horizontal force P applied at the center which is necessary to start the wheel over a 5-in. block. Also find the reaction at the block. (b) If the force P may be inclined at any angle with the horizontal, determine the minimum value of P to start the wheel over the block; the angle P makes with the horizontal; and the reaction at the block.
Solution 324Part (a)
answer
answer
Part (b)
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answer
answer
answer
Problem 325
Determine the amount and direction of the smallest force P required to start the wheel in Fig. P-325 over the block. What is the reaction at the block?
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Solution 325
answer
answer
answer
Problem 326
The cylinders in Fig. P-326 have the indicated weights and dimensions. Assuming smooth contact surfaces, determine the reactions at A, B, C, and D on the cylinders.
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Solution 326
From the FBD of 200 kN cylinder
answer
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answer
From the FBD of 400 kN cylinder
answer
answer
Problem 327
Forces P and F acting along the bars shown in Fig. P-327 maintain equilibrium of pin A. Determine the values of P and F.
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Solution 327
→ Equation (1)
Substitute F of Equation (1)
answer
From Equation (1)
answer
Problem 328
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Two weightless bars pinned together as shown in Fig. P-328 support a load of 35 kN. Determine the forces P and F acting respectively along bars AB and AC that maintain equilibrium of pin A.
Solution 328
answer
answer
Problem 329
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Two cylinders A and B, weighing 100 lb and 200 lb respectively, are connected by a rigid rod curved parallel to the smooth cylindrical surface shown in Fig. P-329. Determine the angles αand β that define the position of equilibrium.
Solution 329
From the figure
Thus,
answer
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answer
Problem 332Determine the reactions for the beam shown in Fig. P-332.
Solution 332
answer
answer
Problem 333
Determine the reactions R1 and R2 of the beam in Fig. P-333 loaded with a concentrated load of 1600 lb and a load varying from zero to an intensity of 400 lb per ft.
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Solution 333
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answer
answer
Problem 334
Determine the reactions for the beam loaded as shown in Fig. P-334.
Solution 334
answer
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answer
Problem 335
The roof truss in Fig. P-335 is supported by a roller at A and a hinge at B. Find the values of the reactions.
Solution 335
answer
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answer
Problem 336
The cantilever beam shown in Fig. P-336 is built into a wall 2 ft thick so that it rests against points A and B. The beam is 12 ft long and weighs 100 lb per ft.
Solution 336
answer
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answer
Problem 337
The upper beam in Fig. P-337 is supported at D and a roller at C which separates the upper and lower beams. Determine the values of the reactions at A, B, C, and D. Neglect the weight of the beams.
Solution 337
answer
answer
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answer
answer
Problem 338
The two 12-ft beams shown in Fig. 3-16 are to be moved horizontally with respect to each other and load P shifted to a new position on CD so that all three reactions are equal. How far apart will R2 and R3 then be? How far will P be from D?
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Solution 338
From FBD of beam CD
answer
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Thus, P is 8 ft to the left of D. answer
From the figure above, Rc is at the midspan of AB to produce equal reactions R1 and R2. Thus, R2 and R3 are 6 ft apart. answer
From FBD of beam AB answer
answer
Problem 339
The differential chain hoist shown in Fig. P-339 consists of two concentric pulleys rigidly fastened together. The pulleys form two sprockets for an endless chain looped over them in two loops. In one loop is mounted a movable pulley supporting a load W. Neglecting friction, determine the maximum load W that can just be raised by a pull P supplied as shown.
Solution 339
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answer
Problem 342
The wheel loads on a jeep are given in Fig. P-342. Determine the distance x so that the reaction of the beam at A is twice as great as the reaction at B.
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Solution 342
The reaction at A is twice as the reaction at B
answer
Problem 343
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The weight W of a traveling crane is 20 tons acting as shown in Fig. P-343. To prevent the crane from tipping to the right when carrying a load P of 20 tons, a counterweight Q is used. Determine the value and position of Q so that the crane will remain in equilibrium both when the maximum load P is applied and when the load P is removed.
Solution 343
When load P is removed
→ Equation (1)
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When load P is applied
From Equation (1), Qx = 120, thus,
answer
Substitute Q = 20 tons to Equation (1)
answer
Problem 346
A boom AB is supported in a horizontal position by a hinge A and a cable which runs from C over a small pulley at D as shown in Fig. P-346. Compute the tension T in the cable and the horizontal and vertical components of the reaction at A. Neglect the size of the pulley at D.
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Solution 346
answer
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answer
Ah= 125 1b
answer
Problem 347
Problem 347
Repeat Problem 346 if the cable pulls the boom AB into a position at which it is inclined at 30° above the horizontal. The loads remain vertical.
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Solution 347
Because θ = 60°, T is perpendicular to AB.
answer
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answer
answer
Problem 348
The frame shown in Fig. P-348 is supported in pivots at A and B. Each member weighs 5 kN/m. Compute the horizontal reaction at A and the horizontal and vertical components of the reaction at B.
Solution 348
Length of DF
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Weights of members
answer
answer
answer
Problem 349
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The truss shown in Fig. P-349 is supported on roller at A and hinge at B. Solve for the components of the reactions.
Solution 349
answer
answer
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answer
Problem 350
Compute the total reactions at A and B for the truss shown in Fig. P-350.
Solution 350
answer
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Thus, up to the left at from horizontal. answer
Problem 351
The beam shown in Fig. P-351 is supported by a hinge at A and a roller on a 1 to 2 slope at B. Determine the resultant reactions at A and B.
Solution 351
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Thus, up to the right at from horizontal. answer
Another Solution
From Equilibrium of Concurrent Force System, three coplanar forces in equilibrium are concurrent.
okay
okay
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okay
Problem 352
A pulley 4 ft in diameter and supporting a load 200 lb is mounted at B on a horizontal beam as shown in Fig. P-352. The beam is supported by a hinge at A and rollers at C. Neglecting the weight of the beam, determine the reactions at A and C.
Solution 352
From FBD of pulley
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From FBD of beam
answer
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Thus, up to the right at from horizontal. answer
Problem 353
The forces acting on a 1-m length of a dam are shown in Fig. P-353. The upward ground reaction varies uniformly from an intensity of p1 kN/m to p2 kN/m at B. Determine p1 and p2 and also the horizontal resistance to sliding.
Solution 353
Horizontal resistance to sliding
answer
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Righting moment
Overturning moment
Eccentricity
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Foundation pressure (See Dams at CE Review for more information)
answer
answer
Related post: Resultant of forces in gravity dam
Problem 354
Compute the total reactions at A and B on the truss shown in Fig. P-354.
Solution 354
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answer
Thus, up to the right at from horizontal. answer
Problem 355
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Determine the reactions at A and B on the Fink truss shown in Fig. P-355. Members CD and FG are respectively perpendicular to AE and BE at their midpoints.
Solution 355
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answer
answer
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answer
Problem 356
Problem 356
The cantilever truss shown in Fig. P-356 is supported by a hinge at A and a strut BC. Determine the reactions at A and B.
Solution 356
From right triangles ACD and ACB.
Notice also that triangle ABD is an equilateral triangle of sides 6 m.
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answer
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Thus, up to the right at from horizontal. answer
Problem 357
Problem 357
The uniform rod in Fig. P-357 weighs 420 lb and has its center of gravity at G. Determine the tension in the cable and the reactions at the smooth surfaces at A and B.
Solution 357
Distance AB
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answer
answer
answer
Problem 358
Problem 358
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A bar AE is in equilibrium under the action of the five forces shown in Fig. P-358. Determine P, R, and T.
Solution 358
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answer
answer
answer
Problem 359
Problem 359
A 4-m bar of negligible weight rests in a horizontal position on the smooth planes shown in Fig. P-359. Compute the distance x at which load T = 10 kN should be placed from point B to keep the bar horizontal.
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Solution 359
From the Force Polygon
From the Free Body Diagram
answer
Problem 360
Problem 360
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Referring to Problem 359, what value of T acting at x = 1 m from B will keep the bar horizontal.
Solution 360
From the Force Polygon
From the Free Body Diagram
answer
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Problem 361
Problem 361
Referring to Problem 359, if T = 30 kN and x = 1 m, determine the angle θ at which the bar will be inclined to the horizontal when it is in a position of equilibrium.
Solution 361
From the Force Polygon
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From the Free Body Diagram
answer
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