resultant of non concurrent force system

7/27/2019 Resultant of Non Concurrent Force System

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RESULTANT OF NON CONCURRENT FORCE SYSTEM

Problem 260

The effect of a certain non-concurrent force system is defined by the following data: ΣFx = +90kN, ΣFy = -60 kN, and ΣMO = 360 kN·m counterclockwise. Determine the point at which the

resultant intersects the x-axis.

Solution 260

The x-intercept is at 6 m to the left of the origin. answer

Problem 261 In a certain non-concurrent force system it is found that ΣFx = -80 lb, ΣFy = +160 lb, and ΣMO =

480 lb·ft in a counterclockwise sense. Determine the point at which the resultant intersects the y-

axis.

Solution 261



The y-intercept of the resultant is 6 ft above the origin. answer

Problem 262 Determine completely the resultant of the forces acting on the step pulley shown in Fig. P-262.

Solution 262

http://www.mathalino.com/image/mech-039-unbalanced-forces-two-step-pullry






Thus, R = 1254.89 lb downward to the right at θx = 44.21° and passes through the axle.

Problem 263 Determine the resultant of the force system shown in Fig. P-263 and its x and y intercepts.

http://www.mathalino.com/image/mech-040-three-non-concurrent-non-parallel-forces-xy-plane






Solution 263



Thus, R = 161.314 lb upward to the right at θx = 21.69° and intercepts at (1.668, 0) and (0, -

0.671).

Problem 264 Completely determine the resultant with respect to point O of the force system shown in Fig. P-

264.

Solution 264



Thus, R = 544.68 N upward to the right at θx = 28.25°. The intercepts of R are (-4.57, 0) and (0,2.46).

Problem 265 Compute the resultant of the three forces shown in Fig. P-265. Locate its intersection with X and

Y axes.

Solution 265



Thus, R = 957.97 lb downward to the right at θx = 32.19°. The x-intercept is at 2.90 ft to the right

of O and the y-intercept is 1.83 ft above point O.

Problem 266 Determine the resultant of the three forces acting on the dam shown in Fig. P-266 and locate its

intersection with the base AB. For good design, this intersection should occur within the middle

third of the base. Does it?

Solution 266

http://civilengineeringreview.com/book/fluid-mechanics-and-hydraulics/dams



http://www.mathalino.com/image/mech-041-gravity-dam







Righting moment

Overturning moment

Moment at the toe (downstream side - point B)



Location of R y as measured from the toe

(within the middle third)

Thus, R = 27 424.02 lb downward to the right at θx = 79.91° and passes through the base at 8.44

ft to the left of B which is within the middle third.

Problem 267 The Howe roof truss shown in Fig. P-267 carries the given loads. The wind loads are

perpendicular to the inclined members. Determine the magnitude of the resultant, its inclinationwith the horizontal, and where it intersects AB.

http://www.mathalino.com/image/mech-042-howe-truss






Solution 267



Thus, R = 10 778.16 N downward to the right at θx = 68.2° passing 4.46 m to the right of A.

Problem 268 The resultant of four forces, of which three are shown in Fig.P-268, is a couple of 480 lb·ft clockwise in sense. If each

square is 1 ft on a side, determine the fourth force completely.

Solution 268

Let F4 = the fourth force and for couple resultant, R is zero.

http://www.mathalino.com/image/mech-043-three-forces-planar-space








Thus,

Assuming F4 is above point O

d is positive, thus, the assumption is correct that F4 is above point O.

Therefore, the fourth force is 200 lb acting horizontally to the left at 5.8 ft above point O.

answer



Problem 269 Repeat Prob. 268 if the resultant is 390 lb directed down to the right at a slope of 5 to 12 passing

through point A. Also determine the x and y intercepts of the missing force F.

Solution 269 Let F4 = the fourth force

http://www.mathalino.com/reviewer/engineering-mechanics/problem-268-resultant-non-concurrent-force-system






Resolve F4 into components at the x-axis

Resolve F4 into components at the y-axis

Thus, F4 = 219.32 lb downward to the right at θx = 43.15° with x-intercept ix = 3.27 to the right

of O, and y-intercept iy = 3.06 ft above point O.

Problem 270 The three forces shown in Fig. P-270 are required to cause a horizontal resultant acting through

point A. If F = 316 lb, determine the values of P and T. Hint: Apply MR = ΣMB to determine R,then MR = ΣMC to find P, and finally MR = ΣMD or R y = ΣY to compute T.



Solution 270 For horizontal resultant, R y = 0 and R x = R

answer



answer

Problem 271 The three forces in Fig. P-270 create a vertical resultant acting through point A. If T is known to

be 361 lb, compute the values of F and P.

Solution 271 For vertical resultant, R x = 0 and R y = R



answer

answer

resultant of non concurrent force system

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