May 2011

Resultant of Non-Concurrent Force System

The resultant of non-concurrent force system is defined according to magnitude, inclination, and position.
 

The magnitude of the resultant can be found as follows

$R_x = \Sigma F_x$

$R_y = \Sigma F_y$

$R = \sqrt{{R_x}^2 + {R_y}^2}$

 

Problem 260 - 261 | Resultant of Non-Concurrent Force System

Problem 260
The effect of a certain non-concurrent force system is defined by the following data: ΣFx = +90 kN, ΣFy = -60 kN, and ΣMO = 360 kN·m counterclockwise. Determine the point at which the resultant intersects the x-axis.
 

Problem 262 | Resultant of Non-Concurrent Force System

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

Unbalanced forces in two-step pulley

Problem 263 | Resultant of Non-Concurrent Force System

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

Three non-concurrent non-parallel forces in xy-plane

 

Problem 264 | Resultant of Non-Concurrent Force System

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

264-four-forces.gif

 

Problem 265 | Resultant of Non-Concurrent Force System

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

Three forces in XY plane

 

Problem 266 | Resultant of Non-Concurrent Force System

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?
 

Gravity Dam

 

Problem 267 | Resultant of Non-Concurrent Force System

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 inclination with the horizontal, and where it intersects AB.
 

Howe roof truss

 

Problem 268 | Resultant of Non-Concurrent Force System

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.
 

Three forces in Planar Space

 

Problem 269 | Resultant of Non-Concurrent Force System

Problem 269
Repeat Prob. 268 is 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.
 

Problem 270 | Resultant of Non-Concurrent Force System

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 Ry = ΣY to compute T.
 

270-271-forces-in-xy-space.gif

 

Problem 271 | Resultant of Non-Concurrent Force System

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.
 

270-271-forces-in-xy-space.gif

 

Equilibrium of Concurrent Force System

Equilibrium of Concurrent Forces Using Complex Numbers | Engineering Mechanics

In static, a body is said to be in equilibrium when the force system acting upon it has a zero resultant.
 

Conditions of Static Equilibrium of Concurrent Forces

The sum of all forces in the x-direction or horizontal is zero.

$\Sigma F_x = 0$   or   $\Sigma F_H = 0$

 

The sum of all forces in the y-direction or vertical is zero.

$\Sigma F_y = 0$   or   $\Sigma F_V = 0$

 

Important Points for Equilibrium Forces

    Problem 308 | Equilibrium of Concurrent Force System

    Engineering Mechanics: Cable and Boom Structure - Equilibrium of Concurrent Forces

    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.
     

    Problem 309 | Equilibrium of Concurrent Force System

    Forces acting on the cylinder by the rod and by the incline - Concurrent Forces in Equilibrium

    Problem 309
    A cylinder weighing 400 lb is held against a smooth incline by means of the weightless rod AB in Fig. P-309. Determine the forces P and N exerted on the cylinder by the rod and the incline.
     

    Problem 310 - 311 | Equilibrium of Concurrent Force System

    Required Force to Hold the Box in a Smooth Plane - Equilibrium of Force System

    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.
     

    Block supported by a force in the incline

     

    Problem 312 | Equilibrium of Concurrent Force System

    Problem 312
    Determine the magnitude of P and F necessary to keep the concurrent force system in Fig. P-312 in equilibrium.
     

    312-concurrent-forces.gif

     

    Problem 313 | Equilibrium of Concurrent Force System

    Problem 313
    Figure P-313 represents the concurrent force system acting at a joint of a bridge truss. Determine the value of P and E to maintain equilibrium of the forces.
     

    313-given-concurrent-forces.gif

     

    Problem 314 | Equilibrium of Concurrent Force System

    Problem 314
    The five forces shown in Fig. P-314 are in equilibrium. Compute the values of P and F.
     

    314-given-concurrent-force-system.gif

     

    Problem 315 | Equilibrium of Concurrent Force System

    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.
     

    315-given-figure.gif

     

    Problem 316 | Equilibrium of Concurrent Force System

    Problem 316
    Determine the values of α and θ so that the forces shown in Fig. P-316 will be in equilibrium.
     

    316-given-concurrent-forces.gif

     

    Problem 317 | Equilibrium of Concurrent Force System

    Tensile Forces in Each Cord of a Knot System - Equilibrium of Concurrent Forces

    Problem 317
    The system of knotted cords shown in Fig. P-317 support the indicated weights. Compute the tensile force in each cord.
     

    System of knotted cords

     

    Problem 318 | Equilibrium of Concurrent Force System

    Equilibrium of Four-Link Mechanism - Concurrent Forces in Equilibrium

    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.
     

    Four-link mechanism

     

    Problem 319 | Equilibrium of Concurrent Force System

    Problem 319 - Finding the unknown angle theta and the normal force acting on the floor

    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.
     

    Cords loop around the spacer of cyliders

     

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