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

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.
 

Problem 257
Replace 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.
 

Problem 256
A vertical shaft AB is 5 ft long and bolted to a rigid support at its lower end A. At its upper end B is attached a horizontal bar BC which is 2 ft long. At the end of C is applied a force P = 180 lb. Force P is perpendicular to the plane containing points A, B, and C. Determine the twisting effect of P on the shaft AB and the bending effect at point A.
 

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.
 

Problem 253
In Fig. P-253 a system of forces reduces to downward vertical force 400 lb through A plus a counterclockwise couple of 800 lb·ft. Determine the single force that will produce an equivalent effect.
 

Problem 252
A force system consists of a clockwise couple of 480 N·m plus a 240 N force directed up to the right through the origin of X and Y axes at θ_x = 30°. Replace the given system by an equivalent single force and compute the intercepts its line of action with the X and Y axes.
 

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 lb·ft. Find the magnitude and direction of forces P and F.
 

Problem 250
The 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 A_v, A_h, and B_h. 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.
 

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 lb·ft. The torque output at the horizontal shaft D, because of the speed reduction, is 400 lb·ft. 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.