Resolution of a Force into a Force and a 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.
 

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.