Resolution of a Force into a Force and a Couple

258 Equivalent horizontal and vertical couples

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.



257 Horizontal couple equivalent to vertical forces

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.



256 Twisting and bending effects

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.

255 Equivalent loads to a compression member with eccentric load

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.

Eccentrically loaded compression member


253-254 Equivalent single force to replace a force and a 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.



252 Equivalent single force for a force and a couple

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 θx = 30°. Replace the given system by an equivalent single force and compute the intercepts its line of action with the X and Y axes.

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