# 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.

## 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 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.