# couple

## Problem 527 and Problem 528 | Friction

**Problem 527**

A homogeneous cylinder 3 m in diameter and weighing 30 kN is resting on two inclined planes as shown in Fig. P-527. If the angle of friction is 15° for all contact surfaces, compute the magnitude of the couple required to start the cylinder rotating counterclockwise.

**Problem 528**

Instead of a couple, determine the minimum horizontal force P applied tangentially to the left at the top of the cylinder described in Prob. 527 to start the cylinder rotating counterclockwise.

## 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.

## 251 Two forces producing a couple and a force

**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.

## 250 Reaction at the supports of cantilever truss

**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.

## 249 - Reactions at the bolts of speed reducer gear box

**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.

## 248 - Broken handwheel replaced by lever to close a gate valve

**Problem 248**

To close a gate valve it is necessary to exert two forces of 60 lb at opposite sides of a handwheel 3 ft in diameter. Through an accident the wheel is broken and the valve must be closed by a thrusting bar through a slot in the valve stem and exerting a force 4 ft out from the center. Determine the force required and draw a free-body diagram of the bar.

## 247 - Resultant of couples in a 3-step pulley

**Problem 247**

The three-step pulley shown in Fig. P-247 is subjected to the given couples. Compute the value of the resultant couple. Also determine the forces acting at the rim of the middle pulley that are required to balance the given system.

## 246 - System with couples and forces on it

**Problem 246**

Determine the resultant moment about point A of the system of forces shown in Fig. P-246. Each square is 1 ft on a side.

## 245 - Couple in the box

**Problem 245**

Refer to Fig. 2-24a. A couple consists of two vertical forces of 60 lb each. One force acts up through A and the other acts down through D. Transform the couple into an equivalent couple having horizontal forces acting through E and F.

## Couples

Couple is a system of forces whose magnitude of the resultant is zero and yet has a moment sum. Geometrically, couple is composed of two equal forces that are parallel to each other and acting in opposite direction. The magnitude of the couple is given by

Where $F$ are the two forces and $d$ is the moment arm, or the perpendicular distance between the forces.

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