# parallel forces

## Support Reactions of a Trapezoidal Slab with Three Points of Support

**Situation**

A reinforced concrete slab in the shape of an isosceles trapezoid weighs 3600 N/m^{2}. It is supported on the three points as shown in the figure.

- Find the reaction at A.

A. 16,848 N

B. 6,716 N

C. 13,372 N

D. 2,010 N - Find the reaction at B.

A. 16,848 N

B. 6,716 N

C. 13,372 N

D. 2,010 N - Find the reaction at C.

A. 16,848 N

B. 6,716 N

C. 13,372 N

D. 2,010 N

## Equilibrium of Parallel Force System

**Conditions for Equilibrium of Parallel Forces**

The sum of all the forces is zero.

The sum of moment at any point O is zero.

## Problem 343 | Equilibrium of Parallel Force System

**Problem 343**

The weight W of a traveling crane is 20 tons acting as shown in Fig. P-343. To prevent the crane from tipping to the right when carrying a load P of 20 tons, a counterweight Q is used. Determine the value and position of Q so that the crane will remain in equilibrium both when the maximum load P is applied and when the load P is removed.

## Problem 342 | Equilibrium of Parallel Force System

**Problem 342**

The wheel loads on a jeep are given in Fig. P-342. Determine the distance x so that the reaction of the beam at A is twice as great as the reaction at B.

## Problem 340 - 341 | Equilibrium of Parallel Force System

**Problem 340**

For the system of pulleys shown in Fig. P-340, determine the ratio of W to P to maintain equilibrium. Neglect axle friction and the weights of the pulleys.

## Problem 339 | Equilibrium of Parallel Force System

**Problem 339**

The differential chain hoist shown in Fig. P-339 consists of two concentric pulleys rigidly fastened together. The pulleys form two sprockets for an endless chain looped over them in two loops. In one loop is mounted a movable pulley supporting a load W. Neglecting friction, determine the maximum load W that can just be raised by a pull P supplied as shown.

## Problem 338 | Equilibrium of Parallel Force System

**Problem 338**

The two 12-ft beams shown in Fig. 3-16 are to be moved horizontally with respect to each other and load P shifted to a new position on CD so that all three reactions are equal. How far apart will R_{2} and R_{3} then be? How far will P be from D?

## Problem 337 | Equilibrium of Parallel Force System

**Problem 337**

The upper beam in Fig. P-337 is supported at D and a roller at C which separates the upper and lower beams. Determine the values of the reactions at A, B, C, and D. Neglect the weight of the beams.

## Problem 336 | Equilibrium of Parallel Force System

**Problem 336**

The cantilever beam shown in Fig. P-336 is built into a wall 2 ft thick so that it rests against points A and B. The beam is 12 ft long and weighs 100 lb per ft.

## Problem 335 | Equilibrium of Parallel Force System

**Problem 335**

The roof truss in Fig. P-335 is supported by a roller at A and a hinge at B. Find the values of the reactions.