Engineering Mathematics

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/m2. It is supported on the three points as shown in the figure.
 

eq-parallel-forces-trapezoid-slab.gif
  1. Find the reaction at A.
    A.   16,848 N
    B.   6,716 N
    C.   13,372 N
    D.   2,010 N
  2. Find the reaction at B.
    A.   16,848 N
    B.   6,716 N
    C.   13,372 N
    D.   2,010 N
  3. 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.

$\Sigma F = 0$

 

The sum of moment at any point O is zero.

$\Sigma M_O = 0$

 

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.
 

Twenty tonner traveling crane

 

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.
 

Wheel loads of a jeep moving across the beam

 

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.
 

System of Five 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.
 

Differential Chain Hoist

 

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 R2 and R3 then be? How far will P be from D?
 

338-nagpatungay-napud.gif

 

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.
 

337-nag-patungay-nga-beam.gif

 

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.
 

336-beam-embedded.gif

 

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.
 

335-fink-truss-na-pud.gif

 

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