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equilibrium

Problem 351 | Equilibrium of Non-Concurrent Force System

Problem 351
The beam shown in Fig. P-351 is supported by a hinge at A and a roller on a 1 to 2 slope at B. Determine the resultant reactions at A and B.
 

Beam with roller support on a slope

 

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Problem 350 | Equilibrium of Non-Concurrent Force System

Problem 350
Compute the total reactions at A and B for the truss shown in Fig. P-350.
 

Overhang truss at both ends

 

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Problem 349 | Equilibrium of Non-Concurrent Force System

Problem 349
The truss shown in Fig. P-349 is supported on roller at A and hinge at B. Solve for the components of the reactions.
 

Truss supported by a roller and a hinge

 

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Problem 348 | Equilibrium of Non-Concurrent Force System

Problem 348
The frame shown in Fig. P-348 is supported in pivots at A and B. Each member weighs 5 kN/m. Compute the horizontal reaction at A and the horizontal and vertical components of the reaction at B.
 

Simple Frame Supported in Pivots

 

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Problem 347 | Equilibrium of Non-Concurrent Force System

Problem 347
Repeat Problem 346 if the cable pulls the boom AB into a position at which it is inclined at 30° above the horizontal. The loads remain vertical.
 

Cable and boom structure

 

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Problem 346 | Equilibrium of Non-Concurrent Force System

Problem 346
A boom AB is supported in a horizontal position by a hinge A and a cable which runs from C over a small pulley at D as shown in Fig. P-346. Compute the tension T in the cable and the horizontal and vertical components of the reaction at A. Neglect the size of the pulley at D.
 

Cable and boom structure

 

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Equilibrium of Non-Concurrent Force System

There are three equilibrium conditions that can be used for non-concurrent, non-parallel force system.
 

The sum of all forces in the x-direction or horizontal is zero.

$\Sigma F_x = 0$   or   $\Sigma F_H = 0$

 

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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.

$\Sigma M_O = 0$

 

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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

 

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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

 

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