Determine the horizontal and vertical components of reaction at pin c

Determine the horizontal component of reaction at

Determine the horizontal component of reaction at pin C. Set F1 = 400 lb and F2 = 350 lb. Determine the vertical component of reaction at pin C.

Answer

General guidance

Concepts and reason
The external force and couple moment acting on a body can be reduced to an equivalent resultant force and resultant couple moment. When this resultant force and resultant couple moment is both equal to zero then the body is said to be in equilibrium.

The major assumption for applying these equilibrium equations is that the body remains rigid.

To apply these equilibrium equations we need to know the known and unknown forces that act on the body. When all the supports are removed by replacing them with forces that prevents the translation of body in a given direction that diagram is called free body diagram.

Fundamentals

Write the equilibrium equations.

ΣF = 0
ΣΕ, = 0
(Μ.), =ΣΜ, = 0

Here, the resultant moment about any arbitrary point is (MR)..

Calculate the magnitude of force using the trigonometric relation:

21+7=141
‎Here, the component of force in x-direction is and the component of force in y-direction is .

Sign Convention for force: Upward and right forces are positive.

Sign convention for moment: Anti clockwise moment is positive and clockwise moment is negative.

Step-by-step

Step 1 of 4

Draw the free body diagram of the system.

AB
+-3ft-+-3ft-*—3ft2

Draw the external forces acting on the system and Reaction forces. At point C, the joint is pinned. Hence, there will be all two reactions . AB is a two force member and hence force acts along member AB.

Step 2 of 4

Take moment about point C.

ΣΜ, = 0
x F(3+3+3) +(400x6) + (350x3) = 0
F. = 479.167 16

Apply the moment equilibrium at point C to calculate the force in the two force member AB.

Step 3 of 4

Apply equations of equilibrium in x-direction.

ΣF, = 0
C = 479.167x
C, =-287.5 16

The horizontal reaction force at point C is -287.5 lb.


Calculation of reaction force at point C in horizontal direction using the equilibrium conditions about x-axis.

Step 4 of 4

Apply equations of equilibrium in y-direction.

ΣF, = 0
C, - F - F - Fox
C, - 400-350-( 479.167-3)-ο
C, = 366.67 16

The vertical reaction force at point C is 366.67 lb.


Calculation of reaction force at point C in horizontal direction using the equilibrium conditions about y-axis.

Answer

The horizontal reaction force at point C is -287.5 lb.

The vertical reaction force at point C is 366.67 lb.

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