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Equilibrium of a Rigid Body Examples

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Equilibrium of a Rigid BodyExamples

Draw the free-body diagram of the plate.

Does this free-body diagram help?

Rx1

Ry1

Rx2

Ry2

Rx3

Ry3

You have to consider one reaction force from the gusset plate. The components of this force are Rx and Ry.

Rx

Ry

Draw the free-body diagram of the weight.

B

A

Determine the force in each supporting wire.

TB

TA

TA and TB are the forces inside the cables and equal to reaction forces at A and B.

W=50lb

Spanner wrench

F

Set up the following problem: Length A= 5 ft, and length B =10 ft and angle α= 30o. Determine the angle β of the smooth incline in order to maintain equilibrium.

Use line-of-action to solve the problem

Set up the problem and how would you solve for the resisting force at pin A to maintain equilibrium.

Set up the problem and how would you solve for the resisting force at pin A to maintain equilibrium.

The tension force in AC is 28 kN, determine the the required values of tension in AB and AD so that the resultant force of the three forces applied at A is vertical. Determine the resultant force.

Free-body diagram:

(Anything missing?)

Add the dimensions!

RA

TAC

TAD

TAB

The vector AB is

The unit vector in the AB direction is

The tension vector TAB is

The vector AD is

The unit vector in the AD direction is

The tension vector TAD is

The vector AC is

The unit vector in the AC direction is

The tension vector TAC is

The tension vector TAC= 28 kN is

The reaction at A

Apply the equilibrium condition.

Combine the vectors

Break the components of the forces:

Use (3) to solve for TAB

Plug into (1), solve for magnitude of TAD

Use the values to solve for RA