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Equilibrium of a Rigid Body Examples. Example Problem. Draw the free-body diagram of the plate. Example Problem. Does this free-body diagram help?. R x1. R y1. R x2. R y2. R x3. R y3. Example Problem.

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example problem
Example Problem

Draw the free-body diagram of the plate.

example problem1
Example Problem

Does this free-body diagram help?

Rx1

Ry1

Rx2

Ry2

Rx3

Ry3

example problem2
Example Problem

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

Rx

Ry

example problem3
Example Problem

Draw the free-body diagram of the weight.

B

A

example problem4
Example Problem

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

example problem6
Example Problem

Spanner wrench

F

example problem7
Example Problem

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.

example problem8
Example Problem

Use line-of-action to solve the problem

class problem
Class Problem

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

class problem1
Class Problem

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

example equilibrium
Example - 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.

fbd example
FBD - Example

Free-body diagram:

(Anything missing?)

Add the dimensions!

RA

TAC

TAD

TAB

example equilibrium1
Example-Equilibrium

The vector AB is

example equilibrium2
Example-Equilibrium

The unit vector in the AB direction is

The tension vector TAB is

example equilibrium3
Example-Equilibrium

The vector AD is

example equilibrium4
Example-Equilibrium

The unit vector in the AD direction is

The tension vector TAD is

example equilibrium5
Example-Equilibrium

The vector AC is

example equilibrium6
Example-Equilibrium

The unit vector in the AC direction is

The tension vector TAC is

example equilibrium7
Example-Equilibrium

The tension vector TAC= 28 kN is

The reaction at A

example equilibrium8
Example-Equilibrium

Apply the equilibrium condition.

Combine the vectors

example equilibrium9
Example-Equilibrium

Break the components of the forces:

Use (3) to solve for TAB

example equilibrium10
Example-Equilibrium

Plug into (1), solve for magnitude of TAD

example equilibrium11
Example-Equilibrium

Use the values to solve for RA