Equilibrium of a Rigid Body Examples

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# Equilibrium of a Rigid Body Examples - PowerPoint PPT Presentation

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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### Equilibrium of a Rigid BodyExamples

Example Problem

Draw the free-body diagram of the plate.

Example Problem

Does this free-body diagram help?

Rx1

Ry1

Rx2

Ry2

Rx3

Ry3

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 Problem

Draw the free-body diagram of the weight.

B

A

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 Problem

Spanner wrench

F

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 Problem

Use line-of-action to solve the problem

Class Problem

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

Class Problem

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

Free-body diagram:

(Anything missing?)

RA

TAC

TAB

Example-Equilibrium

The vector AB is

Example-Equilibrium

The unit vector in the AB direction is

The tension vector TAB is

Example-Equilibrium

Example-Equilibrium

The unit vector in the AD direction is

Example-Equilibrium

The vector AC is

Example-Equilibrium

The unit vector in the AC direction is

The tension vector TAC is

Example-Equilibrium

The tension vector TAC= 28 kN is

The reaction at A

Example-Equilibrium

Apply the equilibrium condition.

Combine the vectors

Example-Equilibrium

Break the components of the forces:

Use (3) to solve for TAB

Example-Equilibrium

Plug into (1), solve for magnitude of TAD

Example-Equilibrium

Use the values to solve for RA