Equilibrium of a rigid body examples
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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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Equilibrium of a Rigid Body Examples

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Equilibrium of a rigid body examples

Equilibrium of a Rigid BodyExamples


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 problem5

Example Problem


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


Example problem9

Example 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.


Class problem2

Class Problem


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


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