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**Equilibrium of a Rigid Body Examples**

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Example Problem Draw the free-body diagram of the plate.

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**Example Problem Rx1 Ry1 Rx2 Ry2 Rx3 Ry3**

Does this free-body diagram help? Rx1 Ry1 Rx2 Ry2 Rx3 Ry3

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

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Example Problem Draw the free-body diagram of the weight. B A

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**Example Problem TB TA Determine the force in each supporting wire.**

TA and TB are the forces inside the cables and equal to reaction forces at A and B. W=50lb

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Example Problem

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Example Problem Spanner wrench F

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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.

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Example Problem Use line-of-action to solve the problem

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Example Problem

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

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

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Class Problem

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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.

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**FBD - Example Free-body diagram: (Anything missing?)**

Add the dimensions! RA TAC TAD TAB

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Example-Equilibrium The vector AB is

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**Example-Equilibrium The unit vector in the AB direction is**

The tension vector TAB is

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Example-Equilibrium The vector AD is

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**Example-Equilibrium The unit vector in the AD direction is**

The tension vector TAD is

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Example-Equilibrium The vector AC is

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**Example-Equilibrium The unit vector in the AC direction is**

The tension vector TAC is

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Example-Equilibrium The tension vector TAC= 28 kN is The reaction at A

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**Example-Equilibrium Apply the equilibrium condition.**

Combine the vectors

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**Example-Equilibrium Break the components of the forces:**

Use (3) to solve for TAB

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Example-Equilibrium Plug into (1), solve for magnitude of TAD

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Example-Equilibrium Use the values to solve for RA

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THREE-DIMENSIONAL FORCE SYSTEMS Today’s Objectives: Students will be able to solve 3-D particle equilibrium problems by a) Drawing a 3-D free body diagram,

THREE-DIMENSIONAL FORCE SYSTEMS Today’s Objectives: Students will be able to solve 3-D particle equilibrium problems by a) Drawing a 3-D free body diagram,

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