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Statics (MET 2214) Prof. Simin Nasseri Equilibrium of a Rigid Body Examples.

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Presentation on theme: "Statics (MET 2214) Prof. Simin Nasseri Equilibrium of a Rigid Body Examples."— Presentation transcript:

1 Statics (MET 2214) Prof. Simin Nasseri Equilibrium of a Rigid Body Examples

2 Statics (MET 2214) Prof. Simin Nasseri Example Problem Draw the free-body diagram of the plate.

3 Statics (MET 2214) Prof. Simin Nasseri Example Problem R x3 R y3 R x2 R y2 R x1 R y1 Does this free-body diagram help?

4 Statics (MET 2214) Prof. Simin Nasseri Example Problem RxRx RyRy You have to consider one reaction force from the gusset plate. The components of this force are R x and R y.

5 Statics (MET 2214) Prof. Simin Nasseri Example Problem Draw the free-body diagram of the weight. A B

6 Statics (MET 2214) Prof. Simin Nasseri Example Problem Determine the force in each supporting wire. TATA TBTB W=50lb T A and T B are the forces inside the cables and equal to reaction forces at A and B.

7 Statics (MET 2214) Prof. Simin Nasseri Example Problem

8 Statics (MET 2214) Prof. Simin Nasseri Example Problem Spanner wrench F

9 Statics (MET 2214) Prof. Simin Nasseri Example Problem Set up the following problem: Length A= 5 ft, and length B =10 ft and angle α= 30 o. Determine the angle β of the smooth incline in order to maintain equilibrium.

10 Statics (MET 2214) Prof. Simin Nasseri Example Problem Use line-of-action to solve the problem

11 Statics (MET 2214) Prof. Simin Nasseri Example Problem

12 Statics (MET 2214) Prof. Simin Nasseri Class Problem Set up the problem and how would you solve for the resisting force at pin A to maintain equilibrium.

13 Statics (MET 2214) Prof. Simin Nasseri Class Problem Set up the problem and how would you solve for the resisting force at pin A to maintain equilibrium.

14 Statics (MET 2214) Prof. Simin Nasseri Class Problem

15 Statics (MET 2214) Prof. Simin Nasseri 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.

16 Statics (MET 2214) Prof. Simin Nasseri FBD - Example Free-body diagram: (Anything missing?) T AB T AD T AC RARA Add the dimensions!

17 Statics (MET 2214) Prof. Simin Nasseri Example-Equilibrium The vector AB is

18 Statics (MET 2214) Prof. Simin Nasseri Example-Equilibrium The unit vector in the AB direction is The tension vector T AB is

19 Statics (MET 2214) Prof. Simin Nasseri Example-Equilibrium The vector AD is

20 Statics (MET 2214) Prof. Simin Nasseri Example-Equilibrium The unit vector in the AD direction is The tension vector T AD is

21 Statics (MET 2214) Prof. Simin Nasseri Example-Equilibrium The vector AC is

22 Statics (MET 2214) Prof. Simin Nasseri Example-Equilibrium The unit vector in the AC direction is The tension vector T AC is

23 Statics (MET 2214) Prof. Simin Nasseri Example-Equilibrium The tension vector T AC = 28 kN is The reaction at A

24 Statics (MET 2214) Prof. Simin Nasseri Example-Equilibrium Apply the equilibrium condition. Combine the vectors

25 Statics (MET 2214) Prof. Simin Nasseri Example-Equilibrium Break the components of the forces: Use (3) to solve for T AB

26 Statics (MET 2214) Prof. Simin Nasseri Example-Equilibrium Plug into (1), solve for magnitude of T AD

27 Statics (MET 2214) Prof. Simin Nasseri Example-Equilibrium Use the values to solve for R A


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