Equilibrium of a Rigid Body Examples

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

Example Problem Rx1 Ry1 Rx2 Ry2 Rx3 Ry3 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 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

Example Problem

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

Example 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.

Class Problem

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?) Add the dimensions! RA TAC TAD TAB

Example-Equilibrium The vector AB is

Example-Equilibrium The unit vector in the AB direction is The tension vector TAB is

Example-Equilibrium The vector AD is

Example-Equilibrium The unit vector in the AD direction is The tension vector TAD 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