statics 3d rigid body equilibrium example problems

We saw in Chapter 3 that particle equilibrium problems can be solved using the force equilibrium equation alone, because particles have, at most, three degrees of freedom and are not subject to any rotation. In many cases we do not need all six equations. Statically indeterminate problems: Different supports provide different reaction forces 5.Working with these scalar equations is often easier than using their vector equivalents, particularly in two-dimensional problems. If a result is negative, the actual force direction should be opposite to the assumed. Sign consideration: ES2501: Statics/Unit 14-7: Equilibrium of Rigid Bodies: 2D Problems Starts forces with an assumed direction. Superposition Principle helps: + = The results for distributed load The results for single P The total resultsĮxample 2: Comments 3. Alternative (moment) equations can be used The same results 2.

ES2501: Statics/Unit 14-5: Equilibrium of Rigid Bodies: 2D Problems Statically equivalent Force: Step 1: FBD (See the above) Note: Different supports provide different reactions Step 2: List Equilibrium equations “-” indicates a force direction opposite to the assumed Step 3:SolutionĮxample 2: Comments ES2501: Statics/Unit 14-6: Equilibrium of Rigid Bodies: 2D Problems 1. friction needs to be considered? - Statically underminateĮxample 2: Find reaction forces of supports in the following sytems.

Infependent of W What if the wall is also rough, i.e. A Step 3: Solution What if weight of the ladder is considered? Law of friction: -Rougher ground and large angle help. ES2501: Statics/Unit 14-4: Equilibrium of Rigid Bodies: 2D Problems Step 1: FBD (See the figure) B Note: There are three unknowns: Step 2: List Equilibrium equations. Find the man can climb up such that the ladder will not slide down.

The static friction coefficient between the ladder and the ground is. Assume that weight of the latter is ignored. Need to know nature reaction forces of supports ES2501: Statics/Unit 14-3: Equilibrium of Rigid Bodies: 2D Problems Constrains of Supports (Reactions): Pin-connected (Hinged, Simply-support) Roller-support Only motion in the y- direction is restricted Motion in both x- and y- directions are restricted Fixed-support (built-in, clamped) Roller-support Only motion in the x- direction is restricted Motion in both x- and y- directions And also rotation about z-axis are restrictedĮxample 1:A ladder stands on a rough ground against a smooth wall. Say, Maximum three independent scalar eqns A Ai y x Statically indeterminate Problems: - Number of unknowns is more than the number of equilibrium equationsĮS2501: Statics/Unit 14-2: Equilibrium of Rigid Bodies: 2D Problems Basic Procedures of Static Analysis Step 1: Draw free-body diagram(s) Step 2: List equilibrium equations Step 3: Any supplementary equations? (for statically inderminate problems) Step 4: Solution Step 5: Interpretation.įree-Body Diagrams: Draw a FBD is still the first step for static analysis.

Equilibrium Equations (2D): ES2501: Statics/Unit 14-1: Equilibrium of Rigid Bodies: 2D Problems Force eqns can be replaced by one or two moment eqn(s).

Statics 3d rigid body equilibrium example problems