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ES2501: Statics/Unit 14-1: Equilibrium of Rigid Bodies: 2D Problems

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). Say,. Maximum three independent scalar eqns. A. A i. y. x. Statically indeterminate Problems:

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ES2501: Statics/Unit 14-1: Equilibrium of Rigid Bodies: 2D Problems

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  1. 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). Say, Maximum three independent scalar eqns A Ai y x Statically indeterminate Problems: ------ Number of unknowns is more than the number of equilibrium equations

  2. ES2501: 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.

  3. Free-Body Diagrams: Draw a FBD is still the first step for static analysis. 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 restricted

  4. Example 1:A ladder stands on a rough ground against a smooth wall. A man of weigh W climbs up. Assume that weight of the latter is ignored. The static friction coefficient between the ladder and the ground is . Find the man can climb up such that the ladder will not slide down. 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. A Step 3: Solution What if weight of the ladder is considered? Law of friction: -Rougher ground and large angle help. - Infependent of W What if the wall is also rough, i.e. friction needs to be considered? --- Statically underminate

  5. Example 2: Find reaction forces of supports in the following sytems. 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:Solution

  6. Example 2: Comments ES2501: Statics/Unit 14-6: Equilibrium of Rigid Bodies: 2D Problems 1. Alternative (moment) equations can be used The same results 2. Superposition Principle helps: + = The results for distributed load The results for single P The total results

  7. Example 2: Comments 3. Sign consideration: ES2501: Statics/Unit 14-7: Equilibrium of Rigid Bodies: 2D Problems Starts forces with an assumed direction. If a result is negative, the actual force direction should be opposite to the assumed. 4. Other supports? 5. Statically indeterminate problems: Different supports provide different reaction forces 5. More complex problems?

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