ES 2501 StaticsUnit 14 1 Equilibrium of Rigid
ES 2501: Statics/Unit 14 -1: Equilibrium of Rigid Bodies: 2 D Problems Equilibrium Equations (2 D): Ai y A Maximum three independent scalar eqns x Statically indeterminate Problems: ------ Number of unknowns is more than the number of equilibrium equations Force eqns can be replaced by one or two moment eqn(s). Say,
ES 2501: Statics/Unit 14 -2: Equilibrium of Rigid Bodies: 2 D 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.
ES 2501: Statics/Unit 14 -3: Equilibrium of Rigid Bodies: 2 D Problems Free-Body Diagrams: Draw a FBD is still the first step for static analysis. Need to know nature reaction forces of supports Constrains of Supports (Reactions): Pin-connected (Hinged, Simply-support) Motion in both xand y- directions are restricted Fixed-support (built-in, clamped) Motion in both xand y- directions And also rotation about z-axis are restricted Roller-support Only motion in the ydirection is restricted Roller-support Only motion in the xdirection is restricted
ES 2501: Statics/Unit 14 -4: Equilibrium of Rigid Bodies: 2 D Problems 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 climb up such that the ladder will not slide down. B Step 1: FBD (See the figure) Note: There are three unknowns: Step 2: List Equilibrium equations. A Step 3: Solution What if weight of the ladder is considered? What if the wall is also rough, i. e. friction needs to be considered? --- Statically underminate Law of friction: -Rougher ground and large angle help. - Infependent of W
ES 2501: Statics/Unit 14 -5: Equilibrium of Rigid Bodies: 2 D Problems Example 2: Find reaction forces of supports in the following sytems. Statically equivalent Force: Step 1: FBD (See the above) Note: Different supports provide different reactions Step 2: List Equilibrium equations Step 3: Solution “-” indicates a force direction opposite to the assumed
ES 2501: Statics/Unit 14 -6: Equilibrium of Rigid Bodies: 2 D Problems Example 2: Comments 1. Alternative (moment) equations can be used The same results 2. Superposition Principle helps: + The results for single P The results for distributed load = The total results
ES 2501: Statics/Unit 14 -7: Equilibrium of Rigid Bodies: 2 D Problems Example 2: Comments 3. Sign consideration: Starts forces with an assumed direction. If a result is negative, the actual force direction should be opposite to the assumed. 4. Other supports? Different supports provide different reaction forces 5. More complex problems? 5. Statically indeterminate problems:
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