Lec_11_ch_5

Copyright 2010 Pearson Education South Asia Pte LtdEquilibrium of a Rigid Body5Engineering Mechanics: Statics in SI Units, 12eCopyright 2010 Pearson Education South Asia Pte Ltd5.6 Equations of EquilibriumVector Equations of EquilibriumFor two conditions for equilibrium of a rigid body in vector form, F = 0 MO = 0

Scalar Equations of EquilibriumIf all external forces and couple moments are expressed in Cartesian vector form F = Fxi + Fyj + Fzk = 0MO = Mxi + Myj + Mzk = 0Copyright 2010 Pearson Education South Asia Pte Ltd5.7 Constraints for a Rigid BodyRedundant ConstraintsMore support than needed for equilibriumStatically indeterminate: more unknown loadings than equations of equilibrium

5.7 Constraints for a Rigid BodyImproper ConstraintsInstability caused by the improper constraining by the supportsWhen all reactive forces are concurrent at this point, the body is improperly constrained

5.7 Constraints for a Rigid BodyProcedure for AnalysisFree Body DiagramDraw an outlined shape of the bodyShow all the forces and couple moments acting on the bodyShow all the unknown components having a positive sense Indicate the dimensions of the body necessary for computing the moments of forces5.7 Constraints for a Rigid BodyProcedure for AnalysisEquations of EquilibriumApply the six scalar equations of equilibrium or vector equationsAny set of non-orthogonal axes may be chosen for this purpose

Equations of EquilibriumChoose the direction of an axis for moment summation such that it insects the lines of action of as many unknown forces as possibleCopyright 2010 Pearson Education South Asia Pte LtdExample 5.15The homogenous plate has a mass of 100kg and is subjected to a force and couple moment along its edges. If it is supported in the horizontal plane by means of a roller at A, a ball and socket joint at N, and a cord at C, determine the components of reactions at the supports.

Copyright 2010 Pearson Education South Asia Pte LtdSolutionFree Body DiagramsFive unknown reactions acting on the plateEach reaction assumed to act in a positive coordinate directionEquations of Equilibrium

Copyright 2010 Pearson Education South Asia Pte LtdSolutionEquations of Equilibrium

Components of force at B can be eliminated if x, y and z axes are used

Copyright 2010 Pearson Education South Asia Pte LtdSolutionSolving, Az = 790N Bz = -217N TC = 707NThe negative sign indicates Bz acts downwardThe plate is partially constrained as the supports cannot prevent it from turning about the z axis if a force is applied in the x-y plane

CxCy5075FBA2500N100150518. Determine the horizontal and vertical components of reaction at pin C and the force in the pawl of the winch .90.138+

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C523. The airstroke actuator at D is used to apply a force of F = 200 N on the member at B. Determine the horizontal and vertical components of reaction at the pin A and theforce of the smooth shaft at C on the member.

AxAyFc15o0.6m0.2m0.6mABC200N60o+

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563. The cart supports the uniform crate having a mass of 85 kg. Determine the vertical reactions on the three casters at A, B, and C. The caster at B is not shown. Neglect the mass of the cart.

0.350.20.50.60.350.40.45BACAzBzCz85x9.81=833.85Nxyz+

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AxAyAzFCD1.25 KNExEz571. The rod assembly is used to support the 1.25-kN (= 125 kg) cylinder. Determine the components of reaction at the ball-and-socket joint A, the smooth journal bearing E, and the force developed along rod CD. The connections at C and D are ball-and-socket joints.Equations of Equilibrium:

Force in Cartesian Vector,

AxAyAzFCD1.25 KNExEz

rAErACrAF