东南大学：《建筑力学 Architectural Mechanics》课程教学课件（英文讲稿）A04 Equilibrium of Rigid Bodies

Reactions at Supports and Connections1Reactionsequivalenttoaforce of unknowndirectionand magnitude.Frictionless pinRough surfaceForce of unknownorhingedirectionReactions equivalent to aorforceofunknowndirectionandmagnitudeand a couple.ofunknownmagnitudeFixed supportForce and couple6

Reactions at Supports and Connections • Reactions equivalent to a force of unknown direction and magnitude. • Reactions equivalent to a force of unknown direction and magnitude and a couple.of unknown magnitude 6

Equilibrium of a Rigid Body in Two DimensionsQ. For all forces and moments acting on a two-dimensional structure,DCF,=0 Mx=M,=0 M,=Mo.Equations of equilibrium becomeAZFx=0 ZF,=0 ZMA=0(a)where A is any point in the plane of thestructure.DThe3eguationscanbesolvedfornomorethan 3 unknowns.B. The 3 equations can not be augmented withadditional equations, but they can be replacedBZFx=0 ZMA=0 ZMB=0(b)7

Equilibrium of a Rigid Body in Two Dimensions • For all forces and moments acting on a two￾dimensional structure, Fz  0 M x  M y  0 M z  MO • Equations of equilibrium become  Fx  0  Fy  0 M A  0 where A is any point in the plane of the structure. • The 3 equations can be solved for no more than 3 unknowns. • The 3 equations can not be augmented with additional equations, but they can be replaced  Fx  0 M A  0 MB  0 7