EGR 280 Mechanics 3 – Rigid-Body Statics

Static Equilibrium of Rigid Bodies In addition to the resultant force being zero, the resultant moment about any point must be zero for any rigid body to be in static equilibrium: ∑ F = R = 0 and ∑ M O = ∑ (r O × F) = 0

Free-body Diagrams Free-body diagrams now consist of both applied forces and reactions with other bodies Reactions at supports and connections are of only two types: 1.If a support or connection prevents translation (linear motion) in some direction, then a force may be developed in that direction. 2.If a support or connection prevents rotation about some axis, then a moment may be developed around that axis.

Graphics and problem statements © 2004 R.C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ.

Graphics and problem statements © 2004 R.C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ.

Graphics and problem statements © 2004 R.C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ.

Statically Indeterminate Problems A problem may contain too many unknowns (more than 3 in two dimensions, more than 6 in three dimensions) to be able to be solved with the methods of statics alone. These types of problems are known as statically indeterminate. In order to solve statically indeterminate problems, one usually has to account for the deformation of bodies. The solution of statically indeterminate problems is a major topic in the study of deformable bodies (mechanics of materials). Example(s)…

Two-force members Consider a body that has forces applied at only two points. If this body is in static equilibrium, then the two forces must be: Equal in magnitude Opposite in direction, and Have the same line of action that passes through the two points where the forces are applied to the body Example(s)… F S F -F F