5 - Equilibrium in 2D and 3D Flashcards
What are the vector equations of equilibrium, expressed in two dimensions?
Sigma*Fx = 0
Sigma*Fy = 0
Sigma*Mo = 0
What is equilibrium?
The condition in which the resultant of all forces and moments acting on a body is zero.
What is translational equilibrium?
An object is in translational equilibrium if the velocity of its translational motion is constant. To be in translational equilibrium, the net force acting on the object must be zero (recall Newton’s first law: if no unbalanced forces act on an object, it does not accelerate).
What are the four categories of 2D equilibrium?
- Equilibrium of collinear forces.
- Equilibrium of forces which lie in a plane and are concurrent at a point O
- Equilibrium of parallel forces in a plane
- Equilibrium of a general system of forces in a plane
What equilibrium equations are needed for a system of collinear forces?
A system that requires only the one force equation in the direction of the forces, since all other equations are automatically satisfied.
What equilibrium equations are needed for a system of forces concurrent at a point O?
A system that requires the two force equations only, since the moment sum about O, that is, about an axis through O, is necessarily zero.
What equilibrium equations are needed for a system of parallel forces in a plane?
A system that requires one force equation in the direction of the forces and one moment equation about an axis normal to the plane of the forces.
What equilibrium equations are needed for a general force system?
A system that requires both force equations and one moment equation about an axis normal to the plane.
Forces in a two-force system must be … to be in equilibrium.
Equal, opposite, and collinear
Forces in a three-force system must be … to be in equilibrium.
Concurrent
What are two alternative sets of equilibrium equations?
The first set:
Sigma Fx = 0
Sigma Ma = 0
Sigma Mb = 0
The second set:
Sigma Ma = 0
Sigma Mb = 0
Sigma Mc = 0
What is meant by constraint?
Restriction of movement.
What is statically indeterminate?
A rigid body which possesses more external supports or constraints than are necessary to maintain an equilibrium position.
What is statically determinate?
A rigid body which is supported by the minimum number of constraints necessary to ensure an equilibrium configuration.
What is the degree of statical indeterminacy?
The number of redundant forces in the structure. Redundant forces are the forces that cannot be found by writing and solving only the equations of equilibrium. They must be independent.
