Static Equilibrium Flashcards
(13 cards)
What is equilibrium?
A system of forces is said to be in equilibrium when the forces balance each other.
What is a moment or couple?
The term couple denotes a pair of parallel vector forces, opposite in sense, equal in magnitude, and separated by a distance d called the arm.
Explain the principle of transmissibility.
A force sliding along its line of action maintains the same position with respect to a point of interest O, so the moment of this force about O remains unchanged by the sliding operation. As a result, the cross product between an arbitrary position vector from O to an arbitrary point of the line of action of the acting force also remains constant.
Explain Parallel Forces.
By definition, a system of forces is parallel when none of the lines of action of the forces intersect.
What is the center of gravity (CG) of a body?
The center of gravity (CG) of a body is the point of application of its weight.
What is a composite body?
A composite body consists of series of ‘simpler’ shaped bodies which may be rectangular, triangular, semicircular, etc.
What are the degrees of freedom?
All components of the forces may cause rotation of the body about any point in the plane.
What are the different types of bearing, DOF wise?
monovalent bearings that block one DOF,bivalent bearings that block two DOFs,trivalent bearings that block three DOFs, andpolyvalent bearings that block more than three DOFs in space.
Explain stability.
A rigid body is said to be in stable equilibrium when it remains at rest under any possible type, direction, sense, and magnitude of external loading.
Explain instability.
A rigid body is said to be in an unstable state if it moves as the result of at least one case of loading, regardless of its type, direction, sense, and magnitude.
Explain unstable equilibrium.
A rigid body is said to be in unstable equilibrium when it remains in equilibrium only under a particular loading, but this equilibrium is broken once the loading changes.
Statically determinate structure.
A structure is said to be statically determinate when it is stable and the number of unknown reaction forces equals the number of equilibrium equations (i.e., six unknowns in 3D and three unknowns in 2D). In this case, all the reaction forces exerted by the supports may be determined by applying the equilibrium equations.
Statically indeterminate structure.
A structure is said to be statically indeterminate when it is stable and when the number of unknown reaction forces exceeds the number of equilibrium equations (i.e., seven or more unknowns in 3D and four or more unknowns in 2D). In that case, the reaction forces exerted by the supports cannot be determined by applying the equilibrium equations alone; additional equations are needed to determine all the reaction forces, which are known as deformation compatibility equations. However, this is an advanced topic that goes beyond the scope of this textbook.
