Statics
Equilibrium of rigid bodies
A system is in static equilibrium if it experiences no acceleration when loads are applied to it.
Free body diagrams are diagrams that show all the forces acting on a body. They are useful in determining the forces that cause the body to be in equilibrium.
A static system:
- Must be in equilibrium
- Does not experience any acceleration
- Can have mechanisms that doesn't undergo movements
Members
A member is a straight and long structural element that is subjected to axial forces. The following are the types of members:
Static systems
Each support will restrict the movement of the rigid body in a certain way. If a certain degree of freedom is restricted, a reaction force will be present to counteract the force that would have caused the movement.
| Support type | Restricted movement and reaction forces | Shape |
|---|---|---|
| Fixed | x, y, r (moment) | Flat |
| Pinned | x, y | Triangle |
| Roller | y | Circle |
A structure is said stable if all members remain in place under any loading conditions. (No mechanisms)
A system's state of equilibrium can be determined by the number of restraints present:
- Insufficient restraints non-static system
- Sufficient restraints static system A static system is said to be statically indeterminate if the number of unknowns is larger than the number of equations of equilibrium.
Where is the number of members, is the number of reaction forces, is the number of internal hinges (circles).
- is the number of members (intersecting beams are separate)
- is the number of reaction forces
- is the number of nodes (all ends and intersections)
- is the number of internal hinges (circles)
Loading
- Concentrated load is a force applied at a single point. ()
- Distributed load is a force applied over a length. ()
A distributed load is a force that is distributed over a length , that has the unit .
The resultant force is the supposed area of the load. To consider the moment by a distributed load, we can treat the load as a single force acting at the centroid of the load.
- Unifrom
- Triangular (from the base of the load)