CIV 2109 Lecture 5: Equilibrium & Support Reactions

Forces that a support exerts on a structure to prevent its motion and keep it in equilibrium.

Forces that act within the structure itself as it responds to external loads.

The property of a structure to remain at rest or in uniform motion unless acted upon by an external force.

Devices that restrict the movement of a structure by exerting reaction forces.

A reaction force that prevents a structure from translating in a specific direction.

A reaction force that prevents a structure from rotating about a specific axis.

The number of independent reactions a support can exert on a structure.

Structures are classified into categories based on the number of reactions they can exert.

A structure's ability to maintain its shape when detached from supports. It's like a sturdy table that stays put without legs, but a wobbly one collapses.

A structure remains stable and rigid even when unsupported. It won't deform significantly under its own weight.

A structure cannot maintain its shape without external support. It deforms easily and might collapse under its own weight.

The ability to calculate all support reactions using only the equations of equilibrium.

Requires more information than equilibrium equations to calculate all support reactions. There are more unknowns than equations.

A structure that has enough supports to maintain its shape and equilibrium. It won't collapse under normal loads.

A minimum of three support reactions are needed for a plane structure to be in equilibrium.

A structure is in equilibrium when all the forces acting on it are balanced. This means that the sum of all forces in each direction (x, y, and z in three dimensions) must equal zero.

Forces that intersect at a single point. The moments created by these forces automatically cancel out, simplifying equilibrium analysis.

For a three-dimensional structure with concurrent forces, the sum of forces in each direction (x, y, and z) must be zero for the structure to be in equilibrium.

For a two-dimensional structure with concurrent forces, the sum of forces in each direction (x and y) must be zero to maintain equilibrium.

Structures with a maximum of two or three forces acting upon them. These structures have specific characteristics that make their analysis simpler.

A two-force structure in equilibrium requires the two forces to be equal in magnitude, opposite in direction, and acting along the same line.

A three-force structure in equilibrium demands that the three forces either intersect at a single point (concurrent) or act parallel to one another.

A plane structure that has the exact number of support reactions needed to solve for all forces using equilibrium equations.

A structure with more support reactions than needed for equilibrium. The extra reactions cannot be calculated using only equilibrium equations.

Extra support reactions present in a statically indeterminate structure. These can't be determined by equilibrium equations alone.

The number of external redundants in a statically indeterminate structure. This indicates how many additional equations are needed.

Equations used to solve for unknown forces in statically indeterminate structures. These relate loads, reactions, and displacements.

A point inside a structure where forces can be transmitted differently, allowing for flexibility. Examples: internal hinges and rollers.

A rigid part within a structure that doesn't bend or rotate. They contribute to the overall stiffness.

A structure with fewer support reactions than needed for equilibrium. It's unstable and can move freely under loads.

A method used to determine if a structure is statically determinate or indeterminate. It involves a simple equation: r + fi = 3nr. Where 'r' is the number of reactions, 'fi' is the number of internal forces, 'n' is the number of rigid bodies, and 'r' is the number of degrees of freedom per rigid body.

A diagram that depicts the external forces acting on a structure. It's a crucial step in analyzing a structure's behaviour.

The forces that a support exerts on a structure due to applied loads. They are essential for maintaining the structure's equilibrium.

A principle in statics that states that the sum of all forces and moments acting on a body in equilibrium must equal zero.

The total force exerted on the structure by its supports, preventing it from collapsing. Computed by summing all support reactions.

The degree of external indeterminacy indicates how many more unknowns there are than equations.

This formula calculates the external indeterminacy: ie = r + fi -3nr, where 'ie' is the external indeterminacy, 'r' is the number of external reactions, 'fi' is the number of fixed internal constraints, and 'nr' is the number of rigid bodies.

A structure is considered externally unstable when there are fewer equations than unknowns, making it impossible to solve using equilibrium alone.

The reactions at the supports of a structure are the forces that the supports exert on the structure to maintain its equilibrium.

The reaction force is a force exerted by a support on a structure to counterbalance the applied loads and keep the structure in equilibrium.

The sum of the moments about any point in a system in equilibrium is zero. This is one of the fundamental equations of statics. Applying this principle helps us understand why objects don't rotate.

Independent equations are equations that are not derived from each other. For example, in statics, the equations for the sum of forces in the x and y directions, and the sum of moments about a point, are independent equations.

Internal constraints are restrictions on the relative movement of the elements within a structure. An example is a fixed support within a structure connecting different elements.