Statically Indeterminate Axially Loaded Members

Group 6Fernando, CarolleKing, Roxanne AddiezaPineda, Ivory

Mapua Institute of Technology

statically indeterminate

Structures and mechanical systems that dont have enough equilibrium equations to solve for all of the unknowns in the system.

A structure will only be indeterminate whenever it is held by more supports than required to maintain its equilibrium.

The general solution process can be organized into a five-step procedure:

Step 1 Equilibrium Equations: Equations expressed in terms of the unknown axial forces are derived for the structure on the basis of equilibrium considerations.

Step 2 Geometry of Deformation: The geometry of the specific structure is evaluated to determine how the deformations of the axial members are related.

Step 3 ForceDeformation Relationships: The relationship between the internal force in an axial member and its corresponding elongation is expressed by Equation (5.2).

Step 4 Compatibility Equation: The forcedeformation relationships are substituted into the geometry-of-deformation equation to obtain an equation that is based on the structures geometry, but expressed in terms of the unknown axial forces.

Step 5 Solve the Equations: The equilibrium equations and the compatibility equation are solved simultaneously to compute the unknown axial forces.

Step 1 Equilibrium EquationsDraw one or more free-body diagrams (FBDs) for the structure, focusing on the joints that connect the members.

Step 2 Geometry of Deformation:

The structure or system should be studied to assess how the deformations of the axial members are related to each other. Most of the statically indeterminate axial structures fall into one of three general configurations:

1. Coaxial or parallel axial members. 2. Axial members connected end-to-end in series. 3. Axial members connected to a rotating rigid element.

Step 3 ForceDeformation Relationships

The relationship between internal force and deformation in axial member i is expressed by

Step 4 Compatibility Equation

The forcedeformation relationships [Equation (d)] can be substituted into the geometry-of-deformation equation [Equation (c)] to obtain a new equation, which is based on deformations, but expressed in terms of the unknown member forces F1 and F2:

Step 5 Solve the Equations

From compatibility equation (e), derive an expression for F1: