When a problem is statically indeterminate, what additional equations do you need to solve?

You have to have additional equations. See this http://www.youtube.com/watch?v=I7i5_qgD5F4

When a problem is statically indeterminate, it means that the number of unknowns in the problem exceeds the number of available equilibrium equations. To solve such problems, additional compatibility equations are needed. These compatibility equations are derived from the deformation characteristics of the structure. The additional equations required are typically obtained from one of the following methods:

1. Method of Superposition: This method involves breaking down the problem into simpler parts, solving each part separately, and then combining the solutions. Compatibility conditions are imposed at the interfaces or connections of the different parts to obtain the necessary additional equations.

2. Method of Virtual Work: This method utilizes the principle of virtual work to derive additional equations for statically indeterminate systems. It involves applying a series of virtual displacements or forces to the system and considering the work done by these virtual actions. Compatibility equations are then formulated by equating the total work done by the external loads to the total work done by the internal stresses in the structure.

3. Method of Strain Energy: This method utilizes the concept of strain energy to derive additional equations for statically indeterminate systems. It involves considering the strain energy stored in the structure under the applied loads. By equating the total strain energy to zero, additional compatibility equations are obtained.

Note that the specific additional equations required depend on the nature and geometry of the problem. Different methods may be more suitable for different types of statically indeterminate problems.

When a problem is statically indeterminate, it means that there are more unknowns than the number of equilibrium equations available. In other words, the system cannot be solved using only the basic equations of static equilibrium (such as force equilibrium or moment equilibrium equations).

To solve a statically indeterminate problem, you need to use additional equations or conditions. These equations can be obtained from compatibility conditions, material properties, geometry, or any other information about the problem.

Here are some common methods used to solve statically indeterminate problems:

1. Method of Virtual Work: This method uses the principle of virtual work to determine the unknowns. It involves considering virtual displacements and the work done by internal and external forces.

2. Method of Superposition: This method assumes that the problem can be solved by adding the solutions of simpler problems. By decomposing the problem into simpler parts, you can solve each part separately and then combine the solutions to obtain the overall solution.

3. Method of Least Work: This method minimizes the potential energy of the structure by varying the unknowns. It involves differentiating the potential energy with respect to the unknowns and setting it equal to zero.

4. Method of Castigliano's Theorem: This method involves using the principle of virtual work to determine the partial derivatives of the strain energy with respect to the unknown displacements. By taking the partial derivatives, you can obtain additional equations that can be used to solve the problem.

5. Method of Slope-Deflection Equations: This method is commonly used to analyze beams and frames. It involves deriving additional equations by considering the relationship between the slopes and deflections at different points of the structure.

In summary, when dealing with statically indeterminate problems, you need to employ additional equations or conditions derived from various methods to determine the unknowns and solve the problem. The specific method used depends on the nature of the problem and the available information.