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Calcul Degré D Hyperstaticité Rdm

Reviewed by Calculator Editorial Team

The degree of hyperstaticity (or redundancy) measures how many more equations a structure has compared to the minimum required for static equilibrium. This calculation is essential in structural engineering to determine if a structure is statically determinate, indeterminate, or hyperstatic.

What is hyperstaticity?

Hyperstaticity refers to a structure that has more equations of equilibrium than the minimum required to solve for all unknown forces and reactions. This means the structure has redundant members that can redistribute loads without changing the external equilibrium.

Key points about hyperstatic structures:

  • Have more members than the minimum required for static equilibrium
  • Can support additional loads without structural failure
  • Require more complex analysis methods like the RDM (Replacement Method)
  • Common in bridges, frames, and trusses

Types of structural systems

Structures can be classified based on their degree of hyperstaticity:

  1. Statically determinate: Number of equations equals the number of unknowns (degree of hyperstaticity = 0)
  2. Statically indeterminate: More unknowns than equations (degree of hyperstaticity = 0)
  3. Hyperstatic: More equations than unknowns (degree of hyperstaticity > 0)

How to calculate hyperstaticity

The degree of hyperstaticity can be calculated using the following formula:

Degree of hyperstaticity = (Number of members + Number of joints) - (2 × Number of joints)

This formula comes from the principle that a structure with m members and j joints has 2j equilibrium equations (3 for 3D structures). The degree of hyperstaticity represents the number of additional equations beyond the minimum required.

Step-by-step calculation

  1. Count the number of members in the structure
  2. Count the number of joints in the structure
  3. Apply the formula: (m + j) - 2j
  4. Interpret the result based on the classification above

Example Calculation

For a simple beam with 3 members and 4 joints:

Degree of hyperstaticity = (3 + 4) - (2 × 4) = 7 - 8 = -1

This indicates the structure is statically indeterminate.

Interpreting the results

The degree of hyperstaticity provides important information about a structure's behavior:

  • Positive value: The structure is hyperstatic and can support additional loads
  • Zero: The structure is statically determinate and requires no additional analysis
  • Negative value: The structure is statically indeterminate and needs more complex analysis

Engineers use this information to select appropriate analysis methods and design approaches. Hyperstatic structures often require the RDM (Replacement Method) or other advanced techniques to determine internal forces accurately.

FAQ

What is the difference between hyperstatic and indeterminate structures?
Hyperstatic structures have more equations than unknowns, while indeterminate structures have more unknowns than equations. Hyperstatic structures are more stable and can support additional loads.
How does hyperstaticity affect structural design?
Hyperstaticity allows for more efficient load distribution and can lead to more economical designs. However, it requires more complex analysis methods to determine internal forces.
What is the RDM method used for?
The RDM (Replacement Method) is used to analyze hyperstatic structures by temporarily removing members and calculating their forces.