Statically indeterminate systems

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SUMMARY

The discussion centers on the application of the principle of virtual work to solve statically indeterminate systems, particularly in the context of beams and trusses. The method, commonly referred to as the 'unit load' method, involves analyzing a beam with multiple pinned supports by first treating it as a determinate system. Subsequently, each support is replaced with a unit load multiplied by the unknown reaction load, allowing for the calculation of unknown reactions and moments by summing the deflections at the supports to zero.

PREREQUISITES
  • Understanding of statically indeterminate systems
  • Familiarity with the principle of virtual work
  • Knowledge of beam and truss analysis
  • Proficiency in solving equilibrium equations
NEXT STEPS
  • Study the unit load method in detail for beam analysis
  • Explore advanced techniques in structural analysis for indeterminate systems
  • Learn about the application of virtual work in different structural scenarios
  • Investigate software tools for structural analysis, such as SAP2000 or ANSYS
USEFUL FOR

Structural engineers, civil engineering students, and professionals involved in the analysis and design of indeterminate structures will benefit from this discussion.

reterty
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I am interested in the following question: whether we can use the principle of virtual work to solve approximately (in the limit of small deformations) the statically indeterminate systems or this principle is ultimately equivalent to the the system of the independent equilibrium equations?
 
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Yes this method is often used in the analysis of indeterminate beams and trusses. Often called the ‘unit load’ method, and considering a beam say supported on multiple pinned supports, the extra supports are removed and the beam analyzed as a determinate system with the equilibrium equations. Then the supports are one by one replaced with a unit load multiplied by the unknown reaction load, and solved again as a determinate beam . Summing the deflections of each result equal to zero at the supports, the beam can then be solved for the unknown reactions and moments, etc.
 

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