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Who proposed the Theorem of Reciprocal Deflection?

Who proposed the Theorem of Reciprocal Deflection? Correct Answer Clerk Maxwell

Concept:

Clerk Maxwell - Betti Theorem:

  • Maxwell-Betti's law of real work is a basic theorem in structural analysis.
  • Using this theorem, it can be established that the flexibility coefficients in compatibility equations, formulated to solve indeterminate structures by the flexibility method, form a symmetric matrix and this will reduce the number of deflection computations.
  • The Maxwell-Betti law also has applications in the construction of influence line diagrams for statically indeterminate structures.
  • The Maxwell-Betti law applies to any stable elastic structure (a beam, truss, or frame, for example) on unyielding supports and at a constant temperature, state.​

Let’s suppose two systems of forces

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According to the Maxwell-Betti theorem,

∴ Pi × y1 = Pj × y2

Where, y = Deflection and P is the force

From the above, we can say that in any beam the deflection at any point 'i' due to load Pi, at any other point 'y' is the same as the deflection at' 'i' due to the same load Pj applied at 'j'.

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