Unit load method used in structural analysis is
- Aapplicable for analyzing statically indeterminate structure
- Banother name of stiffness method
- Can extension of Maxwell’s reciprocal theorem
- Dderived from Castigliano’s theorem.Correct
Solution
Concept
The unit load method is a strain energy technique used to find deflections in structural elements. It is derived from Castigliano's second theorem.
Formula
δ = ∫ (M × m / (E × I)) dx
Step-by-step solution
1. Castigliano's second theorem states that the partial derivative of total strain energy (U) with respect to an applied force (P) gives deflection (δ): δ = ∂U / ∂P. 2. For bending, strain energy is U = ∫ (M² / (2 × E × I)) dx. 3. Differentiating U with respect to P gives δ = ∫ (M / (E × I)) × (∂M / ∂P) dx. 4. Here, ∂M / ∂P is equal to 'm', which is the bending moment caused by a virtual unit load placed at the point of deflection. 5. Replacing ∂M / ∂P with 'm' gives the unit load method formula: δ = ∫ (M × m / (E × I)) dx. Answer: (D) derived from Castigliano’s theorem.
Explanation
The unit load method is based on the principle of virtual work and strain energy. Differentiating strain energy with respect to a load (Castigliano's second theorem) leads directly to the unit load expression. Therefore, the unit load method is derived from Castigliano's theorem.
Why the other options are wrong
A: The unit load method is primarily used to calculate displacements in statically determinate structures. B: It is a flexibility (force) method concept, not a stiffness method. C: It is based on strain energy principles, not derived as an extension of Maxwell’s reciprocal theorem.
Shortcut
Unit load expression δ = ∫ (M × m / EI) dx is the derivative form of strain energy U = ∫ (M² / 2EI) dx with respect to load P.
Common mistake
Students often confuse force methods with stiffness methods, or think unit load method is an extension of Maxwell's theorem.
Correct answer: D) derived from Castigliano’s theorem.