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UPPCL JE CE 2020 Offical Paper

Option 1 : Unit load method

Building Material & Concrete Technology

15599

20 Questions
20 Marks
25 Mins

**Concept:**

The virtual work load method is also known as unit-load method or virtual force method used to find the deflection and slope at a point of a structure with the help of law of conservation.

When considering forces applied to a body in static equilibrium, the principle of least action requires the **virtual work** of these forces to be zero.

**Castigliano’s method**: It is a method for determining the displacements of a linear-elastic system based on the partial derivatives of the energy. He is known for his two theorems.

**1. Castigliano’s first theorem**:- The first partial derivative of total strain energy in a structure with respect to any particular deflection component at a point is equal to the force applied at that point & in the direction corresponding to the deflection component.

\(\frac{{\partial U}}{{\partial \delta }} = P\)

\(\frac{{\partial U}}{{\partial \theta }} = M\)

It is applicable to linearly or non-linearly elastic structure in which the temperature is constant and the supports are unyielding.

**2. Castigliano’s 2 ^{nd} theorem**:- The first partial derivative of total strain energy in a structure with respect to the force applied at that point is equal to the deflection at the point of application of that force in the direction of its line of action.

\(\frac{{\partial U}}{{\partial P }} = \delta\)

\(\frac{{\partial U}}{{\partial M}} = \theta\)

It is applicable to linearly elastic structure with constant temperature and unyielding supports.

**Actual work method**:- It is the real work method which is used to find the slope and deflection of any structure with the help of force and bending moment in real conditions.