I If a beam is subjected to Bending Moment 'M' as shown in Fig. Consider an element dx, the Strain Energy in the element is dU is, Problem no 1 A simply supported beam of length l carries a concentrated load W at distances of 'a' and 'b' from the two ends. Find expressions for the total strain energy of the beam and the deflection under load. Solution: The integration for strain energy can only be applied over a length of beam for which a continuous expression for M can be obtained. This usually implies a separate integration for each section between two concentrated loads or reactions. For the section AB, The bending moment M at distance 'x' from Point A is, The Strain Energy in the section AB is, Similarly by taking a variable X measured from C,The Strain Energy stored In the Section BC is Total Strain Energy is , But if is the deflection under the load, the strai
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