m1l6

# m1l6 - Module 1 Energy Methods in Structural Analysis...

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Version 2 CE IIT, Kharagpur Module 1 Energy Methods in Structural Analysis

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Version 2 CE IIT, Kharagpur Lesson 6 Engesser’s Theorem and Truss Deflections by Virtual Work Principles

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In the above figure the strain energy (area OACO) is not equal to complementary strain energy (area OABO) = = u du F U OACO Area 0 (6.3) Differentiating strain energy with respect to displacement, F du dU = ( 6 . 4 ) This is the statement of Castigliano’s second theorem. Now the complementary energy is equal to the area enclosed by OABO. = F dF u U 0 * ( 6 . 5 ) Differentiating complementary strain energy with respect to force , F u dF dU = * ( 6 . 6 ) Version 2 CE IIT, Kharagpur
This gives deflection in the direction of load. When the load displacement relationship is linear, the above equation coincides with the Castigliano’s first theorem given in equation (3.8).

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m1l6 - Module 1 Energy Methods in Structural Analysis...

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