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  • W.B.C.S. Main 2018 Question Answer – CIVIL ENGINEERING – Castigilano’s Theorems.
    Posted on January 15th, 2019 in Civil Engineering
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    W.B.C.S. Main 2018 Question Answer – CIVIL ENGINEERING – Castigilano’s Theorems.

    WBCS ঐচ্ছিক ২০১৮ প্রশ্নের উত্তর – সিভিল ইঞ্জিনিয়ারিংকাস্টিগিলানোর উপপাদ্য।

    1)Enumerate the Castigilano’s theorems explaining their uses.

    The Theorem of Least Work
    The theorem of least work derives from what is known as Castigliano’s second theorem. So, let’s first state the two theorems of Carlo Alberto Castigliano (1847-1884) who was an Italian railroad engineer. In 1879, Castigliano published two theorems.Continue Reading W.B.C.S. Main 2018 Question Answer – CIVIL ENGINEERING – Castigilano’s Theorems.
    Castigliano’s first theorem: The first partial derivative of the total internal energy (strain energy) in a structure with respect to any particular deflection component at a point is equal to the force applied at that point and in the direction corresponding to that deflection component. This first theorem is applicable to linearly or nonlinearly elastic structures in which the temperature is constant and the supports are unyielding.
    Castigliano’s second theorem: The first partial derivative of the total internal energy in a structure with respect to the force applied at any point is equal to the deflection at the point of application of that force in the direction of its line of action. The second theorem of Castigliano is applicable to linearly elastic (Hookean material) structures with constant temperature and unyielding supports. Note that in the above statements, force may mean point force or couple (moment) and displacementmay mean translation or angular rotation. Proofs of Castigliano’s theorems are given at the end of this document.
    Application:
    1. Calculate deflections along the direction of applied load of a statically determinate structure at the point of application of load.
    2. Castigliano’s Theorem is being used in structural analysis for finding deflection of an elastic structure based on strain energy of the structure.

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