Energy_Methods

Energy_Methods - Energy Methods (5.1-5.7) MAE 316 Strength...

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Energy Methods (5.1-5.7) MAE 316 – Strength of Mechanical Components C. Heeter Tran Energy Methods 1
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astigliano’s Theorem .6) Castigliano s Theorem (5.6) ` This method is a powerful new way to determine deflections in many types of structures – bars, beams, frames, trusses, curved beams, etc. e can calculate both horizontal d rtical ` We can calculate both horizontal and vertical displacements. ` There are actually two Castigliano’s Theorems. ` The first can be used for structures made of both linear and non-linear elastic materials. o ea e ast c ate a s. ` The second is restricted to structures made of linear elastic materials only. This is the one we will use. Energy Methods 2
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astigliano’s Theorem .6) Castigliano s Theorem (5.6) ` “When forces operate on elastic structures, the displacement corresponding t oa n y force may be found by obtaining the partial derivative of the total strain energy w.r.t. that force.” i i F U = δ ` We can also use this method to find the angle of rotation ( θ ). Where: F i = Force at i-th application point; δ i = Displacement at i-th point in the direction of F i ; and U = Total strain energy U = θ Energy Methods 3 i i M
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Energy_Methods - Energy Methods (5.1-5.7) MAE 316 Strength...

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