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(Solved): (c) (i) Using Castigliano's theorem prove that the equation for the deflection of a cantilever beam ...
(c) (i) Using Castigliano's theorem prove that the equation for the deflection of a
cantilever beam subjected to a point load as shown in Figure A1 is given by
Equation 3.
In answering this question, you may find the following equations useful. All
lerms have their usual meanings.
U=\int_0^L (M^(2))/(2EI)dx
\delta =(delU)/(delP)=(\int (M)/(EI)(delM)/(delP)dx)
(c) (ii) Figure A2 details a simple beam (AB) arrangement with constant flexural
rigidity (EI) subjected to a force P acting at a distance (3(L)/(4)) from one end.
Determine the deflection at the point where the load is applied.
In answering this question, you may find the following equations useful. All
lerms have their usual meanings.
U=\int_0^L (M^(2))/(2EI)dx
\delta =(delU)/(delP)=(\int (M)/(EI)(delM)/(delP)dx)