Chapter-5 Deflection of Beam Again integrating both side we get
S K Mondal’s
EI³ dy = ³ M x +A dx Mx 2 Ax + B ...(ii) 2 Where A and B are integration constants.
or EI y
applying boundary conditions in equation (i) &(ii) at x = L,
dy dx
0 gives A = ML
ML2 2 2 Mx MLx ML2 Therefore deflection equation is y = 2EI EI 2EI Which is the equation of elastic curve.
at x = L, y = 0 gives B =
ML2 ML2 2
2
? Maximum deflection at free end
? Maximum slope at free end
T
ML G = 2EI
(It is downward)
ML EI
Let us take a funny example: A cantilever beam AB of length ‘L’ and uniform flexural rigidity EI has a bracket BA (attached to its free end. A vertical downward force P is applied to free end C of the bracket. Find the ratio a/L required in order that the deflection of point A is zero.
[ISRO – 2008]
We may consider this force ‘P’ and a moment (P.a) act on free end A of the cantilever beam.
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