Cantilever: end deflection due to applied moment

[loten]

Please could someone verify (or not) the formula I have attempted to derive for the deflection at the end of a cantilever subjected to a moment about a horizontal axis perpendicular to the axis of the beam.

It's come out as " x = (MLL) / (2EIxx) "

where M is the applied moment
L is length
E is Young's Modulus
Ixx is 2nd moment of inertia for bending in a vertical plane

Many thanks

Loten

 

[csd72]

yes, thats right.

 

[msquared48]

Remember though that if the end of the cantilever is not completely fixed, or can rotate (backspan condition) then this must also come into play to determine the true total deflection. The equation you mention will only give the relative deflection based on complete end fixity.

Mike McCann
McCann Engineering

 

[loten]

Very many thanks. Just what I needed. I will heed your warning too about whether the end is truly fixed.

loten

 

[csd72]

The rotation due to the backspan in radians = ML/3EI

where L = length of backspan, M=moment from cantilever.

Apply this as a rigid body rotation to the cantilever then add the cantilever deflection to get the total deflection.

csd