deflection of short beams
deflection of short beams
(OP)
Can anybody please suggest a formula for the deflection of cantilever beams with very short spans (L/D around 1) subject to concentrated end load?. This would contain a shear term (the highest contribution?) and a bending term (negligible?)
I struggle to find such a formula in literature
Thanks






RE: deflection of short beams
Δc = Δm + Δv
Δm = Ph3 / (3EmI)
Δv = 1.2Ph / (AEv)
P is the end of cantilever load
Em is the modulus of elasticity (your typ. E)
Ev is the shear modulus (sometimes referred to as G)
h is the cantilever length
I is the moment of inertia of the member
A is the area
RE: deflection of short beams
RE: deflection of short beams
PI^3/3EI gives the bending deflection, but I think this formula is only valid for slender beams (L/D>10) (Saint Venant's assumptions)
As for the shear deflection I will use JAE's formula
RE: deflection of short beams
RE: deflection of short beams
JAE
I did notice that Bagman's formula was the flexural term in yours. I think this formula is applicable only under the Saint Venant assumptions, and among them is slenderness of the beam (L/D>10)
I don't know how inaccurate this formula would be for short beams
RE: deflection of short beams
RE: deflection of short beams
That formula is anyway the only one available. And consider that the ratio of bending deflection to shear deflection for a cantilever is of the order of (L/D)2 so that for L/D≈1 the two contributions are of the same order of magnitude.
What I wonder on a more practical basis is why you could be interested in the deflection of a so rigid thing.
Also consider, again on a practical basis, that boundary conditions with their local effects (how and how much the beam is fixed, how is the load applied) may contribute more than the theoretical values.
prex
http://www.xcalcs.com
Online tools for structural design
RE: deflection of short beams
Thanks for your feedback. I am trying to maximise the stiffness of a piston pin of given mass and length. Increasing the diameter results in lower bending but higher shear deflection (because of the reduction in cross section area). The detailed analysis will be done by FEA but I need a starting point close to the optimum.
RE: deflection of short beams
Sorry, I take that back - shear deflection does not depend on diameter as cross section area remains constant
RE: deflection of short beams
RE: deflection of short beams
thanks jmiec, do you also have the factor for hollow circular sections?
RE: deflection of short beams
RE: deflection of short beams
In my case the section is definitely thick-walled...
RE: deflection of short beams