deflection of short beams

huangyhg

deflection of short beams
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
here's a formula that i use for deck diaphragms - contains both a flexural and shear component:
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
what's wrong what pl3/3ei.  (p x l cubed / 3 x e x i).
thanks for your answers
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

if you notice, the flexural portion of δ in the above equation is pl3/3ei, the same as what bagman2524 presents.  you just need to add the shear deflection for short conditions to be more accurate.
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  
the 1.2 factor in the above formula for shear deflection applies to rectangular shapes.  article 7.10 of roarkes formulas for stress and strain shows different factors for round, hollow, or i shapes.
all the above is correct, but quite theoretical. and gio1fff">fff">, the bending formula is not incorrect at short lengths, it simply doesn't account for local effects that may be more important than the pure bending deflection.
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 (lfff">/dfff">)2 so that for lfff">/dfff">≈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
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.
sorry, i take that back - shear deflection does not depend on diameter as cross section area remains constant
for a solid circular section, the shear factor is (10/9), so the shear deflection is (10/9)pl/ag.