For deflection of a uniformly loaded (evenly distributed the full 
length), simple supported (pinned at both ends free to rotate, and one 
end can slide frictionless lengthwise) beam (defined as pure bending, no 
axial load) the formula is: Deflection = (5 * W * L * L *L * L) / (384 * 
E * I)  in inches
All units must be consistent - don't mix pounds and tons or inches and 
feet, I have english units but when you substitute any system of units 
the units will cancel leaving the result in those units
W = Uniform load (pounds per lineal inch along length of beam)
L = length (inches)
E = Modulus of elasticity (Pounds per square inch) (29,000,000 for steel)
I = Moment of inertia (inches to 4th power)
    For a rectangular crossection = B * D * D / 12
B = Width (inches)
So it can be seen, doubling the width (B) will result in 1/2 the 
deflection, and doubling the depth (D) will result in 1/4 the deflection.

Note for design of beam, deflection is one of many design criteria, 
where shear and bending stresses , lateral buckling are some of the 
necessary things to be checked for safety.  Nothing is said of the 
scale, and I have used this formula on everything from a 2" long piece 
to 100 foot long concrete beam.

Lee Jones wrote:
>>>> You have a beam that is ( theoretically )  x long, y wide and z
>>>> thick.  Weight is applied perpendicular to the xz plane. Beam is
>>>> supported at both ends of the length.
>>>> What happens if you compare it to a beam of the same material
>>>> x long, 2y wide and z thick ?
>>>>         
>
> >From your initial description, I believed you meant X was in the
> horizontal plane, Y was in the horizontal plane, and Z was in the
> vertical plane.  My answer was based on those assumptions.
>
>   
>> It appears that doubling the width ( depth ) of the beam causes
>> the deflection to be reduced about 8-fold.
>>     
>
> >From this message, it now appears that your Y dimension is the 
> vertical plane (and X and Z are horizontal).  If so, then yes,
> doubling the vertical thickness is about 8 times stronger.
>
> 						Lee Jones
>
>   
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