I need help in calculating the maximum load for a box beam 1

Hi psalms23

You can get the capacity of the beam using the following analyses:-


beam stress= M*I/y

where M= maximum bending moment

I= second moment of area of the beam

y = distance from the neutral axis to extreme surface
of beam (your case its = 8"/2 = 4&quot


I for your beam = (b1*d1^3/12)- (b2*d2^3/12)

= (8" * 8"^3/12)- (7.25" * 7.25^3/12)

I = 111.0986328 in^4

max bending moment assuming a simple supported beam with a central point load:-

M = 20000lb * 120"/2 =1200000 lbin


stress = 1200000* 4"/11.0986328in^4

stress = 432485.7022lb/in^2

This beam is way over stressed you need to repeat this calculation with a larger beam section untill you get a stress figure which is well inside the allowable stress figure for that particular section.


to calculate the deflection of above beam use :-

deflection = W*L^3/(48*E*I)

where w= point load 40000lb

L= beam length

E= modulus of elasticity of material

I= as above previous


so deflection = 40000 * 120"^3/(48* 30*10^6*11.098328)

deflection = 4.33"

I stated before you need to use a stronger beam section however the above formula will help you.
Also bear in mind that stress calculations need to be carried out for the plates you mentioned in terms of the welded portions and shear,( bending dependant on how the end plates are loaded).

hope this helps

regards desertfox

Thanks desertfox,

In your calc I=111.0986in^4, I used (H^4-h^4)/12 and got the same results. However in the stress & deflection calc the I value had been reduced by a factor of 10. Is this a typo error ? Otherwise the stress & deflection values using the formula provided should be reduced by a factor of ten, thus arriving at 43248.5 lb/in^2 and 0.433".

Hi psalms23

Yes your right my decimal point is out by 10, sorry for the mistake.


regards desertfox