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need help with the sizing of a steel beam?
lets start by saying i am no engineer but i have done a little research, and have found some answers but have gotten stumped on a bit of the figures riquired to calculate the max deflection of a beam. so here is what i have i live in a zone that requires a live load of 20 pound per sq ft and the dead load of the roof is 15 pound per sq ft.
so 35 pound per sq ft being the total and no other loads apply i can continue to the span of 30 feet with two supports one at each end.
the roof is twenty feet across horizontally so this being the ridge is supporting the center ten feet. so 10 * 30= 300 and time the total load per sq foot is 10500 for the whole span now this is where i have got stuck because i have a chart of the properties of the beam i want to use but when i try to calulate i cand figure out one or two of the figures to finnish the equation any help would be appreciated.
It’s difficult to me to imagine what are you talking about without a drawing, but on pages listed below there are some basic equations required to calculate max deflection of a beam supported on both ends. Depending on case, equations can be more complicated than those. Here they are:
http://www.engineersedge.com/beam_bendin g/beam_bending1.htm
http://www.engineersedge.com/beam_bendin g/beam_bending2.htm
http://www.engineersedge.com/beam_bendin g/beam_bending3.htm
There are two terms in these equations that could represent a novelty for you:
First is modulus of elasticity E. It depends on elastic properties of material and is pretty much a constant for most types of steel and it’s E=(200…210) GPa or about 30,000,000 lbf/in^2
Second term is marked with I (capital "i") and it is moment of inertia. It represents influence of size and shape of cross-section of a beam. For standard beam cross-sections you don’t have to calculate moment of inertia since it can be found in tables.
For example, for a structural beam supported on both ends with single load W at center we calculate maximum deflection as
f = W L^3 / (48 E I)
In your case as I imagine it, formulas from first link are probably applicable (uniform loading), where W is total uniform load distributed uniformly along whole length of a beam. In that case formula for max deflection is
f = 5 W L^3 / (384 E I)
If W= 10500 lb = 46723 N, L= 30 ft = 914.4cm, E=2.1*10^7 N/cm^2, and for example I=10000cm^4
f = 5 * 46723 * 914.4^3 / (384 * 2.1*10^7 * 10000) = 2.21 cm
Pay attention to two things:
1. Cross section of a beam should satisfy strength requirements first. Deflection is of less importance than strength.
2. Don’t forget to calculate with weight of a beam itself. 30ft long beam has weight that shouldn’t be neglected, and weight also represents kind of uniform loading..
Sorry I couldn’t help you more.
Slowfinger | Nov 20, 2009
Lester Byers