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Registered Member #30
Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706
I think it's the same. The bending moment doesn't depend on the shape of the beam's cross-section. However, the formula for converting bending moment to stress does depend on the shape, and stress is usually what you want to know. You should be able to find tables that show the formulas for things like tubes, I-beams, box sections etc...
Registered Member #49
Joined: Thu Feb 09 2006, 04:05AM
Location: Bigass Pile of Penguins
Posts: 362
Need more data!
The formula you presented is not a general case, it is the formula for the bending moment at the supported end when a load is placed at the 1/4 point of the beam length. M=Fx, where M= moment, F = load force, and x = distance from point of measurement (supported end). The moment due to a load at the end of the beam is M = Load * Length.
As Steve said, if you want to find the maximum moment, that is the moment that achieves the yield stress of the material, then you need the stress formula in addition to the moment formula you have. Then the shape and material properties become important.
Registered Member #160
Joined: Mon Feb 13 2006, 02:07AM
Location: Melbourne, Australia
Posts: 938
Perhaps you could draw a sketch and we can throw some possible solutions your way. It depends on whether you want to work with an existing section size, or an existing load, and of course how it is supported. With section size, load, and support dimensions, you can work out maximum deflection and see if it fits within the permissible deflection range.
Registered Member #142
Joined: Sat Feb 11 2006, 01:19PM
Location:
Posts: 102
IamSmooth wrote ...
The bending moment for a fixed beam at one end under a point load is M = Load*Length/4
Does anyone know what the max bending moment formula is for a hollow tube?
For a point load, moment is just distance times force IIRC. For a cantilevered beam with a load applied at its free end that's just load times length. But you have a 4 in the denominator. Are you talking about a beam supported at the ends, bearing a load in the center? Generally in the textbooks, a beam like that is drawn supported on pins at the ends, which means no bending moment there, just shear. For that case bending moment increases as you go toward the center, where it would be the product of the load times half the beam length. So I don't know where you got the 4. Maybe your beam, rather than pin supported, is clamped at the ends, which would result in bending moment at those points, but I haven't worked out the numbers. Anyway, once you have the bending moment, which will be different at different points along the beam, then you have to figure out whether your beam can bear the stress (at its maximum point). Calculations for the strength of a beam are based on something mechanical and civil engineers call second moment of inertia. Wikipedia calls it second moment of area. That article includes a formula for cylindrical beams. I didn't check the math, and it's been many years since I studied this stuff in college, so caveat emptor.
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Bending Moments
