Eccentrically loaded beam moment distribution
Eccentrically loaded beam moment distribution
(OP)
Hello all,
So, I am familiar with the derivation of the maximum moment and stress of an eccentrically loaded beam with pinned ends. However how does the calculation change when both ends are fixed? Is such a beam overdetermined?
Thanks for your input! :)
So, I am familiar with the derivation of the maximum moment and stress of an eccentrically loaded beam with pinned ends. However how does the calculation change when both ends are fixed? Is such a beam overdetermined?
Thanks for your input! :)






RE: Eccentrically loaded beam moment distribution
how does the beam interact with the rest of the world ? You show (carefully) no contact at the ends. Say there's a shear connection at the bottom end, then this'll react the beam axial load and the beam will "cock" in the clearances and develop a lateral couple to react the offset load. If the shear attmt is inline with the load then no moment to "the rest of the world", but there'll be an internal moment in the beam.
clear as mud ?
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RE: Eccentrically loaded beam moment distribution
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RE: Eccentrically loaded beam moment distribution
If one end of the beam is fixed against rotation but free to move in an axial direction and the other end is fully fixed, the beam feels an axial stress of F/A but no bending.
What is the meaning of "overdetermined"?
BA
RE: Eccentrically loaded beam moment distribution
RE: Eccentrically loaded beam moment distribution
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RE: Eccentrically loaded beam moment distribution
If both end supports permit axial translation, the beam is unstable. The beam needs one reaction to prevent translation. It can be at an end or anywhere along the beam, but it is necessary for stability.
BA
RE: Eccentrically loaded beam moment distribution
I think the following diagram explains it better.
The case is of an eccentrically loaded tension specimen with the intention of superimposing tension and bending loads.
Fixed supports are actually roller supports, as displacement is allowed in x, but is fixed in y. Under tensile loading the beam center-line (red) should then deflect toward the overall center-line. As a result, there is a bending moment in the beam. What is the distribution of this bending moment along the beam in the x direction?
RE: Eccentrically loaded beam moment distribution
there is some moment restraint at each end. Draw a FBD of 1/2 the specimen. In all likelihood the unsupported mid-span of the specimen will deflect towards the load line of action, reducing the off-set moment; this moment will divide itself between the ends and the mid-span.
Depending on what you're trying to test, you could put a hinge at the end of the specimen, then the specimen would be in tension and the off-set moment reacted at the ends (ie a simple tension test). If you remove the rollers, and maybe load on a single point, you'd see the ends rotate as the mid-span tries to unload moment.
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RE: Eccentrically loaded beam moment distribution
Since 0 rotation, then 0 moment.
The F x e moment is taken "out" by the boundary condition at that point since you dis-allow rotation in the member at the end.
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RE: Eccentrically loaded beam moment distribution
another day in paradise, or is paradise one day closer ?
RE: Eccentrically loaded beam moment distribution
BA
RE: Eccentrically loaded beam moment distribution
another day in paradise, or is paradise one day closer ?
RE: Eccentrically loaded beam moment distribution
BA