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enter image description here

Above table is from Eurocode. According to the table, the stress distribution in a flange of a beam can be negative in part of the flange when the part is subject to bending and compression. Why is this?

If we have a beam that is compressed and bent at the same time, shouldn't the stress vary from positive to negative as a function of distance from the neutral axis (in vertical distance in the picture), not as a function of distance from the web, along the flange as in the picture? Why does the stress vary like that, from the "bottom" of the web to the tip of the flange?

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3 Answers 3

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When the beam bends, the tension and compression at the outer (top and bottom) surface of the flanges is higher than at the inner surfaces. That follows from the basic equation giving the axial stress in the beam = $My/I$.

If Poisson's ratio is not zero, this non-uniform stress will bend the flanges from the web of the beam to the extremity of the flange.

Google for "anticlastic curvature" or "anticlastic bending" for more detail, and pictures.

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  • $\begingroup$ Interesting, this is completely new term for me. However I don't still understand why the shape of the stress distribution is like that. The Eurocode pictures seem to suggest that the stress is uniform in the bending direction and varies along the flange. See the second to last row for example, there is a linear distribution along the flange, which is not direction what your theory would suggest. Instead we should expect it to vary linearly from the bottom surface of the flange to the top, right? $\endgroup$
    – S. Rotos
    Dec 20, 2020 at 11:44
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it is possible the beam top flange not laterally supported warpes and created lateral moments on the flange.

the beam deflects assuming the path of least work, one of which is warping. if we sum the strain energy it would be the least.

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The first column corresponds to bending about the major axis. The other two columns represent bending about the minor axis. I guess so.

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