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Re: Plastic Analysis of steel beam

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On Sep 29, 2006, at 7:57 AM, Padmanabhan Rajendran wrote:

Commonly used carbon steel (A36, A992, A572...) has, not only a yield point, but also, an ultimate strength. While the deformation beyond the yield point can be large, the material can take only so much abuse before it will break, as defined by the ultimate strength.
The ultimate load isn't defined by the ultimate strength, but the fracture strain (which isn't the percent elongation, BTW). what happens in a redundant structure is that the load path tends to shift away from the yielded member until a additional plastic hinges form and the structure becomes kinematically unstable. Like an portal frame with single pin connections. It just falls over.

Therefore, in the plastic analysis of a structure, constructed from above noted material, is it not probable that the section, where the first hinge was formed, would break before the mechanism developed? If it is, is there any procedure, amenable to manual computations, to calculate the load at which the first formed hinge would break?
Nothing manual that will do you any good. It's a highly non-linear type analysis. The structure tends to change shape in effect making itself into a different structure. There's also work hardening to consider.

For example a simple beam centrally loaded will become kinematically unstable when the section becomes plastic under the load. If the ends are restrained it will theoretically collapse when plastic hinges form at mid-span and both ends, but as it deforms, tensile forces develop in the member which also resist load. This aggravates the loading on the supports which becomes both horizontal and vertical and it all has to be considered. FEA can do a certain amount of this, as can highly specialized software like LS-DYNA, but it takes a lot of serious tweaking for FEA results to match testing. It's not really a design tool.
Christopher Wright P.E. |"They couldn't hit an elephant at
chrisw(--nospam--at)   | this distance" (last words of Gen.
.......................................| John Sedgwick, Spotsylvania 1864)

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