Very Simple Section Bending Margin Check Question

[Toran2013]

Hi all,

My question relates to a simple hand calc bending check of a rectangular section of say aluminium

I've noticed its common in stress reports that only an ultimate bending tension stress check is performed using Ftu.
i.e comparing f=6M/(bd^2) against Ftu only.

I understand that the compressive side can be checked if necessary to yield conditions Fcy
I also understand that ultimate compression Fcu is not a real failure mechanism and difficult to test for etc.

Is it considered that the compressive side cannot fail before the tensile side under beding due to the tension supporting the crossection somehow?
However, if the compressive side does weaken and deform the section prior to the tensile side reaching ftu, how can the engineering bending therory i.e. plane sections remain plane, still hold.

Is there a usual method for checking say crippling over half section at ultimate conditions under pure bending say via compressive strains.

Does anyone have a good explination as to why we generally omit compressive side MS checks for simple rectangular sections under pure bending at ultimate loads.

I understand its a simple question but its one I've never really heard an answer for that makes sense.

Cheers

 

[rb1957]

you're 100% right ! ... i Hate bending checks on the tension side; unless the tension stress is the higher stress (significantly).

we should check both sides of the beam, tension and compression; although often it'll be clear that compression is critical.

compression limit can be crippling, fcy, or, if stable and there's no long column effect, even ftu. and remember plastic bending (Cozzone, etc).

ftu ? yes, if the section is stable and a short column ... so the material is crushing. you could do an Et calc (plastic column), but ...

so this answers why we do tension checks for simple rectangular sections under bending. the tension/compression stresses due to bending are the same, the allowable is assumed to be the same and it looks better to check tension against ftu (or 1.4*ftu).

Quando Omni Flunkus Moritati

 

[johnbridge231]

Gents, there is a software that performs all the checks of cross sections of any material and any shape:

http://www.engissol.com/cross-section-analysis-design.html

I am pretty sure that you will find it more than useful (as I did) for cross sectional calculations.

Regards.

 

[Sparweb]

Toran,
Good question. The basic bending stress formula (like the example you gave for a rectangular section) is rather conservative if you stretch it up to the failure condition. It's also important to distinguish between metallic structures, which are ductile, and other materials that may be brittle, having very little distinction between yield and ultimate.

Really, that formula is only valid for perfectly elastic bending. Once the yield point has been exceeded (for compression or tension) then some plastic deformation begins to occur in the outer fibers. Beyond that point you can define failure as the first sign of yielding (limit load) or let the beam bend until it suffers complete failure (ultimate). If you're still using the formula with the ultimate strength plugged in, then you're pretending that the stress-strain curve goes in a straight line up to ultimate. It's a conservative simplification. A solid metallic beam can support a lot more bending stress than the yield stress. Adding load above yield, the plastic deformation doesn't reach all the way through to the neutral axis. Load can be added until the point that the outer fibers reach a rupture stress (comp or tension).

So a solid rectangular section beam can withstand a lot more bending moment than the simple formula would lead you to believe. Using it for calculations of ultimate strength is conservative and usually safe. Using the formula for a thick tube is less conservative, and if the walls of the tube are thin, then the compressive crippling/crushing/stability factors come into play instead.

If you have a copy of Bruhn, I can point you to chapter C3 for a few diagrams to help illustrate.

STF