Plate Bending 1

[lkj]

When considering a plate bending in perpendicular directions, how are the resulting stresses combined and compared with material strength?

I have a design yield strength for the material.

 

[Piro]

You must follow acording to cchapter H of AISC ASD Manual, for combined stresses, axial compression and bending in two perpendicular directions. This is applicable to simetrical shapes or profiles. You must calculate the working stresses due to axial forces and bending, fa=P/A, fbx=Mx/Wx, fby=My/Wy, then calculate the Allowable stresses Fa (according to Chapter E), Fbx, Fby (According to chapter F). Normally if x is the strong axis, Fby=0,6 Fy and Fbx <= 0,6 Fy (Yield Strength of steel) depending of lateral buckling behavior. Also you need to calculate the Eulers's stress F'e, the Cm factor (depending of moment diagram shape, conervativelly =1.0) and finally apply the ec (H1-1), (H1-2) or (H1-3) if Fa/Fa<=0,15. In your case if you do not have axial force you may use ec. (H1-3).

If the result of this ecuation is <= 1.0 the section you choose is OK, otherwise you must change the dimensions.

 

[ishvaaag]

The best advice is to follow what indicated in the structural or mechanical codes for the material and element, since the variety of cases is such that require separate specifications on how to proceed to well ensure the safety of the people whilst not being unduly conservative.

I understand the question refers to 2 way bending of a plate. For ductile materials one conservative approach plate-wise is to check at every point the Von Mises criteria of limit strength. With this you are checking local extenuation of the strength. Some local yielding precedes effective buckling whatever the slenderness, and some elements, and particularly plates, may have significant post-buckling and post-yielding strength, so using the detection of start of yielding at some point through the Von Mises equation is good as a criteria of limit strength, with the limitation of that depending of the kind of element and boundary conditions you may have significant reserve of strength beyond yield that you could (in some cases you can not) put to good use for economy.

For Reinforced Concrete and practical design, use of criteria for limit strength becomes quite unpractical. So sets of rules have developed on what to do. Many times the tensile strength of concrete is entirely dismissed in the calculation (whilst it is expected be normal to gain the normal expected behaviour). Hence, by the notional scheme, all the tension needs be taken by the steel. So the main task is to find reinforcements able to meet the tensile actions that appear, this abated to the direction in which the rebar is to be laid. Ideally steel should follow the tensile stresses but this is impractical, so grillages of orthogonal groups of rebar are laid to ensure that the resultants of tension anywhere are met. So the main issue is to find what the tensile actions are and their resultant, then the idealized tensile stress blocks be met through steel reinforcement.

Then in RC you have to consider crushing of the concrete and tensile failure of the steel, both can happen. Even if theoretical studies give better insight on the actual local behaviour, for practice what one needs is to follow the design guides, which care of both ways of failure.

So all reverts to my advice in my 1st paragraph above.