modeling two plates stacked

[Randy2002]

I am looking at a steel plate girder bearing on a steel/elastomeric bearing pad. I am looking at the required thickness of a "sole plate" between the girder bottom flange and the bearing pad. The bearing pad and sole plate are an inch wider than the girder flange, which complicates the situation. To model it, I mentally turned it upside down and put a uniform pressure on a plate with the girder web and bearing stiffeners acting as a cross shaped support (I actually just modeled half of it).

The sole plate will be welded to the girder flange by fillet weld around edges. I was planning to ignore this connection as far as the sole plate design, thinking it would be more conservative, and it would be difficult to count on that connection and it's effects, the fatige issues related to the weld, etc. (comments ?)

I used calculated the plate thickness that gives me an inertia equal to I_flange + I_sole and used that for the plate elements that correspond to the bottom flange and sole plate together. My intent is to look at the resulting moments and calculating the stresses in the sole plate manually with it's actual inertia. I was planning on just taking Mx and My, calculate the RMS moment and then the stress. Since I'm not going to make the plate the exact minimum required thickness anyway, I really just need to be confident that my results are a reasonable approximation of the plate stresses. What are your opinions on that?

Thanks,
Randy

 

[vonlueke]

Randy: I think your described method will give a correct result. (Shouldn't "RMS" be "RSS"? I assume so.) And as I'm sure you know, your resultant moment M_RSS would be distributed to each plate in proportion to its moment of inertia. After algebraic simplification, this (interestingly) becomes the following, where I_total = I_flange + I_sole.

sigma_flange = (M_RSS)(0.5 t_flange)/I_total
sigma_sole = (M_RSS)(0.5 t_sole)/I_total

You could, as you described, extract moments to obtain M_RSS. You might alternately consider using von Mises stress, sigma_vm, directly from your model instead of extracting moments. It might give you about the same or a conservative result. As such, the resultant moment would then be M_RSS = (sigma_vm)(b)(t_elem^2)/6, where t_elem = thickness of plate finite elements in your model, and b = 1.0 mm (i.e., one unit of plate width).

I think your described method will give a correct and conservative result for bending stress. Concerning bearing stress, the length of web in bearing should also be checked against an applicable design code to ensure bearing stress on the web is code-compliant.