I made some revisions in the two calculation worksheets of the "MONORAIL.xls" workbook which eliminated some unnecessary conservatism in the analysis as noted below.

At the bottom of the 2nd page of the calculations where bottom flange bending is checked via a simplified approach, the worksheets were originally taking the wheel load to be at the edge of the flange, which was conservative. Now the moment arm for bending has been reduced by subtracting the input distance "a" from the edge of the flange to the center of wheel.

In the 3rd page of the calculations where bottom flange bending is analyzed per CMAA Specification No. 74, the worksheets were using the originally computed bending stress values of "fbx" and "fby" (taken to the extreme outer edges) in the biaxial stress formulas for the analyzed point locations 0, 1, and 2. Again these values were in some cases conservative, depending on the point which was being investigated. Now the bending stress values "fbx" and "fby" are determined at the specific point under consideration (fbxo, fbx1, fbx2 and fbyo, fby1, fby2).

It was brought to my attention in both the "S-shaped Monorail Beam" and the 'W-shaped Monorail Beam" worksheets that for the lateral flange bending moment from torsion for the overhang (cantilever) portion, the program calculation cell (cell O69) was incorrectly using the simple span length, "L", when it obviously should have been using the overhang (cantilever) length, "Lo". The text display of the formula was correct in showing "Lo", but again it was the calculation cell that had the error.

With this error of using "L" instead of "Lo", the result from the calculation would have been conservative, but not nearly as much as one might expect. That is due to the fact that the formula used includes a hyperbolic function in the expression.....TANH(Lo*12/at).....where at = SQRT(E*Cw/(J*G)). When the value of (Lo*12/at) is >= say 3.0, the TANH of that approaches 1.0. Thus, the larger the overhang (cantilever) length was, the smaller the conservative error became. Plus, the error that was involved was a good bit less when using the more common "S" shapes as opposed to using "W" shapes for the monorail beam.

I have made the corrections and the new version of this workbook is now version 2.0.