monorail beams 2

[EL]

I am curently working on the design of a monorail beam. I am using the CMAA #74 (1994) specifications and I do not understand the source of the coefficients used for local bending of flanges due to wheel loads.
I am looking for other specifications or books where I can find a detailed calculation for crane/monorail beams.

 

[prex]

A problem close to this one is treated in Timoshenko's Theory of Plates and Shells: an infinite strip fixed on one side (acting as an infinitely wide cantilever) with a point load at varying distance from the other side.
If you want to try a rough explanation of those misterious coefficients, from the position of the wheel load take two lines at 45° towards the web, and take the strength of the intersected portion of flange.
If d is the distance of point load to web face, the width of that resisting portion is 2*d and the thickness t is the flange thickness just before the corner radius. So you take sigma=F*d/(2*d*t²/6)=3*F/t² (and as you see the result does not depend on d).
I would like to know if this approach gives a result close to what you find in that standard.
prex
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[svc430]

I don't know for a fact, but I'm guessing the coefficients and equations were taken from FEM; Federation Europeena De La Manutention, as indicated on page 6 of the CMAA Specification No. 74 (1994 edition). Specifically, Local Girder Stresses, FEM.9.341 1st Edition (E) 10.1983. I've never seen these standards but CMAA does make reference to them in their top running crane specifications also (CMAA No. 70).

The current edition of CMAA No. 74 is now the 2000 edition, which I don't believe has changed any as far as the local flange bending stress from under running hoists.

It might be of interest to you to know that a prior edition of this CMAA standard (1974 edition in particular) referred to R.J. Roarks "Formulas for Stress and Strain" for calculation of the local bending stress on the lower flange. The section of this book that CMAA referenced delt with the bending of very wide cantilever slabs under concetrated loads. This appears on pages 189-190 of 5th edition of this book (pages 206-208 of the 6th edition). It appears that this calculation only delt with stresses running spanwise to the cantilever (90 degrees to the overall simple beam bending stresses in the girder). CMAA then required this stress to be combined with the other stresses by means of Mohr's Circle for biaxial stress. The formula presented by Roark for this stress is fairly simple, = Km(6P/t^2), where Km is coefficient dependent on the location of the load (a chart for Km was included in the CMAA standard; duplicate to the chart shown in Roarks book).

At present, CMAA now includes a rather tedious set of equations and coefficients that include calculation of localized stresses acting in both the x and y directions due to the local wheel loading effect. Accordingly, these stresses that act in the y direction would have to be added directly to the overall bending stress of the beam section (y axis running in the plane of the web).

Good Luck!!