BOR Engineering Monograph 27 Interpolation Help

[cuels]

I have been working through the example (Appendix I) in the Bureau of Reclamation's Engineering Monograph 27 - Moments and Reactions for Rectangular Plates. My only hold-up on understanding the process for determining the Moment Coefficients, based on the example, is the interpolation method for finding a moment coefficient value with an a/b ratio that is in between the a/b table values. For example, the example explains that the a/b ratio for the wall slab is 0.2, which is between 0.25 and 0.125 in the tables. It goes on to say that it uses second degree interpolation. I am not familiar with this method of interpolation. I attempted using a linear interpolation method, and the results did not match the example's solutions. If anyone could please explain the second degree interpolation, it would be greatly appreciated.

 

[Ron]

Second degree interpolation is a curve fitting exercise. If you have two points, a linear interpolation is appropriate. If three or more, then a curve should be fit to those points and your point selected from the curve. The easiest method is graphically, otherwise you'll have to define the curve and compute your point on the curve.

I'm curious...the monograph is a tortuous process to get an answer that only has slide rule accuracy. I doubt that there would be a great deal of difference between a linear interpolation value and a 2nd degree interpolation. I must assume you're doing this as a part of a learning process and if that is the case, I applaud your effort. Otherwise, any good FEA program that handles plates should be able to do this for you. It would be interesting to compare the results obtained from the monograph with FEA results.

Good luck.

 

[cuels]

Thanks all for your help. After sleeping on it last night I came to the same conclusions. Sometimes I can't connect thoughts until I mull it over in a discussion with someone, so thanks!