On Tue, 09 Jun 2009 22:40:52 GMT, "Lew Hodgett"
wrote:

Now that you see what a total PITA beam deflection calculations are
along with the incorrect assumption that the beam is supported on
knife edges unless cantilevered, you can understand why stress
calculations are used with a serious safety factor derate to CTA, for
beam design.


Plus the fact that the algebraic equations result from integration of
the governing differential equations which are themselves linearized
because the actual non-linear equations frequently do not have a
closed form solution in any but the most trivial cases.

All of engineering mathematics is an approximation of the real world
but the nice thing about it is that the linearized versions of the
equations generally yield conservative results when compared to
numerical solutions of the non-linear equations. One of the
linearizing simplifications that is non-conservative with respect to
deflections is ignoring the contribution of shear deformation. That
particular effect isn't usually introduced in undergraduate level
courses.

Your point about the assumptions underlying the model is well taken.
The simplifying assumptions are rarely a true and exact picture of the
real world. That's why it's called "Engineering Approximation" and why
"Safety Factors" (civil engineering) or "Margins of Safety"
(aeronautical engineering) are always applied to any critical stress
analysis.

In response to a question asked in another post: No, I didn't recall
that from memory. I believe Albert Einstein is credited with the
advice to never try memorizing something that you can easily look up.
I went back to an old Strength of Materials text from my undergraduate
days in the '60s. The case of a uniform beam, simply supported, with a
uniform distributed load is one of the introductory examples of beam
analysis..

Tom Veatch
Wichita, KS
USA