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Re: MATRIX ANALYSIS

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Christopher Wright wrote:

. > Check three things--
. > Force equilibrium overall
. > Member force equilibrium
. > For a few selected joints, check the force balance on the node points.
. > Also check a few of the members for proper displacements.

But, what if the person that wrote the program had the program check for 
equilibrium unbalance in these items and distributed the unbalance in some 
manner just to make the statics work out? The statics would always check out, 
but the program may be completely wrong because the programmer was unable to 
find the error in his/her code.  (Checking for unbalance due to rounding 
errors is a common procedure in programming, whether it is in structural 
analysis or in computing payroll taxes.)

The first engineering program that I wrote was a FORTRAN program for a 
uniformly loaded square flat plate, ideal for a computer because the 
equations were all infinite series.  My answers were only slightly different 
from the results of Timoshenko, and we all know that Timo is right!  Going 
thru the program again and again, I finally focused on the code to raise -1 
to an integer power.  We all know that the easiest number to raise to an 
integer power is 1, and the second easiest is -1.  In those days we were given 
some idea of how the compiler handled certain operations.  When the FORTRAN 
code indicated that a number was to be raised to a power, the compiler took 
the logarithm of the number, expressed as an infinite series, multiplied the 
logarithm by the exponent, then took the anti-log of the product, again 
expressed as an infinite series.  However, the logarithm of a negative number 
does not exist!  I revised the code to have the -1 raised to an integer power 
alternate between -1 and 1 and the answers immediately agreed with Timo's.

. > The reason you don't want to check it against another program is that you 
. > can never be sure which one's right.

I agree with your final premise, but would add, "... or if both are wrong."

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