Example of the Exact Method
Book 1 published by Universal Publishers of Boca Raton, Florida in 2004 entitled “Analytical Method in Reinforced Concrete” showed the exact method in structural analysis for a reinforced concrete rectangular section. See pp. 50-80 Article 2.2.2 “The Rectangular Column with Biaxial Bending”
To appreciate the deliberate ignorance of world experts and the brainwashing by reference literature on approximate methods, this book must be read and digested by proclaimed experts in structural analysis in this era of electronic digital computer and Microsoft Excel.
Unfortunately because of the preponderance of reference literature invented before the advent of Microsoft Excel, world experts are copying reference books for expediency and compliance.
By copying these references invented by well- intentioned authors, experts and professors before the advent of computers, they took these references as accurate because of finite-element methods on fixed XYZ axes. Microsoft Excel, however can numerically confirm the hundreds of integral calculus equations derived using basic mathematics and physics on Euler’s, Hooke’s Law and Pythagorean Theorem. It proved that these approximate methods with finite-element are simply wrong and therefore should not be copied without rational thinking.
The proof of this exact method is in a software programmed in Microsoft Excel 95 by William R. Mulford of Westbury, New York in 1996. It was advertised in an ASCE magazine and registered in the Library of Congress in 1996 but unfortunately ignored by the structural community worldwide.
A computer expert can program this software in 2 pivot points (one for concrete and the other for steel) by using the equations listed in the book above-mentioned. The current method using one pivot point without rotation of XYZ axes and without using the coordinates of reinforcing bars is indeed wrong when computers are used.
The by-product of this software is a graphical representation of the minimum column yield capacity referenced to a column capacity axis (rotated X-axis) along a diagonal for rectangular section. The boundary of this graph is controlled by a short and long column definition. A short column is defined in which the whole section is in compressive stress. A long column is that in which the stress in the section is tensile and compressive stresses. The graph is constant for a specified strength of material.
When an external load (variable in any location) is plotted inside this envelope, the real factor of safety in design is calculated. Currently the fictitious safety factor is calculated by the so-called standard interaction formula which is guesswork and unreliable. The charts and examples in the book can only be verified by an investigator if a software is available to confirm these charts in the book.
Nobody will admit to the mistake of experts in the non-rotation and non-use of the power of Microsoft Excel in exposing the truth based on established Euler’s, Hooke’s Law and Pythagorean Theorem. Current practice will continue deliberate ignorance because of laziness to derived hundreds of integral calculus equations to satisfy Euler’s principle for a rectangular section.
Ramon V. Jarquio, P.E.