The Exact Method

Tips

“The True Analytical Method in Structural Analysis”

This is the title of the unpublished blockbuster book that any USA refutable technical publisher can print for the world to see. The current worldwide practice of deliberate ignorance uses only one pivot point (that for concrete) and non-rotation of orthogonal XYZ axes to obtain the minimum column yield capacity for a composite circular and rectangular section in reinforced concrete. It also did not use the coordinates of reinforcing bars at the center of the given composite circular and rectangular sections in reinforced concrete. We are now in the age of electronic digital computer and Microsoft Excel that the exact method using our knowledge of basic mathematics and physics can be numerically authenticated by Microsoft Excel program of the hundreds of integral calculus equations derived from the established principles of Euler’s, Hooke’s Law and Pythagorean Theorem.

I am still waiting for the questions that researchers would like to ask me about my books. They may not know what questions to ask since we have been brainwashed and buried for many years accepting literature done by authors and professors using the approximate method. We are now in the age of computers and this practice is no longer correct. I may not solve everything in life but I showed the way in my books to find the truth in anything. Note that I am the only one in the world doing the ‘rotation of axes’ while everyone is copying the principal axes to any section. The following are my tips for their understanding of the things exposed in my website at https://www.ramonjarquio.com and the equations in my books which were published by Universal Publishers in 2004, the second one was by CRC Press/Taylor and Francis in 2007 and the third one published by Xlibris in March, 2012.

(1)  For structural analysis, apply the Leonhard Euler’s principle which states that any section is subjected to ‘an axial load and a moment’. Note: This refers to the capacity of any rectangular or circular section at all eccentricities.

(2)  Apply basic mathematics and physics learned in school to derive the equations involved in any problem. From analytic geometry, the equation of a circle or a rectangle is known.

(3)  From physics we know the equation of parabola to define the stress/strain relation for concrete. For steel the stress/strain ratio is linear.

(4)  Sketch the free body diagrams with ‘rotation of axes’ to enable the engineer to analyze for equilibrium of internal and external forces. Current method does not draw the correct free-body diagram because of non-rotation of axes.

(5)  Use our knowledge of differential and integral calculus to derive the equations for axial load and moment to any rectangular or circular section. The stress/strain diagram over the given section for any position is given in the free body diagram and therefore we can integrate the volume generated for axial load and a moment at the centroid of the section.

(6)  The Microsoft program can now do the numerical calculations of the equations derived above at all eccentricities. The graph produced is now what we call capacity of any section. There was no need to define ‘short’ or ‘long’ column as others do. However, if you want to do that, a short column is that which the given section is at full compression. A long column can then be defined as that where the stress at the section is now compression and tension. The external load when plotted in this envelope will define itself whether it is short or long. Therefore, we do not need the short or long column terms.

(7)  My discovery is that the minimum capacity of a rectangular section is at a diagonal. For a circular section reinforced with steel bars the minimum capacity is between reinforcement. However, for a circular section, assume a diameter through the center of any bar as the capacity axis since the variation between any two reinforcing bars is very small when the number of bars are in odd number. When bar number is even, the column axis is thru the center of any bar.

(8)  Now that the capacity of any section in rectangular and circular section is known from Microsoft Excel solutions, we can now determine the real factor of safety from the yield capacity versus the external load which can vary due to local regulations and applicable codes. Worldwide the practice is still what I call the ‘factor of ignorance’ in determining the factor of safety. Note that the real factor of safety in design cannot be correctly obtained by the standard interaction formula in use universally.

(9)  Apply the 3 tools of basic mathematics, physics and the computer that we learned in college to find the truth in anything that we encounter in our profession. The educational system must be revamped for a student to be familiar in the use of these 3 tools for discovery of the truth in anything that we do.

(10) I started the exact analysis in 1980 and I was able to finish my research and produced my books after retirement from the TA. I would like all engineers to know the truth now that we have computers to perform all the numerical calculations. A new paradigm from the approximate to the exact method can now be implemented if one is interested in the truth. Expediency and compliance with regulations is not always the best approach in finding the truth. As a matter of fact, the current method of non-rotation of axes is wrong. The numerical proof is possible when all the derived equations involved can be programmed in a Microsoft Excel software and the by-product is an envelope of minimum column yield capacity as per Euler’s principle, Hooke’s law and Pythagorean Theorem.

(11) The external load (variable in any locality) is now plotted inside this envelope to preclude any failure of the given circular and rectangular section. The real factor of safety is readily calculated and known for any application.

(12) The interpretation of measurements done in the laboratory from modelling can now be reconciled with the derived analytical equations of minimum column yield capacity and incorrect conclusions can be avoided.

(13) To all those self-proclaimed structural experts, follow the saying “Seek the truth and the truth shall make you free from ignorance” for enlightenment.

Ramon V. Jarquio, PE

Email 1: [email protected]

Email 2: [email protected]

Website: https://www.ramonjarquio.com