“The Analytical Method in Structural Analysis”
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 web site at http://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 and rectangular section 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) Draw the free body diagrams with ‘rotation of axes’ to enable the engineer to analyze for equilibrium of internal and external forces.
(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.
(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.
(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. ‘Seek ye the truth and the truth shall make you free’ should be followed for enlightenment.
Ramon V. Jarquio, PE