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“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 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



Book Description

The first book entitled “The Analytical Method in Reinforced Concrete” was published in 2004 by Universal Publishers of Boca., Raton, Florida. The assumption made by the author of this book is different from the stress/strain diagram used by CRSI and standard assumed worldwide. We know from cylinder and cube tests that the stress in concrete is almost parabolic in nature. This is accepted worldwide. We also know that the stress/strain property of steel is linear and symmetrical in compression and tension.

In USA, concrete strain is assumed as 0.003 and this is used for any concrete stress and is almost linear with stress. For reinforced concrete, the strain for the steel in tension and the concrete in compression is equal at balanced condition. However, in concrete compression the strain in steel is less than 0.003 at concrete edge and therefore the steel bars are stressed beyond the strain at yield stress. In Hooke’s Law bars are limited at yield stress when steel strain is equal to or more than fy/20,000 fy is in ksi in order for concrete in compression to be able to develop its entire compressive stress fc’.  Concrete cannot develop tensile stress and hence steel bars are assumed to be stressed at fy since at the tension side the strain is now more than 0.003 if the standard pivot at this point is considered and the compressive concrete depth is less than the balanced condition.

The author assumed in this strain that fy is fully developed by the bar furthest from the neutral axis and succeeding bars are prorated to this value. Proper embedment of the reinforcing bars into concrete should be implemented for bars to develop the yield stress. The resulting yield capacity of any rectangular or circular section in reinforced concrete is smaller than the pivoting of the strain at concrete edge by CRSI or the standard method. Since the difference is small, either method can be adopted. However, ‘rotation of axes’ should be employed to equate the internal load to the external load in the free body diagram. Worldwide the principal axes are being used in the analysis for yield capacity. To compound the problem the ‘standard interaction formula’ is being copied by everyone to determine the factor of safety.

As you know the factor of safety is just the ratio of internal load (yield capacity) of any rectangular or circular section in reinforced concrete to the external load which can vary due to specifications and local practice. Since the yield capacity at all eccentricities is determined using the Euler’s principle, basic mathematics and physics, by an envelope of axial load and moment about the neutral axis, plotting the external load on this envelope, the real factor of safety is determined. It is indeed strange that the ‘factor of ignorance’ is being practiced worldwide because of copying all these years of existing literature. The standard interaction formula is not correct to implement in this case, yet it is being copied and implemented to determine the factor of safety.

The second book entitled ‘Structural Analysis: The Analytical Method’ was published in 2007 by CRC Press/Taylor & Francis of Boca Raton, Florida. This book contained the procedure for steel structures and contains the symmetrical stress/strain property of the steel material. The properties of the I-sections in the AISC Steel Manual are utilized to determine the capacities of these sections using author’s equations and free body diagrams. The chapter on reinforced concrete shows how pivoting of the strain diagram should be implemented accordingly and using the principles learned in the first book above. The strain diagram for concrete as adopted by CRSI and the standard method is shown here for derivation of equation required in the analysis. The title was changed by the publisher and because this is a reputed publisher of technical books, I consented. I was disappointed however that this book despite my review and word files submitted to the publisher, this book has so many typographical errors in equations and text. The publisher also failed to list my book before the international structural conference in Melbourne, Australia in 2007 and the international structural conference in Zurich, Switzerland in 2011. The typos were blamed on the typesetters but the truth is that they published the book without me seeing the final draft before publications. I determined then that I had to publish the correct book.

The third book was published officially in March, 2012 by Xlibris. All the 4 chapters have an article added and the book is now entitled ‘The Analytical Method in Structural Analysis’. In chapter 1 an article on the bearing capacity factors are included using trigonometric identities. The 2nd chapter includes the yield capacity of channel sections using AISC geometric properties as shown in AISC steel manual. The 3rd chapter includes the development length of the reinforcing bars using ACI equations. The 4th chapter includes the real factor of safety instead of the factor of ignorance by the conventional method of copying the standard interaction formula. Since the yield capacity envelope can be obtained using the Euler principle, basic mathematics and physics for any rectangular or circular section, the external load dictated by codes and local practice can be plotted on this envelope to get the real factor of safety. I submitted my word file to Mary Flores (working in Cebu with other Filipinos) for Xlibris with the instructions to copy my trim and format similar to second book by CRC Press. This book is the only book that tells the truth about structural engineering using only our knowledge of basic mathematics and physics learned in school. I recommend that any reader or researcher used this book as a reference for the truth. We are now in the age of computers and approximate methods and slide rule concepts are no longer correct. A new paradigm from the approximate to the exact method can now be applied because we have Microsoft Excel to use with our computers to do the numerical calculations required in our derived equations.

For additional details, the reader can visit my web site for information about these books and the proper application of basic principles to the analytical method in structural analysis. These books use the ‘rotation of axes’ of the principal axes to enable equilibrium of internal load to the external load while others use the principal axes and the standard interaction formula from conventional books. This rotation of axes is apparent from the free body diagrams used by the author although the author never mentioned the term ‘rotation of axes’ in any of the his books above mentioned. We are now in the year 2013 and I started the analytical method in 1980 by submitting my articles to ASCE for publication in their journals. I retired as Director of Engineering Support from the NYCTA in 2000. Today authors, professors and researchers are still buried in the approximate and slide rule methods. It is now time to move forward and find the truth as the saying ‘seek ye the truth and the truth shall make you free’ goes. Because of computers, a new paradigm should now be adopted using Microsoft Excel and the power of computers for numerical calculations required in our derived equations for a particular problem. The educational system in school should be revamped to emphasize the use of computers, basic mathematics and physics.  If you follow my lead, you will always make the right decision as a Professional Engineer.

Ramon V. Jarquio, PE (NY State)


The Truth

You cannot be blind and ignorant of the truth! Visit my web site for the information to follow my lead. Move forward! Use Microsoft Excel and the power of computers to do the numerical calculations.


The Truth

You may be busy with something else but you should read the attachment for tips to use in the analytical method in structural analysis. I have been circulating the following to emails of engineers that I know of. I hope you will forward the following information to your friends, members of your organization and researchers so that they too can benefit from the truth exposed in my books and web site.

“Visit my web site at for the truth in engineering. Follow my lead to discover other truths. Correct input yields correct output. I am the only one in the world doing the ‘rotation of axes’ instead of the principal axes copied by everyone. We are now in the age of computers and approximate method is no longer correct and thus a new paradigm from the approximate to the exact method should be employed using basic mathematics, physics and the computer. There was no need to copy anyone using the approximate method. Tons of literature would have to be discarded.  Remember the saying ‘seek ye the truth and the truth shall make you free’ that should be followed for enlightenment.”