The True Analytical Method in Structural Analysis (4th Book)

by Ramon V. Jarquio



The book illustrates the true analytical procedures for predicting the yield capacity of given structural sections in concrete and steel structures. It introduces the column capacity axis for proper analysis employing basic mathematics and physics in the application of well-established Euler’s principle and Hooke’s Law. More importantly, it shows that the current methodology of approximation using finite-element procedures are no longer acceptable in this age of digital computers, where time is no longer a problem in simplifying the derived equations. A new paradigm of exactitude is therefore mandatory if truth is to be told.


The book starts with Chapter 1 in the derivation of footing foundations in rectangular and circular sections subjected to bi-axial bending. The well-established Euler’s principle and Hoke’s Law were applied in the analysis using basic mathematics and physics. It also shows the integration of Boussinesq’s elastic equation in which no one including Terzaghi was successful in doing so and therefore resulted in an inaccurate conclusion by Terzaghi. The application of point loads are shown in embankment problems where pressure distribution from surface loads are indicated.

Chapter 2 shows the integration of forces developed in rectangular and circular sections in steel materials and equations derived were used in the preparation of tables using AISC (American Institute of Steel Construction) properties of manufactured steel sections. Again, basic mathematics and physics including calculus were used in the application of Euler’s principle and Hooke’s Law.

Chapter 3 starts with the derivation of the true parabola to use in the true analytical procedure for reinforced concrete. Formulas for singly-reinforced, double-reinforced and T-beams for biaxial bending are included to enable the analyst to perform the analysis of these sections. From Euler’s principle, consider XZ as the horizontal plane, all sections are subjected to an axial load and bending moment. From this property all section are considered as short and long columns. A short column can be defined as that in which the section is in full compressive stress. A long column can be defined as that in which the section is in tensile and compressive stresses. From Hooke’s Law, consider the XY as the vertical plane where stress/strain characteristics of the materials are pivoted. For steel, the pivot point at the edge is either the tensile or compressive stress. For concrete, the pivot point when the point is equal or greater then balanced condition is at the compressive edge. For bar reinforcement, the pivot point is now at the tensile stress of the reinforcing bar when considering cases less than balanced condition. Bar forces are determined by using the coordinates of steel reinforcement with respect to the column capacity axis. Reinforcing bars must comply with ACI (American Concrete Institute) requirements of concrete clearance and bar spacing. Beams are special cases of columns where bending is predominant in one axis. The column capacity axis for minimum yield capacity in a rectangular section is the diagonal. The column capacity axis for a reinforced concrete circular section is a diameter thru the center of any bar.

Chapter 4 is the derivation of equations for concrete-filled tubes (rectangular and circular section) using basic mathematics and physics and the well-established Euler’s principle and Hooke’s Law. Hundreds of equations are listed to derive the steel forces to be added to concrete forces. The total of these forces is now the CFT (concrete-filled tube) yield capacity at the column capacity axis.


Practicing structural and civil engineers as well as authors and professors will benefit from knowing the true analytical method in structural analysis involving rotation of axes in a 3D and use of Pythagorean Theorem to obtain the minimum yield capacity of a given section. A CD of Microsoft Excel validating all the derived equations can be copied and other truths can be discovered by devoting concentrations on other matters.


Current books and literature do not cover or indicate the true analytical method in structural analysis nor invoke the column capacity axis using well-established principles such as Euler’s and Hooke’s Law. Hence, the fundamental requirement of equilibrium of external and internal forces is not be satisfied by current procedure of non-rotation of axes and non-use of Pythagorean Theorem, for resultant yield capacity.

The Book

The book is 290 pages with a trim of one inch less all around on 8-1/2 x 11 inches standard paper which includes References and an Index. A CD of Microsoft Excel is also included to confirm all the derived equations in Chapters 1 - 4. There are 21 Excel (1 = 11, 2 = 4, 3 = 3 and 4 = 3) sheets to obtain a workable factor of safety when the external load is plotted on the graph of minimum yield capacity envelope from the Excel spreadsheets.

E Book

The publisher may set the price of the book, CD as well as the e book.

Author’s Info

• He is a registered professional engineer in the State of New York and a lifetime member of ASCE (American Society of Civil Engineers). He obtained his BSCE degree in 1961 from MIT (Mapu’a Institute of Technology), Manila, Philippines.

• From 1964-1974 he was for 8 years a Bridge Engineer and for 2 years Engineer-in-Charge of highway design and construction programs by the Ministries of Communications of Saudi Arabia and Libya respectively.

• From 1975-2000 he joined the New York City Transit where he eventually became the Director of Engineering Support in 1989.

• During 1980-1984 ASCE Geotechnical Journal published his formulas on vertical distribution of surface loads through soil and footing design with biaxial bending. The papers were as follows:

1.      Total Lateral Surcharge Pressure Due to Strip Load    ASCE Journal Issue October 1980

2.      Design Footing Area with Bi-axial Bending                    ASCE Journal Issue October 1983

3.      Vertical Stress Formulas for Triangular Loading           ASCE Journal Issue January 1984

• He participated and presented papers included in the proceedings of ISEC (International Structural Engineering and Construction) international conferences from 2001-2011 held in Honolulu, Rome, Shunan, Melbourne & Zurich. He also attended and presented papers in the proceedings of SEMC (Structural Engineering Mechanics and Computation) 2001 held in Cape Town, South Africa. He also submitted a paper in the proceedings of SEMC 2004.

• He also attended the ASCE International conferences held in Cancun, Nashville, New York and Montreal. All his papers in the true analytical method in structural analysis were included in the proceedings of these conferences.

• His paper in the true analytical method in reinforced concrete column was published in the proceedings of RILEM conference in Moscow, Russia.

• His article for the reinforced concrete column analysis was published in the 2005 HKIE (Hong Kong Institute of Engineers) structural journal.

• He attended and submitted his papers in the proceedings of the 2005 Global Concrete Conference held in Dundee, Scotland

Suggested Reviewers

I have no particular names to suggest, but experts (authors & professors) can verify all the equations I derived for the true analytical method in structural analysis because I used basic mathematics and physics plus the well-established principles of Euler’s and Hooke’s Law as well as the Pythagorean Theorem. The CD of derived equations can confirm the veracity of the analysis resulting from many years of research. The introduction of a variable for the rotation of XYZ axes in a 3D analysis and the use of Pythagorean Theorem for the resultant yield capacity of a given section at the column capacity axis was never done by anybody except the author of this book.