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)