The Analytical Method in Structural Analysis
This is the title of my 3rd book published by XLIBRIS of Indiana in 2012 after my participation in the ISEC-06 Zurich, Switzerland on September, 2011. This book contains the personal research of the author up to this period. Each chapter of my 2nd book was added an article that is described below.
Chapter 1 – Deals with the bearing capacity factors for cohesion less sand or rock in which the listed equations were derived using trigonometric identities. Planar distribution of bearing stress using failure wedges were used instead of the curvilinear slip failure assumed by others. Most of the actual bearing stress is triangular since actual vertical axial load and bending moment must be resisted. There were 6 cases of bearing stress distribution considered.
Chapter 2 – Includes the article for yield capacities of channel sections with geometric properties shown in the AISC Steel Manual using the one pivot point for a symmetrical tension and compressive stress. The correct free body diagram was drawn using a rectangular box with one side removed. Integral calculus equations were derived using the well-established principles of Euler’s, Hooke’s Law and Pythagorean Theorem with rotation of orthogonal XYZ axes to implement correctly basic mathematics and physics.
Chapter 3 - Includes the equation for development length as a bond strength of reinforcing steel as opposed to the current practice of compliance with ACI regulations. Reinforcing rods are imbedded in concrete and pulled out tests are made to determine the embedment lengths. It is known that basic mathematics and physics do not lie. ACI regulations for spacing and clearances of reinforcing bars are followed for accuracy. Development length of rebar is evaluated from the equation, Ld = 0.094 Asfy/(fc’)1/2 where As = area of rebar, fy = yield stress of steel bar and fc’ = ultimate compressive stress of concrete.
Chapter 4 – Deals with the use of safety factor in design by plotting the external load (variable in any locality) on the constant (varies only on the strength of materials used) minimum column yield capacity of a given section in reinforced concrete or steel material. The by-product of the software is a graphical envelope of minimum column yield capacity of a circular or rectangular section. Plotting the external load on this envelope automatically consider whether the use of the section is short or long column. For failure not to occur, the external load must lie inside the envelope of minimum column yield capacity and away from the boundaries of the standard key points of short and long column definitions.
Note: Rotation of the orthogonal axes XYZ in 3D analysis invoking Euler’s, Hooke’s law and Pythagorean Theorem should be employed for accuracy of analysis in structural mechanics. Rotation of axes was the main difference of my method to the current non-rotation of axes as well as the inclusion of the coordinates of reinforcing bars at the centers of the sections not done in the approximate methods. Since the community appears to maintain the status quo of expediency and compliance, the author prepared and finished the recommended Book 4 to be accompanied by a CD of Microsoft Excel workbook. The title of this book is “The True Analytical Method in Structural Analysis”. It employed the 2 pivot points for a composite circular and rectangular sections and combined the correct analytical method exposed in Book 1, Book 2 and Book 3. The author is still waiting for a refutable USA publisher (McGraw-Hill, John Wiley & Sons, Addison-Wesley, ASM International, etc. so that all antiquated books can be discarded and replaced accordingly in this age of electronic digital computers. I also maintain as proof of the exact method a CD of a column software programmed in Microsoft Excel to show the accuracy and power of Microsoft Excel 95 should a technical lawsuit versus deliberate ignorance worldwide becomes necessary.
Ramon V. Jarquio, P.E.
Email: [email protected] or [email protected]
Engineering website: https://www.ramonjarquio.com