The True Analytical Method in Structural Analysis
The True Analytical Method in Structural Analysis
This is the title of the completed text and a CD of Microsoft Excel workbook for the unpublished Book 4 which showed that in this age of electronic digital computer and Microsoft Excel, the current universal method of approximation is incorrect.
This book showed the two pivot points required in the exact method with rotation of orthogonal XYZ axes for the analysis of a composite circular or rectangular section not done in the current method. The free body diagrams shown includes the coordinates of reinforcing bars at the center of the given section and the angle of rotation of the X-axis from the horizontal to the diagonal of a rectangular section.
Basic mathematics and physics learned in school is correctly applied such that rotation of orthogonal XYZ axes is feasible – a feat not done in the current method. World practice is satisfied in copying existing literature in approximate methods invented before the advent of computers. It is inconceivable to assume that finite-element methods of fixed orthogonal XYZ axes made the present analysis accurate.
World experts have been convinced in the practice of deliberate ignorance by just copying what is available from the tons of existing literature and not spend time to find the truth by the established principles of Euler’s, Hooke’s Law and Pythagorean Theorem.
To apply Euler’s principle, it is incumbent to the analyst to derive the hundreds of integral calculus equations involved in a given composite circular or rectangular section. It is worthy of note that the rectangular section can be derived using the straight line equations in Analytic Geometry that the current method failed to do for an analytical solution to a structural problem.
Hooke’s Law is known from the formula ? = PL/AE where ? is the elongation, P is the axial load, L is the length of the section, A is the area of the section and E is the Young’s modulus of elasticity. For concrete it is known that parabola represents the behavior of concrete cylinders and cubes under breakage. The equation of the parabola is known in Analytic Geometry and therefore can be drawn and analyzed in the free body diagram. The current method uses the mediocre rectangular stress block not even statically equivalent to a parabolic stress and everybody is copying this error.
Pythagorean Theorem is applied to obtain the resultant bending moment in a given composite circular and rectangular section. It is expressed in a formula, M2 = Mx2 + My2. At every inch of a given circular or rectangular section, this is applied to hundreds of integral calculus for the forces that are developed in a given section.
It is becoming very clear that a software is required to simplify these hundreds of derived equations in a structural problem and Microsoft Excel is preferred to numerically authenticate these equations. The by-product of this software is an envelope of minimum column yield capacity bounded by the definitions of a short and long column concepts or simply the standard key points mentioned in many books. However, nobody in the world has this exact software except the author who advertised this software in an ASCE magazine and registered in the Library of Congress in 1996, but ignored by the structural community. The preponderance of reference materials made to look accurate by finite-element procedures made the practice of deliberate ignorance for expediency and compliance unavoidable to these world experts.
The envelope of minimum column yield capacity is constant and just a function of the strength of materials used. When the external load (variable in any locality) is plotted inside the boundaries of this envelope, failure is impossible to occur. The real factor of safety in the design is calculated instead of the factor of ignorance used in the current method by the standard interaction formula.
It is noteworthy to mention that measurements in the laboratory from modelling can result in a correct conclusion, if it can be reconciled with the minimum yield capacity represented by the hundreds of integral calculus equations or the graphical envelope from this software.
This book with a CD of Microsoft Excel worksheets for the hundreds of integral calculus equations will disclose the truth about a structural analysis. Any refutable USA publisher is welcome to contact the author at [email protected] if they are willing to publish this blockbuster book of the correct 2 pivot points using basic mathematics and physics.
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 to confirm all the derived equations in Chapters 1-4 should be published. There are 21 Excel worksheets in the four chapters of the book (1=11, 2=4, 3=3, and 4=3) to obtain a workable factor of safety in design when the external load (variable in any locality) is plotted inside the envelope of minimum column yield capacity.
Ramon V. Jarquio, P.E.