A new method of basic structural analysis

Post date: Nov 30, 2009 10:07:57 AM

Dr. Joshy

November 2007 ::

Abstract:

In the present practice of basic structural analysis, Force response is given the top priority and the word ‘Analysis’ often means plotting the moment and shear diagrams of beams and frames. Deformation response, on the other hand, is not credited with its due share of importance neither in analysis nor in design. Based on the features of the moment diagram the elastic curve is qualitatively sketched with no mention of the absolute values of deflection anywhere on the structure. In computer aided analysis too the focus seldom shifts to the exact determination of the elastic curve even though modern analysis packages, which are based on Finite Element Methods, are capable of evaluating deflections and slopes at any desired point on a structure.

No analysis of any structure is ever complete unless its Deformation response and Force response are both fully defined and that too preferably in terms of explicit mathematical expressions.

The new method of basic structural analysis presented is known as the Method of Initial Parameters (MIP) and is based on evolving the equations of deflection, slope, moment, and shear of a structure as segmentally continuous functions of x, ‘f(x)’ applicable throughout the structure. MIP adopts a ‘Differential path’ which is significantly different from the ‘Integral path’ followed in classical methods where moment is a prerequisite to obtain deflection. These features, that are absent in the conventional methods of analysis, makes MIP a new method of analysis. MIP generates closed from solutions so long as the intensities of distributed loads are expressible as polynomial functions, which normally is the case. From a purely academic standpoint, even when the intensities are expressible as trigonometric, exponential or functions of any other nature, the method generates sufficiently accurate solutions after approximating such functions to polynomials.

An analysis based on deformations, something that we physically see, realize and understand, is much more relevant than merely toying with the concept of stress, something that has limited physical appeal. After all it is the deformations that dictate the state of strain in the body which in turn dictates the state of stress in it. It is in this aspect that MIP stands out a mile.