Ebook Fundamentals of structural analysis (5th edition): Part 2

(BQ) Part 2 book "Fundamentals of structural analysis" hass contents: Analysis of indeterminate structures by the flexibility method, analysis of indeterminate beams and frames by the slope deflection method, analysis of indeterminate beams and frames by the moment distribution, influence lines for moving loads,.and other contents. | C H A P T E R Analysis of Indeterminate Structures by the Flexibility Method 9 Chapter Objectives ●● Show that the equations of static equilibrium alone are not enough to analyze indeterminate structures; additional equations are needed. ●● Learn in the flexibility method to establish additional equations (., compatibility equations) by using e ­ xtra unknown reactions or internal forces as the redundants. ●● Identify redundants and then use any method learned in Chapter 7 or 8 to compute the deflections produced by both external loads and redundants on a released structure to establish the compatibility equations. Introduction The flexibility method, also called the method of consistent deformations or the method of superposition, is a procedure for analyzing linear elastic indeterminate structures. Although the method can be applied to almost any type of structure (beams, trusses, frames, shells, and so forth), the compu­ational t effort increases exponentially with the degree of indeterminancy. Therefore, the method is most attractive when applied to structures with a low degree of indeterminancy. All methods of indeterminate analysis require that the solution satisfy equilibrium and compatibility requirements. By compatibility we mean that the structure must fit together—no gaps can exist—and the deflected shape must be consistent with the constraints imposed by the supports. In the flexibility method, we will satisfy the equilibrium requirement by using the equations of 377 378  Chapter 9  ■  Analysis of Indeterminate Structures by the Flexibility Method static equilibrium in each step of the analysis. The compatibility requirement will be satisfied by writing one or more equations (., compatibility equations) which state either that no gaps exist internally or that deflections are consistent with the geometry imposed by the supports. As a key step in the flexibility method, the analysis of an indeterminate structure is replaced by the .