10.3: Analysis of Indeterminate Beams and Frames
Apr 22, 2021 · There are several methods of computation of flexibility coefficients when analyzing indeterminate beams and frames. These methods include the use of the Mohr integral, deflection tables, and the graph multiplication method. These methods are illustrated in the solved example problems in this section.
Convert the indeterminate structure to a determinate one by removing some unknown forces / support reactions and replacing them with (assumed) known / unit forces. Using superposition, calculate the force that would be required to achieve compatibility with the original structure.
Chapter 10 Statically Indeterminate Beams 10.1 Introduction in this chapter we will analyze the beam in which the number of reactions exceed the number of independent equations of equilibrium integration of the differential equation, method of superposition compatibility equation (consistence of deformation)
Example Problem 9.1 ‐ Draw the shear and moment diagrams for the beam. EI is constant. When Maxwell developed the force method of analysis, he also published a theorem that relates the flexibility coefficients of any two points on an elastic structure—be it a truss, a beam, or a frame.
Procedure for Statically Indeterminate Problems Solve when number of equations = number of unknowns For bending, Force-Displacement relationships come from Moment-Curvature relationship (ie: use Method of Integration or Method of Superposition)
Find all reaction and the tensile force in the steel support cable. Consider both bending and axial deformation.
Several classical methods have been developed to solve for the forces and displacements of statically indeterminate systems. In this course, we will introduce two important classical approaches: the force method and the slope-deflection method. Force Method –Basic Idea. The basic idea of this method is to identify the redundant forces first.
Slope-Deflection Method: Beams Application of Slope-Deflection Equations to Statically Indeterminate BeamsIndeterminate Beams: ::: The procedure is the same whether it is applied to beams or frames. It may be summarized as follows: 1. Identify all kinematic degrees of freedom for the given problem. Degrees of freedom are treated as unknowns
For the indeterminate beam subject to the point load, P, find the support reactions at A and C. EI is constant. Primary structure is not unique – there are several choices. Calculate relevant deflections at points where redundants were removed. A !" '#( !" = − 16+,
For the indeterminate beam from Lab 11, subject to the point load at B, find the support reactions at A and C and construct the shear and moment diagram for the beam. Neglect axial force effects. Primary structure is not unique – there are several choices. Calculate relevant deflections at points where redundants were removed. !& !" = ? ? !& = ? ?