Chapter8.1 - Chapter 8 Iterative Displacement Method by...

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© K. H. Ha - BCEE 343 Chapter 8 - v2.0 Chapter 8 Iterative Displacement Method by Moment Distribution Moment distribution method is an iterative procedure for finding the member-end moments of statically indeterminate beam and frame systems. It is essentially a displacement-based method where the nodal rotations are adjusted in order to achieve nodal moment equilibrium. In this Chapter, the method is presented first for systems with one rotational degree of freedom. This defines the necessary terminology and establishes the fundamental concept of moment distribution. The same concept is then applied to more complex systems having many DOFs including translations. While traditional application of moment distribution method tends to emphasize the determination of member-end moments, we will find that little additional effort is needed for computing rotations and deflections. 8.1 Introduction Prior to the advent of computers which popularizes the modern matrix techniques, the slope deflection method and the moment distribution method were the main workhorse for beam and frame analysis. As the slope deflection method is just a restricted form of the matrix displacement method, it holds no advantages over the latter. The moment distribution method is also a form of the displacement method; however, it is still very useful since it does not require setting up large set of simultaneous equations. In addition, its numerical iterative procedure parallels a physical process which is attractive to engineers. The method was first published by Hardy Cross in his paper "Analysis of Continuous Frames by Distributing Fixed-End Moments", Transaction, ASCE, 96, 1932.
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© K. H. Ha - BCEE 343 Chapter 1 - v2.0 8.2 The moment distribution method is primarily used for the analysis of statically indeterminate beam and plane frame systems. As a form of the displacement method, it attempts to adjust the compatible deformed shape systematically, leading to the correct shape that satisfies the nodal equilibrium requirement. While nodal displacements are supposed to be the primary unknown variables in all variants of the displacement method, the moment distribution method deals directly with member-end moments. It will be, therefore, instructive for the readers to be conscious of the primary variables, namely the nodal displacements, lurking behind the scene. 8.2 The Process of Moment Distribution Consider a beam or frame system with N free nodal displacements, which can be classified into two categories: rotations and translations. i.e. N = N r + N t where N r is the number of nodal rotational displacements and N t is the number of nodal translational displacements. Note that N r is also the number of nodal rotational equilibrium equations and N t is the number of nodal translational equilibrium equations.
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Chapter8.1 - Chapter 8 Iterative Displacement Method by...

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