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m3l21 - Module 3 Analysis of Statically Indeterminate...

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Version 2 CE IIT, Kharagpur Module 3 Analysis of Statically Indeterminate Structures by the Displacement Method
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Version 2 CE IIT, Kharagpur Lesson 21 The Moment- Distribution Method: Frames with Sidesway
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Instructional Objectives After reading this chapter the student will be able to 1. Extend moment-distribution method for frames undergoing sidesway. 2. Draw free-body diagrams of plane frame. 3. Analyse plane frames undergoing sidesway by the moment-distribution method. 4. Draw shear force and bending moment diagrams. 5. Sketch deflected shape of the plane frame not restrained against sidesway. 21.1 Introduction In the previous lesson, rigid frames restrained against sidesway are analyzed using moment-distribution method. It has been pointed in lesson 17, that frames which are unsymmetrical or frames which are loaded unsymmetrically usually get displaced either to the right or to the left. In other words, in such frames apart from evaluating joint rotations, one also needs to evaluate joint translations (sidesway). For example in frame shown in Fig 21.1, the loading is symmetrical but the geometry of frame is unsymmetrical and hence sidesway needs to be considered in the analysis. The number of unknowns is this case are: joint rotations B θ and C θ and member rotation ψ . Joint B and C get translated by the same amount as axial deformations are not considered and hence only one independent member rotation need to be considered. The procedure to analyze rigid frames undergoing lateral displacement using moment-distribution method is explained in section 21.2 using an example. Version 2 CE IIT, Kharagpur
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