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m3l22 - Module 3 Analysis of Statically Indeterminate...

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Module 3 Analysis of Statically Indeterminate Structures by the Displacement Method Version 2 CE IIT, Kharagpur
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Lesson 22 The Multistory Frames with Sidesway Version 2 CE IIT, Kharagpur
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Instructional Objectives After reading this chapter the student will be able to 1. Identify the number of independent rotational degrees of freedom of a rigid frame. 2. Write appropriate number of equilibrium equations to solve rigid frame having more than one rotational degree of freedom. 3. Draw free-body diagram of multistory frames. 4. Analyse multistory frames with sidesway by the slope-deflection method. 5. Analyse multistory frames with sidesway by the moment-distribution method. 22.1 Introduction In lessons 17 and 21, rigid frames having single independent member rotational ( Δ = h ψ ) degree of freedom (or joint translation Δ ) is solved using slope- deflection and moment-distribution method respectively. However multistory frames usually have more than one independent rotational degree of freedom. Such frames can also be analysed by slope-deflection and moment-distribution methods. Usually number of independent member rotations can be evaluated by inspection. However if the structure is complex the following method may be adopted. Consider the structure shown in Fig. 22.1a. Temporarily replace all rigid joints of the frame by pinned joint and fixed supports by hinged supports as shown in Fig. 22.1b. Now inspect the stability of the modified structure. If one or more joints are free to translate without any resistance then the structure is geometrically unstable. Now introduce forces in appropriate directions to the structure so as to make it stable. The number of such externally applied forces represents the number of independent member rotations in the structure. Version 2 CE IIT, Kharagpur
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Version 2 CE IIT, Kharagpur
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