m3l22

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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In the modified structure Fig. 22.1b, two forces are required to be applied at level and level CD BF for stability of the structure. Hence there are two independent member rotations () ψ that need to be considered apart from joint rotations in the analysis. The number of independent rotations to be considered for the frame shown in Fig. 22.2a is three and is clear from the modified structure shown in Fig. 22.2b. From the above procedure it is clear that the frame shown in Fig. 22.3a has three independent member rotations and frame shown in Fig 22.4a has two independent member rotations. Version 2 CE IIT, Kharagpur
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For the gable frame shown in Fig. 22.4a, the possible displacements at each joint are also shown. Horizontal displacement is denoted by and vertical displacement is denoted by v . Recall that in the analysis, we are not considering u Version 2 CE IIT, Kharagpur
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the axial deformation. Hence at B and only horizontal deformation is possible and joint C can have both horizontal and vertical deformation. The displacements and should be such that the lengths and must not change as the axial deformation is not considered. Hence we can have only two independent translations. In the next section slope-deflection method as
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m3l22 - Module 3 Analysis of Statically Indeterminate...

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