m2l11

m2l11 - Module 2 Analysis of Statically Indeterminate...

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Module 2 Analysis of Statically Indeterminate Structures by the Matrix Force Method Version 2 CE IIT, Kharagpur
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Lesson 11 The Force Method of Analysis: Frames Version 2 CE IIT, Kharagpur
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Instructional Objectives After reading this chapter the student will be able to 1. Analyse the statically indeterminate plane frame by force method. 2. Analyse the statically indeterminate plane frames undergoing support settlements. 3. Calculate the static deflections of a primary structure (released frame) under external loads. 4. Write compatibility equations of displacements for the plane deformations. 5. Compute reaction components of the indeterminate frame. 6. Draw shear force and bending moment diagrams for the frame. 7. Draw qualitative elastic curve of the frame. 11.1 Introduction The force method of analysis can readily be employed to analyze the indeterminate frames. The basic steps in the analysis of indeterminate frame by force method are the same as that discussed in the analysis of indeterminate beams in the previous lessons. Under the action of external loads, the frames undergo axial and bending deformations. Since the axial rigidity of the members is much higher than the bending rigidity, the axial deformations are much smaller than the bending deformations and are normally not considered in the analysis. The compatibility equations for the frame are written with respect to bending deformations only. The following examples illustrate the force method of analysis as applied to indeterminate frames. Example 11.1 Analyse the rigid frame shown in Fig.11.1a and draw the bending moment diagram. Young’s modulus E and moment of inertia I are constant for the plane frame. Neglect axial deformations. Version 2 CE IIT, Kharagpur
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The given one- storey frame is statically indeterminate to degree one. In the present case, the primary structure is one that is hinged at A and roller supported at . Treat horizontal reaction at , as the redundant. The primary structure (which is stable and determinate) is shown in Fig.11.1.b.The compatibility condition of the problem is that the horizontal deformation of the primary structure (Fig.11.1.b) due to external loads plus the horizontal deformation of the support , due to redundant D D Dx R D Version 2 CE IIT, Kharagpur
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Dx R (vide Fig.11.1.b) must vanish. Calculate deformation due to unit load at in the direction of . Multiplying this deformation with , the deformation due to redundant reaction can be obtained.
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m2l11 - Module 2 Analysis of Statically Indeterminate...

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