m3l16

m3l16 - Module 3 Analysis of Statically Indeterminate...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Version 2 CE IIT, Kharagpur Module 3 Analysis of Statically Indeterminate Structures by the Displacement Method
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Version 2 CE IIT, Kharagpur Lesson 16 The Slope-Deflection Method: Frames Without Sidesway
Background image of page 2
Instructional Objectives After reading this chapter the student will be able to 1. State whether plane frames are restrained against sidesway or not. 2. Able to analyse plane frames restrained against sidesway by slope-deflection equations. 3. Draw bending moment and shear force diagrams for the plane frame. 4. Sketch the deflected shape of the plane frame. 16.1 Introduction In this lesson, slope deflection equations are applied to solve the statically indeterminate frames without sidesway. In frames axial deformations are much smaller than the bending deformations and are neglected in the analysis. With this assumption the frames shown in Fig 16.1 will not sidesway. i.e. the frames will not be displaced to the right or left. The frames shown in Fig 16.1(a) and Fig 16.1(b) are properly restrained against sidesway. For example in Fig 16.1(a) the joint can’t move to the right or left without support A also moving .This is true also for joint . Frames shown in Fig 16.1 (c) and (d) are not restrained against sidesway. However the frames are symmetrical in geometry and in loading and hence these will not sidesway. In general, frames do not sidesway if D 1) They are restrained against sidesway. 2) The frame geometry and loading is symmetrical Version 2 CE IIT, Kharagpur
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Version 2 CE IIT, Kharagpur
Background image of page 4
For the frames shown in Fig 16.1, the angle ψ in slope-deflection equation is zero. Hence the analysis of such rigid frames by slope deflection equation essentially follows the same steps as that of continuous beams without support settlements. However, there is a small difference. In the case of continuous beam, at a joint only two members meet. Whereas in the case of rigid frames two or more than two members meet at a joint. At joint in the frame shown in Fig 16.1(d) three members meet. Now consider the free body diagram of joint C as shown in fig 16.2 .The equilibrium equation at joint C is C = 0 C M 0 = + + CD CE CB M M M Version 2 CE IIT, Kharagpur
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
At each joint there is only one unknown as all the ends of members meeting at a joint rotate by the same amount. One would write as many equilibrium equations as the no of unknowns, and solving these equations joint rotations are evaluated.
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 24

m3l16 - Module 3 Analysis of Statically Indeterminate...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online