m3l17

m3l17 - Module 3 Analysis of Statically Indeterminate...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

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

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

View Full DocumentRight Arrow Icon
Lesson 17 The Slope-Deflection Method: Frames with Sidesway Version 2 CE IIT, Kharagpur
Background image of page 2
Instructional Objectives After reading this chapter the student will be able to 1. Derive slope-deflection equations for the frames undergoing sidesway. 2. Analyse plane frames undergoing sidesway. 3, Draw shear force and bending moment diagrams. 4. Sketch deflected shape of the plane frame not restrained against sidesway. 17.1 Introduction In this lesson, slope-deflection equations are applied to analyse statically indeterminate frames undergoing sidesway. As stated earlier, the axial deformation of beams and columns are small and are neglected in the analysis. In the previous lesson, it was observed that sidesway in a frame will not occur if 1. They are restrained against sidesway. 2. If the frame geometry and the loading are symmetrical. In general loading will never be symmetrical. Hence one could not avoid sidesway in frames. For example, consider the frame of Fig. 17.1. In this case the frame is symmetrical but not the loading. Due to unsymmetrical loading the beam end moments and are not equal. If is greater than , then . In BC M CB M b a CB BC M M > 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
such a case joint B and C are displaced toward right as shown in the figure by an unknown amount Δ . Hence we have three unknown displacements in this frame: rotations C B θ , and the linear displacement Δ . The unknown joint rotations B and C are related to joint moments by the moment equilibrium equations. Similarly, when unknown linear displacement occurs, one needs to consider force-equilibrium equations. While applying slope-deflection equation to columns in the above frame, one must consider the column rotation Δ = h ψ as unknowns. It is observed that in the column AB , the end B undergoes a linear displacement with respect to end Δ A . Hence the slope-deflection equation for column AB is similar to the one for beam undergoing support settlement. However, in this case is unknown. For each of the members we can write the following slope-deflection equations. Δ [ AB B A F AB AB ] M M ψθ 3 2 2 + + = h EI where h AB Δ = AB is assumed to be negative as the chord to the elastic curve rotates in the clockwise directions. [] AB A B F BA BA h EI M M 3 2 2 + + = C B F BC BC h EI M M θθ + + = 2 2 B C F CB CB h EI M M + + = 2 2 CD D C F CD CD h EI M M 3 2 2 + + = h CD Δ = [ CD C D F DC DC h EI M M 3 2 2 + + = ] (17.1) As there are three unknowns ( C B , and Δ ), three equations are required to evaluate them. Two equations are obtained by considering the moment equilibrium of joint B and C respectively. 0 0
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 21

m3l17 - Module 3 Analysis of Statically Indeterminate...

This preview shows document pages 1 - 5. Sign up to view the full document.

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