Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

**Scribd will begin operating the SlideShare business on December 1, 2020**
As of this date, Scribd will manage your SlideShare account and any content you may have on SlideShare, and Scribd's General Terms of Use and Privacy Policy will apply. If you wish to opt out, please close your SlideShare account. Learn more.

Successfully reported this slideshow.

Like this presentation? Why not share!

1,295 views

Published on

Analysis of Indeterminate Beams by Slope Deflection Method

Published in:
Engineering

No Downloads

Total views

1,295

On SlideShare

0

From Embeds

0

Number of Embeds

1

Shares

0

Downloads

55

Comments

2

Likes

3

No embeds

No notes for slide

- 1. SLOPE DEFLECTION METHOD • Introduction • Assumptions • Sign conventions • Derivation of slope deflection method • Example
- 2. Introduction • The methods of three moment equation, and consistent deformation method represent the FORCE METHOD of structural analysis, The slope deflection method use displacements as unknowns, hence this method is the displacement method. • In this method, if the slopes at the ends and the relative displacement of the ends are known, the end moment can be found in terms of slopes, deflection, stiffness and length of the members.
- 3. ASSUMPTIONS IN THE SLOPE DEFLECTION METHOD • This method is based on the following simplified assumptions. • 1- All the joints of the frame are rigid, i.e , the angle between the members at the joints do not change, when the members of frame are loaded. • 2- Distortion, due to axial and shear stresses, being very small, are neglected.
- 4. Sign Conventions:- • Joint rotation & Fixed end moments are considered positive when occurring in a clockwise direction.
- 5. Derivation of slope deflection equation:-
- 6. • Required Mab &M ba intermof • θA , θ B atjoint • rotation of member (R) • loads acting on member • First assume , • Get Mfab & Mfba due to acting loads. These fixed end moment must be corrected to allow for the end rotations θA,θB and the member rotation R. • The effect of these rotations will be found separately
- 7. • by Superposition;
- 8. Example • Calculate the support moments in the continuous beam having constant flexural rigidity EI throughout ,due to vertical settlement of the support B by 5mm. Assume E=200 GPa and I=4* 10^-4 M^4.Also plot quantitative elastic curve.
- 9. • In the continuous beam, two rotations Bθ and Cθ need to be evaluated. Hence, beam is kinematically indeterminate to second degree. As there is no external load on the beam, the fixed end moments in the restrained beam are zero.
- 10. • For each span, two slope-deflection equations need to be written. In span AB, B is below A. Hence, the chord AB rotates in clockwise direction. Thus,ABψ is taken as negative.
- 11. Now, consider the joint equilibrium of support B
- 12. Reactions are obtained from equations of static equilibrium
- 13. • The shear force and bending moment diagram and elastic curve Is shown in fig.

No public clipboards found for this slide

Login to see the comments