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# Slope deflection method

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This will be helpful to the various students for understanding the slope deflection method for portal frame.

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### Slope deflection method

1. 1. Subject : Structural Analysis 2 Subject Code:- 2510608
2. 2. Prepared By: Bambhroliya Rishabh 151103106001 Dudhat Pritesh 151103106002 Gohil Harish 151103106005 Kansara Abhishek 151103106007 Pandya Dhrumil 151103106010 Guided by: Assi. Prof. Pritesh Rathod Civil Engg. Dept.
3. 3. Slope Deflection Method:- Portal Frame
4. 4. 1. ASSUMPTIONS IN THE SLOPE DEFLECTION METHOD . 2. APLICATION OF SLOPE DEFLECTION METHOD. 3. SIGN CONVENTION. 4. PROCEDURE. 5. SLOPE DEFLECTION EQUATION. 6. EXAMPLE.
5. 5. This method is based on the following simplified assumptions:  All the joints of the frame are rigid,  Distortion, due to axial and shear stresses, being very small, are neglected.
6. 6. 1. Continuous Beams 2. Frames with out side sway 3. Frames with side sway
7. 7. (1) ROTATIONS:– Clockwise joint rotations are considered as (-ve). (2) END MOMENTS:– clockwise end moments are considered as (+ve).
8. 8. The procedure is as follows: 1. Determine the fixed end moments at the end of each span due to applied loads acting on span by considering each span as fixed ended. Assign ± Signs w.r.t. above sign convention. 2. Express all end moments in terms of fixed end moments and the joint rotations by using slope – deflection equations. 3. Establish simultaneous equations with the joint rotations as the unknowns by applying the condition that sum of the end moments acting on the ends of the two members meeting at a joint should be equal to zero. 4. Solve for unknown joint rotations. 5. Substitute back the end rotations in slope – deflection equations and compute the end moments. 6. Determine all reactions and draw S.F. and B.M. diagrams and also sketch the elastic curve
9. 9. EXAMPLE FOR FRAME:
10. 10. w KN/m w P Ha Hd B h C D A L1 L2
11. 11. 12 KN 10 KN 2.4 KN/m A 4 m B C 1.5 m 1.5 m ( I ) ( I ) D 1.5 m  Example :
12. 12. Determine support moments using slope deflection method for the frame shown in figure. Also draw bending moment diagram. (a)Fixed end moments (FEM):
13. 13. (b) Slope – Deflection equation :
14. 14. (c) Equilibrium equation : At joint B,
15. 15. (c) Equilibrium equation : At joint B,
16. 16. (d) Simply supported moments :
17. 17. 0.30 4.8 10.20 15 4.8 9 9.15D C B A