SLOPE DEFLECTION METHOD

Subject : Structural Analysis 2

Subject Code:- 2510608

Prepared By:

Bambhroliya Rishabh 151103106001Dudhat Pritesh 151103106002Gohil Harish 151103106005Kansara Abhishek 151103106007Pandya Dhrumil 151103106010

Guided by:Assi. Prof. Pritesh Rathod

Civil Engg. Dept.

Slope Deflection Method:-

Portal Frame

1. ASSUMPTIONS IN THE SLOPE DEFLECTION METHOD .

2. APLICATION OF SLOPE DEFLECTION METHOD.3. SIGN CONVENTION.4. PROCEDURE.5. SLOPE DEFLECTION EQUATION.6. EXAMPLE.

Contents

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.

ASSUMPTIONS IN THE SLOPE DEFLECTION METHOD:

1. Continuous Beams 2. Frames with out side sway 3. Frames with side sway

Applications of slope deflection method:

(1) ROTATIONS:– Clockwise joint rotations are considered as (-ve).

(2) END MOMENTS:– clockwise end moments are considered as (+ve).

SIGN CONVENTION:–

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

PROCEDURE:–

SLOPE DEFLECTION EQUATION:

EQUATION FOR FIXED END MOMENT:

EXAMPLE FOR FRAME:

w KN/m

w

P

Ha

Hd

B

h

C

D

A

L1

L2

12KN

10 KN2.4 KN/m

A4 m

BC

1.5 m

1.5 m

( I )

( I )

D

1.5 m

Example :

Determine support moments using slope deflection method for the frame shown in figure. Also draw bending moment diagram.

(a)Fixed end moments (FEM):

(b) Slope – Deflection equation :

(c) Equilibrium equation :

At joint B,

(c) Equilibrium equation :

At joint B,

(d) Simply supported moments :

0.30

4.810.20

15

4.8

9

9.15D

CBA

Thank You