Slope deflection method

Subject : Structural Analysis 2
Subject Code:- 2510608

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.

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.

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.

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

(1) ROTATIONS:– Clockwise joint rotations are
considered as (-ve).
(2) END MOMENTS:– clockwise end moments are
considered as (+ve).

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

w KN/m
w
P
Ha
Hd
B
h
C
D
A
L1
L2

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 :

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,

(d) Simply supported moments :

0.30
4.8
10.20
15
4.8
9
9.15D
C
B
A

Slope deflection method

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Slope deflection method