Slope Deflection Method

1. SNS COLLEGE OF ENGINEERING
Kurumbapalayam (Po), Coimbatore – 641 107
An Autonomous Institution
Accredited by NBA – AICTE and Accredited by NAAC – UGC with ‘A’ Grade
Approved by AICTE, New Delhi & Affiliated to Anna University, Chennai
DEPARTMENT OF CIVIL ENGINEERING
COURSE NAME: CE8502 – STRUCTURAL ANALYSIS I
III YEAR/V SEMESTER
Unit 2 – Slope Deflection Method
Topic 1 : Basics of SDM and Equations

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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
 The joints of a frame is assumed to be rotating as a
whole unit without relative movement of members
joining at one joint.
 The rotations of the joint are treated as unknowns.
Slope Deflection Method
FIRST PRESENTED BY PROF G A MANEY OF UNIVERSITY OF MINNESOTA DURING 1915

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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
Assumptions

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Advantages
This method can be used for both statically determinate and
indeterminate structures.
In this method primary unknowns are rotations and displacements
Static indeterminacy is irrelevant in this method
In case of force method, as degree of indeterminacy increases the method
become laborious.
But in case of SDM this do not happen as the degree of static indeterminacy is
irrelevant.
All beams and rigid frames can be analyzed using this method
Due to its general nature this method is suitable for computerization.

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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
Limitations
Since the slope deflection method make use of
the relative stiffness of members in the analysis
it is essential to know the moment of inertia of
members in advance.

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Joint moment or joint force equilibrium is made use of for solution of
slope deflection equations.
 Joint moments and forces are expressed in terms of unknown
deformations which are solved using equilibrium conditions at each
joint.
The deformations are then back substituted in moment equations to
find out the moments in each members.
Limitations

7. End moments of each member is written down in terms of the
stiffness of the member and the rotation there.
Equilibrium equation for each joint is framed using the above
calculated moments.
These equations are then solved and the rotations are obtained.
The rotations so obtained is substituted in the equations to obtain
the moments on each member.
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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
Procedure

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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
Sign Convention
Figure (b),(c) and (d) show the positive signs of forces, moment,
deflection and rotation of the ends of members.

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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
Basic definitions
For moments and rotations clockwise is positive
For differential sinking, right upward movement is positive, For support
moments clockwise is positive.

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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
Slope Deflection Equations
Slope deflection equations express the final end moments of each
member in a frame in terms of
 Fixed end moments due to external loads.
 Moment due to rotation at A (to the final value of rotation θA).
 Moment due to rotation at B
 Moments due to differential transverse displacement of B above A.
The values 4EIθ / l, 2EIθ / l and 6EI Δ / l 2 obtain from earlier figure.
The slope deflection equations are

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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
Slope Deflection Equations
.

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Fixed End Moments

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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
Fixed End Moments

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Fixed End Moments

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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
Thank You