Basics of sdm and equations - - Structural Analysis
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This document provides an overview of the slope deflection method for structural analysis. It discusses the basics, assumptions, advantages, limitations, and procedures of the slope deflection method. The key assumptions are that joints rotate as a whole unit without relative movement of connecting members, and joint rotations are treated as unknowns. The method can be used for both determinate and indeterminate structures, and its primary unknowns are joint rotations and displacements.
Basics of sdm and equations - - Structural Analysis
- 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
- 2. 12/4/2020 2/15 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
- 3. 12/4/2020 3/15 SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil Assumptions
- 4. 12/4/2020 4/15SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil 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.
- 5. 12/4/2020 5/15 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.
- 6. 12/4/2020 6/15SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil 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. 12/4/2020 7/15 SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil Procedure
- 8. 12/4/2020 8/15 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.
- 9. 12/4/2020 9/15 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.
- 10. 12/4/2020 10/15 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
- 11. 12/4/2020 11/15 SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil Slope Deflection Equations .
- 12. 12/4/2020 12/15SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil Fixed End Moments
- 13. 12/4/2020 13/15 SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil Fixed End Moments
- 14. 12/4/2020 14/15SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil Fixed End Moments
- 15. 12/4/2020 15/15 SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil Thank You