what is static and kinematic indeterminacy of structure
- 1. eBook STRUCTURAL ANALYSIS DETERMINACY AND INDETERMINACY NIROB KR DAS B.TECH CIVIL ENGINEERING (S5CE) GOVERNMENT COLLEGE OF ENGINEERING 1 KANNUR,KERALA
- 2. FOR MY MOTHER,FATHER AND SISTER NIROB KR DAS (B.TECH CIVIL ENGINEERING) Email id – nirob991995@gmail.com 2 FROM ANDAMAN AND NICOBAR ISLAND
- 3. Civil Engineering CONTENTS Static and kinematic determinacy Examples NIROB KUMAR DAS 3
- 4. Statically determinate structures When the static equilibrium equations are sufficient for determining the internal forces and reactions on that structure. For 2D Σ V = 0 Σ H = 0 Σ MA = 0 Example of determinate structures are: simply supported beams, cantilever beams, single and double overhanging beams, three hinged arches.etc 4 NIROB KUMAR DAS
- 5. statically indeterminate structure when the static equilibrium equations are insufficient for determining the internal forces and reactions on that structure. 5 NIROB KUMAR DAS
- 6. Static indeterminacy (DS) DS = DSE+ DSI External Static Indeterminacy (DSE): It tells ‘how many force’s value cannot be found using with the available equilibrium equations.’ External Reactions - Equilibrium Equations available 6 NIROB KUMAR DAS
- 7. Internal static indeterminacy (DSI) It refers to the geometric stability of the structure .If after knowing the external reactions it is not possible to determine the all internal forces or reaction using static equilibrium equations alone .then the structure is said to be internally indeterminate. Kinematics determinacy. Kinematic determinacy is a term used in structural mechanics to describe a structure where material compatibility conditions alone can be used to 7 calculate deflections. NIROB KUMAR DAS
- 8. Kinematic indeterminacy(K.I) kinematic indeterminacy- when number of unknown displacement greater than number of compatibility equations 1. Static indeterminacy For beam 2D DSE= (Re-3) DSI=(-Rr) NIROB KUMAR DAS 8
- 9. For frame 2D 3D DSE= (Re-3) DSE=(Re-6) DSI=(3C-Rr) DSI=(6C-Rr) For truss 2 D 3D DSE= (Re-3) DSE=(Re-6) DSI=(M-2J+3) DSI=(M-2J+6) 9 NIROB KUMAR DAS
- 10. 2. Kinematic indeterminacy For beam 2D K.I=(3J-Re-M’+Rr) For Frame 2 D 3 D K.I=(3J-Re-M’+Rr) K.I=(6J-Re-M’+Rr) 10 NIROB KUMAR DAS
- 11. For truss 2D 3D K.I=(2J-Re) K.I=(3J-Re) Rr = summation of (m’’-1) for 2D summation of 3(m’’-1) for 3D NIROB KUMAR DAS 11
- 12. Notations Re= External reactions C = No.of closed loops M = No.of members J = No.of joints M’ =No.of axially rigid members M’’=No.of member connected at internal hinged location Equilibrium Equations For 2D structure - 3 Equilibrium Equations are available For 3D structure - 6 Equilibrium Equations are available 12 NIROB KUMAR DAS
- 13. External reactions (Re) 13 NIROB KUMAR DAS
- 14. Closed loop (C) This exists only in frames and not for beams and trusses Axially inextensible members (m’) Here m’ represents number of axially rigid members In the problem, if the beams alone are mentioned axially inextensible/rigid, then m’ will be equal to number of beams in the structure NIROB KUMAR DAS 14
- 15. In the problem, if the columns alone are mentioned axially inextensible/rigid, then m’ will be equal to number of columns in the structure If it is mentioned all members are inextensible, then m’ will be sum of all beams and columns If nothing is mentioned in the question regarding the axial rigidity, then m’ will take zero as its value 15 NIROB KUMAR DAS
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- 17. Remaining coming soon… 17 NIROB KUMAR DAS