Lecture Number 1 Determinate and Indeterminate

1. STRUCTURAL ANALYSIS
Definitions
Concepts of Stability of
1
Structures
Statically Determinate /
2
Indeterminate Structures
Advantages &
3 disadvantages of
indeterminate structures
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2. STRUCTURES
■ Definition
Structure is defined as an assembly of connected parts
(members) used to support loads.
Buildings, bridges, tunnels, tanks and chimneys are example
g , g , , y p
structures commonly encountered in practice.
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3. Civil Structures
■ BUILDINGS
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4. Civil Structures
■ BRIDGES
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5. Civil Structures
■ LARGE HALLS
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6. Civil Structures
■ STADIUMS
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7. Civil Structures
■ WATER STRUCTURES
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8. Support Types
■ Fixed Support
pp
Rx
M
Ry
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9. Support Types
■ Hinged Support
g pp
Rx
Ry
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10. Support Types
■ Roller Support
pp
R
R
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11. Statically Determinate / Indeterminate Structures
■ CONDITIONS OF DETERMINATE STRUCTURE
Determinate if
No. of Equilibrium Equations = No. of unknowns
2D Beams 3 + c r
2D Frames 3j + c r + 3m
2D Trusses 2j r + m
3D Beams 6 + c r
3D F
Frames 6j + c r + 6
6m
3D Trusses 3j r + m
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12. Statically Determinate / Indeterminate Structures
■ BEAM STRUCTURE
2D Beams
3 + c > r
Unstable
3 + c = r
Determinate
3 + c < r
Indeterminate
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13. Statically Determinate / Indeterminate Structures
■ FRAME STRUCTURE
2D Frames
3j + c > 3m + r
Unstable
3j + c = 3m + r
Determinate
3j + c < 3m + r
Indeterminate
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14. Statically Determinate / Indeterminate Structures
■ TRUSS STRUCTURE
2D Trusses
2j > m+r
Unstable
2j = m+r
Determinate
2j < m+r
Indeterminate
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15. Statically Determinate / Indeterminate Structures
■ EXAMPLE FRAMES
Fra M R J C 3M 3J Class. M R J C 3M 3J Class.
me +R +C +R +C
A 3 6 4 - 15 12 Indet. 3 B 4 4 5 - 16 15 Indet 1
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16. Statically Determinate / Indeterminate Structures
■ EXAMPLE FRAMES
M R J C 3M 3J+ Class. M R J C 3M 3J Class.
+R C +R +C
D 10 9 9 - 39 27 Indet 12 E 6 3 6 4 21 22 Unst.
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17. Statically Determinate / Indeterminate Structures
■ EXAMPLE FRAMES
Fra M R J C 3M 3J Class. Fra M R J C 3M 3J Class.
me +R +C me +R +C
F 8 6 9 3 30 30 Det. G 7 6 7 - 27 21 Indet. 6
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18. Statically Determinate / Indeterminate Structures
■ TRUSSES
M R J M+R 2J Class. M R J M 2J Class.
+
25 3 14 28 28 Det. R
33 3 18 36 36 Unst.
Unst (Parallel
reactons)
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19. Statically Determinate / Indeterminate Structures
■ TRUSSES
M R J M 2J Class. M R J M 2J Class.
+ +
R R
27 4 15 31 30 Indeterminate 1 16 3 10 19 20 Unstable
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20. Advantages / Disadvantages of Indeterminate Structures
■ FORCES (ECONOMY)
( )
Determinate Indeterminate
20
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21. Advantages / Disadvantages of Indeterminate Structures
■ DEFLECTIONS
Determinate Indeterminate
4
1
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22. Advantages / Disadvantages of Indeterminate Structures
■ REDUNDANCY
Determinate Indeterminate
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23. Advantages / Disadvantages of Indeterminate Structures
■ TEMPERATURE EFFECT
Determinate Indeterminate
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24. Advantages / Disadvantages of Indeterminate Structures
■ SUPPORT MOVEMENTS
Determinate Indeterminate
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25. Problems
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