1. Program: Statically indeterminate panels Plastic distribution
Elastic distribution
Example
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2. Last - time: Statically over-determinate (2 times).
2 columns are placed below panel D.
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3. Last time we studied statically determinate panels
Last time we studied statically determinate panels. If we apply an extra wall ”E” the structure becomes statically indeterminate and the distribution of the horizontal load to the walls can not be calculated by the use of the 3 equilibrium equations. E
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4. Plastic distribution Assumption:
The structure has to behave plastic. For concrete structures:
Walls have to be made out of reinforced concrete
Reinforcement in the connection (Danish - Nødvendig fugearmering)
The solution should be statically possible in other words the 3 equilibrium equations has to be fulfilled
The structure has to be safe and we have to make sure that the walls and the decks can withstand the load we apply (ULS).
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5. Plastic distribution- Example
The number of reaction is chosen until the remaining reactions can be calculated by the 3 equilibrium equations
Is the structure statically determinate or indeterminate?
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6. Elastic distribution Assumption:
The deck panels which are distributing the horizontal load is assumed to be endless stiff in its own plane.
The wall panels are elastic and the distribution is done according to the stiffness of the walls
There is a correlation between the size of the applied load to the wall and the stiffness of the wall. A large stiffnes will result in a large load.
Stiffness is measured as a reference to the moment of inertia or the web area. Which stiffness should we use? it depends on the height of the building/element (Stiffness: Area or moment of inertia?)
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7. Elastic distribution Stiffness of a wall:
For tall walls/buildings the moment of inertia has the greatest influence for the stiffness.
For small (not tall) walls/buildings the area has the greatest influence for the stiffness.
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8. Elastic distribution
Contribution to the deflection from the shear force and the moment in an elastic wall. The x-axis shows the relation between h/l and the y-axis shows the deflection.
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9. Elastic distribution – Example from the book:
When do you use the moment of inertia and when do you use the web area?:
H=3m – Area
H=45m – Moment of inertia
H=18m – they comebine the deformation from the shear stress and the normal stress. (look in the book – example 5.4)
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10. Elastic distribution – how?
Symmetric buildings:
Easy to use because there is no torsion in the deck panel.
Asymmetric buildings:
Torsion will occur and therefor the distribution to the walls will be a bit different
“Centroid of stiffness” is the point that the resultant of the external forces must go through to avoid rotation in the deck panel
Calculated the torsional stiffness
Load are distributed. One part from the parallel load and a contribution from the torsion
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11. Elastic - Example Asymmetric
In this case the moment of inertia is used same principle when the area is used
t= 200mm FC
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12. Elastic distribution (Book page. 158)
Væg
Nr.
Iix
Iiy
x’i
y’i xi yi
Iix*xi2
Iiy*yi2 1
1,1 2 6
-7,4 3
9,9 -3 4
-5,4
32,1
3,6 11
1,6
9,2 ∑
4,7
2,2
41,3
19,8
xF=9,4m; yF=3m; V=41,3+19,8 = 61,1; T = 40*(-3,9) = -156kNm P1 P2 P3 P4
8,4
-8,4
24,5
15,5
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13. You have the possibility to make more than choice when you choose your system and you can also choose several methods (elastic and plastic)
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14. Example: (Spar Nord) FC Solution 1: Non symmetric but a lot of walls.
Elastic distribution is more comprehensive than the plastic method.
Solution 2:
Symmetric but not a lot of walls.
More simple when designing in the elastic and the plastic method FC
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15. Conclusion Plastic distribution: The conditions have to be okay!
Easy to use but the solution should not be fare away from the elastic solution. Extreme utilization of the plastic solution can course large deformations and cracks.
Elastic distribution:
Easy in symmetric buildings but more complicated in non symmetric buildings
Is often used in not tall buildings and in building where the material is light weight concrete and masonry. It can also be used in concrete structures.
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16. Next time – Stability of a wall panel
Design the wall so it is able to withstand a horizontal force
2 method: Elastic and plastic
Lift/rotation
Sliding
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17. Project Distributed the horizontal forces to stability walls
Elastic or plastic
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