Program: Statically indeterminate panels Plastic distribution Elastic distribution Example Det Tekniske Fakultet

Last - time: Statically over-determinate (2 times). 2 columns are placed below panel D. Det Tekniske Fakultet

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 Det Tekniske Fakultet

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). Det Tekniske Fakultet

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? Det Tekniske Fakultet

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?) Det Tekniske Fakultet

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. Det Tekniske Fakultet

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. Det Tekniske Fakultet

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) Det Tekniske Fakultet

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 Det Tekniske Fakultet

Elastic - Example Asymmetric In this case the moment of inertia is used same principle when the area is used t= 200mm FC Det Tekniske Fakultet

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 Det Tekniske Fakultet

You have the possibility to make more than choice when you choose your system and you can also choose several methods (elastic and plastic) Det Tekniske Fakultet

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 Det Tekniske Fakultet

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. Det Tekniske Fakultet

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 Det Tekniske Fakultet

Project Distributed the horizontal forces to stability walls Elastic or plastic Det Tekniske Fakultet