1. Building calculations
Statically determinate panels
Ole Christiansen
Det Tekniske Fakultet

2. Program: Spar Nord – The load bearing system
Accidental load and imperfection load
Statically determinate panels
Panel: When is it stable
How are forces transferred between panels, columns ect.
Distribution of horizontal forces to the walls
Example
Assignment in statically determinate panels
Project
Det Tekniske Fakultet

3. Spar Nord – Statically analysis
Go together with another group and explain why you have chosen the load bearing system as you did
The direction of the roof?
Where have you placed the columns?
Where have you placed the beams?
The direction of the decks/hollow-deck?
Det Tekniske Fakultet

4. Accidental- and seismic load
Asses the possibility of Accidental load - Example explosion or collision
Seismic load is categorizers as an accidental load and should be considered when designing the building:
The seismic load is applied to the building and designed according to formula 6.12a/b.
Long buildings: It is often the seismic load which is the design load when designing a long building and comparing it to the wind load ( wind along the building- vind på langs af bygningen)
Det Tekniske Fakultet

5. Accidental load – (Påkørselslast)
Det Tekniske Fakultet

6. Imperfection load - simplified
Extra horizontal load (V). The horizontal load is included in the centroid of the floor panel: it is included as an extra load to the wind- and the seismic load (STR 2B).
V=θiN
Safe assessment: θi=1/200
N is the vertically load acting on the panels.
Det Tekniske Fakultet

7. Exact!
Det Tekniske Fakultet

8. Exact!
Det Tekniske Fakultet

9. Panels Definition of a panel:
Two of the dimensions are significant larger then the third dimension.
The load is acting in its own plan it will function as a panel (figure b).
It is only forces in the plan which is relevant when designing a panel
Forces/loads acting vertical on the plan is characterized as a plate (figure a).
Det Tekniske Fakultet

10. Panel structure
Det Tekniske Fakultet

11. Panels Distribution of forces between panels:
If the panels are not in the same plane, only shear forces/stresses can be transferred. It is possible to transfer normal forces if the panels are connected in a point.
Example – connection between walls and decks.
Det Tekniske Fakultet

12. Panels
If two panels are connected such that they are in the same plane normal stresses and shear stresses can be transferred between the panels (normal forces, shear forces and moments). This is also the case when designing the connection between wall panel and foudation
Det Tekniske Fakultet

13. Panel structures Distribution of forces between columns and panels:
If the column and the panel are in the same plane only normal forces can be transferred
Det Tekniske Fakultet

14. Statically determinate structures
A panel structure i statically determinate if its reactions can be determined by the equilibrium equations alone
Alternatively the structure is unstable (statically over-determinate) or statically indeterminate.
Statically over-determinate /ustable
Statically determinate
Statically indeterminate
Det Tekniske Fakultet

15. Stability
The term stability have several meanings in structural design. For builds the term is use to describe a builds ability to restrain horizontal forces (is not to be compared to instability when designing a column)
Are the structures stable?
Det Tekniske Fakultet

16. Statical determinate structure
The correlation between the number of panel and reactions in a statically determinate structure can normally be describe as: (Not always!):
3N=R
R – Number of reactions
N – Numbers of panels
Or when its for columns:
3N=R+M
M- Number of columns
Det Tekniske Fakultet

17. Statisk bestemt skivekonstruktion
The equation 3N=R is fulfilled but are the structures stable.
Det Tekniske Fakultet

18. Statical determinate structure– Example:
The correlation between the number of panel and reactions in a statically determinate structure can normaly be describe as: (Not always!):
3N=R
R – Number of reactions
N – Numbers of panels
Or when its for columns:
3N=R+M
M- Number of columns
Kontrol 3N=R:
3*4=12 OK!
But is it stable
Det Tekniske Fakultet

19. Statisk bestemt skivekonstruktion – Eksempel:
Distribution of horizontal load from floor panel ”D” to the wall panels ”A”, ”B” and ”C”
Equlibrium in the direction of the y-axis:
Equlibrium in the direction of the x-axis:
Moment:
Det Tekniske Fakultet

20. Example:
In the same way the reaction are determine for panel and foundation for A, B and C
The reaction are use to design the connection between walls, panels etc.
Equlibrium in the direction of the y-axis:
Equlibrium in the direction of the z-axis:
Moment:
Det Tekniske Fakultet

21. Method from teaching book – is the structure statically determinante
Det Tekniske Fakultet

22. Design procedure
Determine which reaction/panel can be solved by the use of the 3 equations
The reaction for the panel are determinate
Afterwards the next panel i chosen and the reaction is determinate
Continue, until all the reactions for all panels are determinate
If the reactions cant be determinate by use of the equilibriums the structure is indeterminate
Det Tekniske Fakultet

23. Stability – design phase
It is important to assess what’s the minimum requirements to secure that the structure is stable. This should be included as early as possible in the design phase.
The forces transferred through the connection is determinate by the use of equilibriums (lecture 6)
Det Tekniske Fakultet

24. Which walls are a part of the stability
The stability system
Which element/walls are include to secure that the building is stable
In many cases it is possible to chose more than one solution (Lower bound solution)
Chose walls without holes and continues walls from top of the building to the foundation.
If its not possible walls with holes are chosen.
The builder is interested in being free to move internal walls so it is important that the stability system is chosen with the lowest possible walls.
Det Tekniske Fakultet

25. Stability- example 1., 2. and 3 floor Ground floor
Det Tekniske Fakultet

26. Stability- example
Facade
Det Tekniske Fakultet

27. Stability- example1 1., 2. and 3 floor Statically determinate
Ground floor
Det Tekniske Fakultet

28. Stability- example 2 1., 2. and 3 floor Statically indeterminate
Ground floor
Det Tekniske Fakultet

29. Assignment
Determine the reaction which can be solved by the use of the 3 equations
The reaction for the panel are determinate
Afterwards the next panel i chosen and the reaction is determinate
Continue, until all the reactions for all panels are determinate
If the reactions cant be determinate by use of the equilibriums the structure is indeterminate
Det Tekniske Fakultet

30. Project Consider: Which walls will be a part of the stability?
Det Tekniske Fakultet

31. Next– Lecture 5 Statically indeterminate
Is it better to have a statically determinate- or a indeterminate structure?
Det Tekniske Fakultet