Program Continuing - Stability of wall panels Example with combined section in a stability wall Floor level (Etageadskillelse) Beam model (Bjælkemodel) Stringer method (Stringermetoden) Project Det Tekniske Fakultet

Clasical procedure for building calculations: Define the building Class of consequents Location of the building (Wind category) Define the loads Design the load bearing system Floor levels (Etagedæk) Walls, columns, beams ect. Design the stability system (plastic or elastic) Design the wall panels for rotation and gliding Design the floor levels (beam method or stringer method) Connection – walls, decks ect. (Samlinger, støbeskel) Robustness. Det Tekniske Fakultet

Example of wind load >< mass load on the gable Wind load on the gable: we=qp(D-E)ρ D og E is a formfactor for wind on the facade and is calculates to D=0,74 og E=-0,38 (Because of h/d=22/40=0,55) correlationsfactor ρ=0,85 we=0,939*(0,74-(-0,38))*0,85=0,89kN/m2 This value is use in formula 6.10b 6.10b: 0,9*G 1,5*ψ0*Q 1,5*V*KFI (Q=0, when it is favorable) 6.12a/b: 1,0*G ψ2*Q + Ad (ψ2=0,2 for domestic- and office areas) (ψ2=0,2 for både boliger og kontorer) Which situation is the most dangerous one? What's the contribution from geometrical imperfection Vθ? This is not at sum. Combination of loads is a describtion on how to combine loads. Det Tekniske Fakultet

Wall panel – Elastic design, tension Stresses in the bottom of the wall is found by the use of Navier: If there is tensile stress in the wall the wall will rotate and we need to aplly some reinforcement in the foundation (anchor the wall/in Danish: trækforankres). Example P=15kN i LAK 6.10b: σ = -123kN/m2 og 383kN/m2 Tension! I.e. the wall has to be anchored Det Tekniske Fakultet

Shear force in a vartical connection in a wall Elastic design: Connections in walls the shear stress can be calculated by the use of Grashoffs formula: When using Grashoff the horizontal shear stress is determinate and this is equal to the vertical shear stress and can therefore be use. See example 7.2 in the book Det Tekniske Fakultet

Wall panel – Plastic design. Eccentric vertical reaction By the use of static equivalent the normal force can be moved the distance “e” and distributed over a smaller area The effective area and the compressive stress is determinate. The eccentric is calculated: e=M/N Det Tekniske Fakultet

Plastisk design – Shear in a wall connection When combining profiles the force between the web and flange is determinate. The flange i cut free. Normal stresses in top and bottom of the flange is determinate. The normal stress from the profile dead load is added. Se the example in the book (7.4) Now the shear force in the connection can be determinate by the means of equalibrium. Det Tekniske Fakultet

Design - wall panel, plastic 3 storeys high Wind on the facade The wall carries no decks or a roof structure. Design the wall for: Rotation Gliding Shear force in the connection between body and flange What would be different if the wind from the other side ? (from the right side) Det Tekniske Fakultet

The Deck Function of the deck: Vertical load Designed as a plate/beam Horizontal load is distributed to the stability walls: Designed as a panel To secure that the gable against suction from the wind Det Tekniske Fakultet

Panel made of hollow decks Eample of a deck plan with reinforcement. (Eksempel på dækelementplan med fugearmering): Det Tekniske Fakultet

Reinforment in decks and their function Edge reinforcement: Secures the outer deck elements in the gable from the wind Tension in the deck panel when the deck is functioning as a beam Shear forces between hollow decks can be obtained and transferred U-bars around the edge reinforcement: Makes sure that the façade elements are secured for suction on the facade. The same goes for the gable Also function as reinforcement against shear forces – Like a beam Det Tekniske Fakultet

Horizontal load on the deck panel -0,3 til -0,7 0,7 til 0,8 -1,2 til -0,5 Wind pressure and suction on the facade Wind suction on the gable Det Tekniske Fakultet

Horizontal load on the deck panel The load on the deck panel is distributed as a uniformed load [kN/m] Det Tekniske Fakultet

Beam model The deck panel is disigned as beam. It has 6 supports and we get the following section forces: Det Tekniske Fakultet

Beam model L<2zcotθ Deck panel: The Moment Deteminate the reinforcement in the connection at the facade for the maximale moment: In most cases the reinforcement detemainate for Mmax is use in for the hole buildings length. Design for shear forces: The reinforcement are place in the gab between the deck so it function as a beam Reinforcement for shear can be neglected, if: L<2zcotθ L, is the distant between the supports (stability walls) Det Tekniske Fakultet

Example: Beam model Walls Shear Max moment The panel is raktangular and can be considered as a beam. The beam has 3 supports. The horizontal load is distributed equally to the three walls (Ithere are no walls vertically to the load because of equilibrium) Walls Shear Max moment Det Tekniske Fakultet

Eksempel: Bjælkemodellen Trækarmering. Normalt kaldet stringerarmering: Choice: 1 Y8 med et As=50mm2. Beware: robustness might increase the area of the reinforcement! Shear: Okay. No need for shear force reinforcement! robustness might increase the area of the reinforcement! L<2zcotθ → 10m<2*0,8*8*2,5=32m Det Tekniske Fakultet

Intro - Stringermetoden As an alternativ to the beam model the stringer method can be use. Devide the building up in zones. The zones are shear zones and are inclosed by a stringer in tension or in compression. Se betonkonstruktioner kap. 12 Det Tekniske Fakultet

Assignment- Etageadskillelser How can you design the deck panel in case A and B according to the beam model? A Stability walls B Det Tekniske Fakultet

The deck panel – Stringer method vs. Beam model Easy to apply and use for simple cases You might have to divide the deck panel up into smaller beams Stringer method The method is a bit more complicated but god is you have a structure with a allot of holes. Det Tekniske Fakultet

Project Can you use the beam model? Det Tekniske Fakultet

Næste gang – Forankring af gavl Ved bygninger med bærende facader skal det sikres at gavlen er forankret til etageadskillelsen. Ikke altid nødvendigt med bøjler! Det/de yderste dækelement virker som en bjælke, og skal derfor altid designes i ”fuld” bredde. Dvs. evt. paselement placeres længere inde i bygningen. Det Tekniske Fakultet

Næste gang – Støbeskel Det Tekniske Fakultet