Building calculations Statically determinate panels Ole Christiansen Det Tekniske Fakultet

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

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

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

Accidental load – (Påkørselslast) Det Tekniske Fakultet

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

Exact! Det Tekniske Fakultet

Exact! Det Tekniske Fakultet

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

Panel structure Det Tekniske Fakultet

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Stability- example Facade Det Tekniske Fakultet

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

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

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

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

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