Design of buildings using EC8

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Derick Dennis
6 years ago
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1 Design of buildings using EC8 & 1 can be applied to all buildings and is obligatory for buildings which do not satisfy the regularity criteria specified by EC8. The response of all modes of vibration contributing significantly to the global response shall be taken into account. This may be satisfied by either of the following: By demonstrating that the sum of the effective modal masses for the modes taken into account amounts to at least 90% of the total mass of the structure. By demonstrating that all modes with effective modal masses greater than 5% of the total mass are considered. Of course, if possible, all modes can be taken into account 2 1

A six storey 2D frame is a 6DOF system (6 modes) The sum of the effective modal masses for the first two modes amounts for more than 90% of the total mass of the structure Only the first two modes

2 A six storey 2D frame is a 6DOF system (6 modes) The sum of the effective modal masses for the first two modes amounts for more than 90% of the total mass of the structure Only the first two modes effective masses are greater than 5% of the total mass Therefore only the first two modes can be take into account 3 1 st mode 2 nd mode 3 rd mode 4 th mode 5 th mode 6 th mode Only the first two (or three) modes are important for the vibration of this structure. EC8 permits us to ignore the rest of them. 4 2

vibration modes i and j (including both translational and torsional modes) may be considered as independent of each other, if their periods T i and T j satisfy (with T j T i ) the following

3 When using a spatial model, the above conditions have to be verified for each relevant direction. A six storey 3D building is a 18DOF system The first 5 modes should be taken into account to amount for more than 90% of the total mass of the structure for both directions 5 The response in two vibration modes i and j (including both translational and torsional modes) may be considered as independent of each other, if their periods T i and T j satisfy (with T j T i ) the following condition: T j 0,9 T i (1) Whenever all relevant modal responses may be regarded as independent of each other, the maximum value E E of a seismic action effect may be taken as: Combination of modal responses (SRSS rule) (2) E E seismic action effect under consideration (force, displacement, etc.) E Ei value of this seismic action effect due to the vibration mode i. If (1) is not satisfied, more accurate procedures for the combination of the modal maxima shall be adopted such as the "Complete Quadratic Combination (CQC rule) 6 3

4 General This type of analysis may be applied to buildings whose response is not significantly affected by contributions from higher modes of vibration. These requirements are deemed to be satisfied in buildings which fulfill the two following conditions: a) they have fundamental periods of vibration T1 in the two main directions smaller than the following values b) they meet the criteria for regularity in elevation 7 Base shear force The seismic base shear force F b is a very important quantity in earthquake engineering. The base shear force value is the summary of the shear forces of all vertical elements at the ground floor level when a lateral loading (usually seismic loading) is applied to the structure Lateral loading Shear force diagram 8 4

5 Base shear force The seismic base shear force F b, for each horizontal direction in which the building is analyzed, is determined as follows: F b = S d (T 1 ) m λ S d (T 1 ) ordinate of the design spectrum (see ) at period T1 T 1 m λ fundamental period of vibration of the building for lateral motion in the direction considered total mass of the building, above the foundation or above the top of a rigid basement correction factor, the value of which is equal to λ = 0,85 if T 1 < 2 T C and the building has more than two storeys, or λ = 1,0 otherwise. 9 Distribution of the horizontal seismic forces The fundamental mode shapes in the horizontal directions of analysis of the building may be calculated using methods of structural dynamics (usually this is done automatically by programs like SAP2000) or may be approximated by horizontal displacements increasing linearly along the height of the building. The seismic action effects shall be determined by applying, to the two planar models, horizontal forces F i to all storeys. F i horizontal force acting on storey i F b seismic base shear s i, s j displacements of masses m i, m j in the fundamental mode shape When the fundamental mode shape is approximated by horizontal displacements increasing linearly along the height, the horizontal forces F i are given by: z i, z j heights of the masses m i, m j above the level of application of the seismic action 10 (foundation or top of a rigid basement). 5

6 Combination of the effects of the components of the seismic action Horizontal components of the seismic action In general the horizontal components of the seismic action shall be considered as acting simultaneously. The combination of the horizontal components of the seismic action may be accounted for as follows: a) The structural response to each component shall be evaluated separately, using the combination rules for modal responses as above b) The maximum value of each action effect on the structure due to the two horizontal components of the seismic action may then be estimated by the square root of the sum of the squared values of the action effect due to each horizontal component. 11 Combination of the effects of the components of the seismic action Horizontal components of the seismic action As an alternative to the previous combination rule the action effects due to the combination of the horizontal components of the seismic action may be computed using both of the two following combinations: 1) E Edx "+" 0,30E Edy 2) 0,30E Edx "+" E Edy "+" implies "to be combined with'' E Edx E Edy action effects due to the application of the seismic action along the chosen horizontal axis x of the structure action effects due to the application of the same seismic action along the orthogonal horizontal axis y of the structure. 12 6

Design of buildings using EC8 Configuration of the structural system

Design of buildings using EC8 Configuration of the structural system Regularity in plan and elevation 1 For the purpose of seismic design, building structures are distinguished as regular and non-regular.