# Structural Dynamics and Earthquake Engineering

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Structural Dynamics and Earthquake Engineering

Structural Dynamics and Earthquake Engineering Course 10 Design of buildings for seismic action (2) Course notes are available for download at http://www.ct.upt.ro/users/AurelStratan/ Combination of the effects of the components of the seismic action Seismic action has components along three orthogonal axes: – 2 horizontal components – 1 vertical components Vrance a, 04.03.1977, INCERC (B), NS 1 0 -1 -2 -1.95 0 5 10 2 15 20 25 30 Vrancea, 04.03.1977, timp, sINCERC (B), EW 35 40 35 40 1.62 acceleratie, m/s 2 Peak values of ag for horizontal motion are NOT recorded at the same time instant Peak values of response are NOT recorded at the same time instant acceleratie, m/s 2 2 1 0 -1 -2 0 5 10 15 20 25 30 timp, s 1 Combination of the effects of the components of the seismic action Simultaneous action of two orthogonal horizontal components (lateral force or spectral analysis): – Seismic response is evaluated separately for each direction of seismic action – Peak value of response from the simultaneous action of two horizontal components is obtained by the SRSS combination of directional response: 2 2 EEd EEdx EEdy Alternative method for combination of components of seismic actions Combination of the effects of the components of the seismic action When vertical component is considered as well: 2 2 2 EEd EEdx EEdy EEdz 2 Vertical component Vertical component of seismic action shall be considered when vertical peak ground acceleration agv0.25g, and the structure has one of the following characteristics: – – – – – has horizontal elements spanning over 20 m has cantilever elements with a length over 5 m has prestressed horizontal elements has columns supported on beams is base-isolated Conceptual design of buildings Seismic response of structures subject to considerable uncertainties: – characteristics of future seismic motions – diff. between structural models and real structural behaviour • elastic model inelastic response • static analysis dynamic behaviour • … Conceptual design of buildings located in seismic areas is necessary, in order to provide an adequate seismic response: – – – – – – structural simplicity uniformity, symmetry and redundancy bi-directional strength and stiffness torsional resistance and stiffness diafragmatic behaviour at storey levels adequate foundation 3 Structural simplicity Simple, compact, symmetric structures Modelling, analysis, design, detailing and construction of structures subjected to smaller uncertainties Uniformity, symmetry and redundancy Structures should be as regular as possible, with a uniform plan layout, allowing for a short and direct transmission of inertia forces to lateral resisting system Redundancy: failure of a single member does not imply failure of the whole structure 4 Bi-directional strength and stiffness Gravity - force resisting systems Lateral - force resisting systems sistem de preluare a fortelor gravitationale sistem de preluare a fortelor laterale Seismic motion has components on both horizontal directions Structures should have similar strength and stiffness along two main directions Torsional resistance and stiffness Seismic forces centre of mass (CM) Resisting forces centre of rigidity (CR) Torsionally flexible systems large forces and deformations in perimetral elements lateral-force resisting system lateral-force resisting system gravity-force resisting system gravity-force resisting system Conclusion (1): lateral force resisting systems are more efficient away from the centre of rigidity 5 Torsional resistance and stiffness Seismic forces centre of mass (CM) Resisting forces centre of rigidity (CR) Eccentricity torsion increased displ. and forces 2x 2x D2y Fx CR=CM Fx CM CR e0y D1y Y D1x D1x X Conclusion (2): lateral force resisting systems should be located as symmetrical as possible Storey diaphragms Behaviour of floors as rigid diaphragms – Collect and transmit forces to lateral-force resisting systems – Lateral-force resisting systems work together – Especially relevant in case of complex and non-uniform layouts of lateral-force-resisting systems, or combination of such systems of different stiffness F F 6 Foundations Design and construction of the foundations and of the connection to the superstructure shall ensure that the whole building is subjected to a uniform seismic excitation Recommendations: – discrete number of structural walls, of different width and stiffness box-type or cellular foundation – individual foundation elements foundation slab or tie-beams between these elements Criteria for structural regularity Structural regularity: – plan – elevation Regularity of a structure affects: – structural model, 2D or 3D – analysis method, lateral force method or modal response spectrum analysis – value of the behaviour factor q, that need to be reduced for structures irregular in elevation 7 Criteria for regularity in plan A symmetrical distribution of stiffness and mass Compact plan configuration, close to a convex polygonal shape (set-backs of max 10% from floor area) Rigid diaphragms at storey levels At each level, in each principal direction of the structure, the eccentricity shall satisfy: eox 0,30 rx eoy 0,30 ry eox , eoy - the distance between the centre of stiffness and the centre of mass, measured in the direction normal to the direction of analysis considered rx, ry – the square root of the ratio of the torsional stiffness to the lateral stiffness in each direction ("torsional radius") Criteria for regularity in elevation Lateral-force resisting systems shall run without interruption from their foundations to the top of the building Mass and lateral stiffness shall be constant or reduce gradually with height In framed buildings the ratio of the actual storey resistance to the resistance required by the analysis should not vary disproportionately between adjacent storeys Stiffness: reductions are no larger than 30% with respect to adjacent storeys Strength: reductions are no larger than 20% with respect to adjacent storeys Mass: is not larger than 50% of the mass of adjacent storeys 8 Criteria for regularity in elevation Restrictions on setbacks Consequences of structural regularity on analysis and design Regularity Allowed simplification Behaviour factor (q) Plan Elevation Model Linear-elastic analysis YES YES Planar * Lateral force Reference value YES NO Planar Modal Reduced value (by 20%) NO YES Spatial Modal Reference value NO NO Spatial Modal Reduced value (by 20%) *Only if building height is less than 30 m and fundamental period of vibration T1 < 1.50 s Plan irregularity: large torsional eccentricities 3D models Vertical irregularities: significant contribution of higher modes of vibration – modal response spectrum analysis – reduced values of behaviour factor 9 Structural model The model of the building shall adequately represent the distribution of stiffness and mass Floors that cannot be modelled as infinitely rigid in-plane translational masses (only) can be considered lumped in nodes Floors that can be modelled as infinitely rigid in-plane storey masses can be lumped at the centre of mass of each storey: M M m x – 2 translational components – 1 rotational components y i M zz mi d i2 myi mi mxi di My Y Mx CM Mzz X Accidental torsional effects Uncertainties associated to distribution of storey masses and/or spatial variation of ground motion Accidental eccentricity e1i = 0.05 Li Spatial structural model: M 1i e1i Fi ±e1x Y Fx CM ±e1y Ly CM X Fy Lx 10