The effects of the accidental torsional eccentricity on the seismic behaviour of building structures

Size: px

Start display at page:

Download "The effects of the accidental torsional eccentricity on the seismic behaviour of building structures"

Aldous Stanley
5 years ago
Views:

The effects of the accidental torsional eccentricity on the seismic behaviour of building structures João Miguel Parece Pereira Raposo October 2014 Civil Engineering Department, Instituto Superior

1 The effects of the accidental torsional eccentricity on the seismic behaviour of building structures João Miguel Parece Pereira Raposo October 2014 Civil Engineering Department, Instituto Superior Técnico, Universidade de Lisboa, Portugal Key-words: Accidental eccentricity, Torsion, Natural Torsion, Centre of mass displacement; Regularity; Regulations 1. Introduction and Objectives The torsional motion of building structures is a characteristic that tends to aggravate the linear and nonlinear response, being responsible for introducing additional uneven forces, stresses and deformation in the loadbearing structural elements. Rosenblueth (1960), when studying the effects of 1957 Mexico City s earthquake, concluded that torsion effects introduced a combination of shear, bending and axial forces, creating serious complications in structural concrete columns. According to De la Llera and Chopra (1994a), torsion could be originated from natural or accidental causes. Natural causes are associated with the imbalance between the stiffness and mass distributions (figure 1.1) or the presence of low torsional stiffness (figure 1.2) while accidental causes are due to the uneven distribution of mass, uncertainties in the distribution of rigidity and the rotational effects at the base of the building. Figure 1.1- Eccentricity between centres of mass and stiffness Figure 1.2- Low torsional stiffness 1

2 The main objective of this work is to deepen the knowledge on accidental eccentricities, their origin and effects, in the light of regulations such as EN in order to evaluate its underlying assumptions. 2. Regulation 2.1. Introduction Introducing notions about regulation of accidental eccentricity used, this chapter describes the prescriptions enunciated in EN , indicating the combination methods of seismic actions and accidental eccentricities in the two directions of seismic actions Accidental eccentricities Several codes use the same approach on analysing accidental eccentricities. EN in chapter introduces this question through the moving of the centre of mass in the amount of 5% of the dimension of the floor in the perpendicular direction to the seismic analysis. The European seismic code, EN1998-1, distinguishes two ways of analysing accidental eccentricity, separating them into static and simplified analysis. Depending on the type of analysis and the presence of masonry walls, it could change the considered fraction s floor. Other codes like American code, ASCE 7-10, prescribe a multiplication of the value of accidental eccentricity by a factor of amplification. Fardis (2009) suggest that the most accurate way to take into account the effect of accidental eccentricity is using a 3D model and proceeding to the displacement of the mass in the percentage of 5% of the floor in the perpendicular direction of seismic action in study Static analysis The study of accidental eccentricities through a static analysis is characterized by introducing an accidental torsion moment (Z-axis) in the centre of mass of each floor. The model is a spatial model, according to clause (1) of EN The torsional moment applied is measured according to the equation 2.1: M ai = e ai F i (2.1) 2

This accidental torsion moment is calculated through the multiplication of accidental eccentricity by the force induced by the seismic action.

3 This accidental torsion moment is calculated through the multiplication of accidental eccentricity by the force induced by the seismic action. This force corresponds to a portion of base seismic shear defined through the displacement of the mass of the first vibration mode in the direction of the horizontal component Simplified analysis In Clause of EN1998-1, proposes a simplified method where the forces and stresses in structural components efforts are increased by a coefficient δ (3.13). This conservative method can only be applied in symmetric structures. δ = 1 + 0,6 x L (2.2) In this analysis, the variable x is the distance of the element in the perpendicular direction of seismic action, and L is the dimension of the floor in the perpendicular direction of seismic action. According to Bisch et al (2011) it is also important to consider the design s calculation. If these effects are determined by a spatial model, this approach is correct. However, if these effects are determined by a planar analysis the coefficient changes to = 1 + 1,2 x L Resume The table below resumes the application of seismic action. Tabel 2.1- Resume of seismic action application The presence of masonry walls doubles all the coefficients, whatever the design method. 3

4 2.2. Combination of seismic action and accidental torsional moments The regulation stipulates that the horizontal components of the seismic action should act simultaneously, bearing in mind that each seismic direction should be calculated separately. The regulation EN is unclear in respect to the combination mode to be carried out between the seismic components and the effects of accidental eccentricities in the presence of excitation of two orthogonal components. Clause of EN only admits that the torsional moments "(...) may be determined as the envelope of the effects resulting from the application of static loadings, consisting of sets of torsional moments Mai about the vertical axis of each storey (...) ". Fardis (2009) and Bish et al (2011) also propose other combination modes, which depend essentially on the analysis model used in computing the internal forces, as can be seen in Table 3.3. Tabel 2.2-Combinations betw een Accidental Eccentricities and Seismic action in both seismic directions Seismic Combination + MT First Combination Method of Combination E sx = (E x + Mt x ); E sy = (E y + Mt y ) (2.3) E d = (E sx ) 2 + (E sy ) 2 (2.4) E S = (E x ) 2 + (E y ) 2 (2.5) Second Combination Mt = (Mt x ) 2 + (Mt y ) 2 (2.6) E d = Es + Mt (2.7) Third Combination M t = (+M x ; M x ; + M Y ; M Y ) (2.8) E d = (E x ) 2 + (E y ) 2 + M T (2.9) Linear Combination E sx = E x + M Tx ; E sy = E dy + M Ty (2.10) E dx = E dx + 0,3 E dy ; E dy = E dy + 0,3 E dx (2.11) 4

3. Study of the method of application of accidental eccentricities The study herein consists of a comparative analysis of the effects on accidental eccentricity as a result of displacement of the

5 3. Study of the method of application of accidental eccentricities The study herein consists of a comparative analysis of the effects on accidental eccentricity as a result of displacement of the centre of mass when compared with the simplified prescriptions of EN The first phase of the study takes place through the excitation of just one direc tion of seismic action and the second phase the seismic action is performed through the two seismic directions. Two types of model were built: Model DM was performed with the centre of mass displaced from its original position. Model EC8 built through the insertion of an accidental torsion moment in the centre of mass, according with the static prescription of EN Structural concept A diaphragm translational movements in the orthogonal directions and deformation in the vertical axis is ensured by a slab with thickness of 0,18m 5x5m area. The floor structure (slab) is supported in four 0,25 mx 0,3 m beam. The collumns considered in both models have an modification of the cross section in height, depending on the number of floors of the system. The foundation has been considered as rigid. Figure 3.1-Generic model studied The interaction between accidental and natural eccentricities was studied through the application of three natural eccentricities in both model types. Those three natural eccentricities considered were null, medium (displacement of 10% of the floor) and high (displacement of 30% of the floor). 5

6 A more comprehensive comparative analysis is required in the development of models with 1, 2, 5 and 10 floors. Therefore, the variables in question are the number of floors (1,2,5,10) and the presence of natural eccentricity (zero, medium and high). A constant acceleration of 0.3a g was introduced in the two types of models. The representation of values was performed in a dimensionless form in order to exclude a possible error factor in the present study. Therefore, the coefficients were divided according to the various analyses by the value of the normal force that these elements were exposed DM model- Particular Structural Concepts The DM model has the particularity of recreating the displacement of mass with respect to the centre of mass according to the EN Hence, a displacement of 5% of the floor in the perpendicular direction of seismic action was implemented, and the system was subjected to a modal response spectrum analysis, combined in one direction or both directions, depending on the case in the study. Figure 3.2- Displacement of mass The displacement points of the centre of mass was determined based on the New Zealand Standard NZS regulation, which considers the displacement of the centre of mass through an ellipse with semi-axes with the value of the orthogonal directions of eccentricities, in this case 5% of the dimension perpendicular to the action of seismic movement, instead of the 10% recommended by this regulation. For each static eccentricity the centre of mass was displaced according to figure 3.1. Torsion component was isolated through the subtraction of the displacements done (P1 to P8) by the point P0. 6

3.1.3. EC8 model- Particular Structural Concepts The model in question was subject to static prescription of EN1998-1 through the application of an accidental torsional moment (z axis) at the point

7 EC8 model- Particular Structural Concepts The model in question was subject to static prescription of EN through the application of an accidental torsional moment (z axis) at the point P0 of each natural eccentricity in study. The base shear of each system was determined through a modal response spectrum analysis and distributed in height by equation 4.3 of the prescription presented in EN Comparison between DM model and EC8 model A comparison between the coefficients from DM model and EC8 model by fractional error was made. Fardis (2009) admits that the most accurate way of determining the effects of accidental eccentricity is by moving mass associated with model DM. As such, the error was determined by: Coefficiente DM Coefficiente EC8 Error (%) = ( ) 100 Coefficiente EC Description of Studies Study 1- Error between DM model and EC8 model through a unidirectional action DM model was used with the mass shifted in x axis (positions P1 and P5) to take into account the accidental eccentricity result of a seismic action according to y, as showed in Figure 3.2. Moreover, the eccentricity result of accidental seismic second X was represented by the mass shift of y by the points P3 and P7. Figure 3.2- Displacement of mass P1/ P5 and P3/P7 The analysis performed in DM models was a modal response spectrum analysis. 7

Prescription 4.3.3.3.3(2) of EN 1998-1 requires the implementation of accidental torsional moments in positive and negative senses.

8 Prescription (2) of EN requires the implementation of accidental torsional moments in positive and negative senses. This was ensured through the use of the points P1 / P5 and P3 / P7, as can be seen in Figure The EC8 model was subject to the application of an accidental torsional moment (z-axis), corresponding to directional analysis in question, according to of EN The application of accidental bending moment happened at the point P0 of each natural eccentricity Study 2- Error between DM model and EC8 model through a bidirectional action The second study is based on the same comparison carried out in Study 1, with the particularity of the action transmitted to the structure in two seismic directions. The DM model has a mass displacement on x and y directions, as revealed in Figure 3.3. The positive and negative senses were guaranteed by the displacement of the mass P4 / P2 and P8 / P6. The action performed in DM models is a modal response spectrum combined in both directions by a SRSS seismic combination. Figure 3.3- Displacement of mass P2/ P6 and P4/P8 EC8 model is subjected to the combined accidental torsion moments of the seismic action in the two horizontal directions, calculated from independent way and applied in the centre of mass of each natural eccentricity (P0). The combination is performed by the first three combination methods, in which was isolated the portion corresponding to accidental torsional moment. This isolation was made to avoid larger proportions that would happen if the study was conducted through a full seismic action. 8

9 4. Unidirectional analysis study An analysis of the first study has proved to be satisfactory in many structural systems analysed, both with different eccentricities and a different number of floors. It was verified that in most cases the values for DM model were higher than those in EC8 models. The difference between the two models was more pronounced in buildings with a smaller number of floors and higher natural eccentricity, mainly in irregularity plan structures. The modification in height of the cross section of the pillars was implemented in different models, and revealed an increase of the relative error in all natural eccentricities studied, especially in high natural eccentricity. 5. Bidirectional analysis study The comparative study by seismic activity in the two perpendicular directions proceeded in a first step through the choosing two of the six possible movements of mass. Second phase of the study had the intention to analyse which combinations of accidental torsional moments applied in EC8 models, would provide better results when compared with the DM models. All combinations presented higher values than performed in DM models. This situation resulted from the coefficient decrease in the seismic model DM, due to the smaller eccentricity inherent of a smaller displacement mass, and the fact that the bidirectional seismic action was combined in both directions via SRSS. Structure classification demonstrated some compliance between the results obtained in models with zero and medium natural eccentricity, while the models with high natural eccentricity exposed more anarchic values. The change of the cross section continues to reveal an increase in error between the two models. The combinations tested in EC8 model, in order to combine the effect of the earthquake with the accidental torsional moments in both directions of analysis were instructive allowing the combination MaxMt choice, which by the way is the easiest to apply, as it presents better results compared to the coefficients from the model DM subjected to mass displacement in two orthogonal directions. 9

10 6. Conclusion The study was carried out on the best way to account the effect of accidental eccentricity in order to make the most correct design in support of a common designer. Both studies proved to be satisfactory, as the values were relatively similar in the various structural systems studied. It was verified, however, more irregular results in the presence of natural systems with high eccentricities. Unidirectional study reveal DM model coefficients superior than EC8 model coefficients, on the other side the bidirectional study reveal the opposite. MaxMt combination reveals the best choice to combine the accidental torsional moments in two direction of seismic analysis. 7. Bibliography ASCE Minimum Design Loads for Buildings and other structures, ASCE Standard ASCE/SEI 7-10, American Society of Civil Engineers, Reston, Virginia, Bisch P.; Carvalho E.; Degee H.; Fajfar P.; Fardis M.; Franchin P.; Kreslin M.;, Pecker,P. Pinto A.; Plumier V; Somja V; Tsionis G. (2013) Eurocode 8: Seismic Design of Buildings Worked examples, Worked examples presented at the Workshop EC 8: Seismic Design of Buildings, Lisboa, Feb CEN (Ed.). NP EN Eurocódigo 8 - Projecto de estruturas para resistência aos ismos Parte 1 - Regras Gerais, acções sísmicas e regras para edifícios, Portugal, Março, De la Llera J.C.; Chopra A. K., (1994a)- Accidental and natural torsion in earthquake response and design of buildings, Proceedings of the 11 th Word Conference on Earthquake Engineering, Acapulco, Mexico, June, Fardis, M., (2009) Seismic Design, Assessment and Retrofitting of Concrete Buildings, Geotechnical, Geological and Earthquake Engineering, Vol. 8, Springer. New Zealand Standard (2004)- NZS , Council of Standards New Zealand,2004. Rosenblueth, E. (1960) The earthquake of 28 July 1957 in Mexico City, Proceedings of the second World Conference on Earthquake Engineering: Tokyo and Kyoto, Japan, July,

COLUMN INTERACTION EFFECT ON PUSH OVER 3D ANALYSIS OF IRREGULAR STRUCTURES

th World Conference on Earthquake Engineering Vancouver, B.C., Canada August -6, Paper No. 6 COLUMN INTERACTION EFFECT ON PUSH OVER D ANALYSIS OF IRREGULAR STRUCTURES Jaime DE-LA-COLINA, MariCarmen HERNANDEZ