Seismic response of composite frames—II. Calculation of behaviour factors

Seismic response of composite frames—II. Calculation of behaviour factors

" ' EngineeringStructures,Vol. 18, No. 9, pp. 707-723, 1996 "'4 Copyright© 1996ElsevierScienceLtd Printed in GreatBritain.All rights reserved 0141...

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EngineeringStructures,Vol. 18, No. 9, pp. 707-723, 1996

"'4

Copyright© 1996ElsevierScienceLtd Printed in GreatBritain.All rights reserved 0141~0296/96$15.00+ 0.00

0141-0296(95)00212-X

ELSEVIER

Seismic response of composite frames II. Calculation of behaviour factors A . S. E l n a s h a i

Engineering Seismology and Earthquake Engineering Section, Imperial College, London, UK B. M . B r o d e r i c k

Department of Civil, Structural and Environmental Engineering, Trinity College, Dublin, Ireland (Received October 1994; revised version accepted October 1995)

The response criteria and earthquake ground motions selected in a companion paper are applied to the evaluation of the actual behaviour factors of a number of moment-resisting composite frames designed to the requirements of the structural Eurocodes. These behaviour factors are obtained through the use of nonlinear dynamic analysis by comparing the ground motion intensities at which yield and failure occurs in each frame. The principal features affecting the seismic response of composite frames are identified, in which special emphasis is placed on those features which differ significantly in the response of steel frames. It is concluded that the present design guidance on behaviour factors for composite frames is excessively conservative and improved recommendations are suggested. Other areas in which design guidance needs to be amended to reflect the seismic behaviour of composite frames are also discussed. Keywords:

transient analysis, behaviour factors, Eurocode 8

ordinates of the elastic acceleration spectrum used to define the seismic hazard of a site to those of the inelastic spectrum employed in the derivation of the seismic design forces, Thus,

Introduction

Earthquake-resistant design codes make no attempt to quantify the deformation demands imposed upon structures during their response to earthquakes of different magnitudes. Rather, each structural form is assumed, when properly designed and detailed, to be capable of undergoing a known level of stable inelastic deformation which is expressed in terms of the code-prescribed force modification or structural behaviour factor. These factors, denoted as Rw and q, respectively, may be viewed as global measures of displacement ductility capacity. The behaviour factor is employed to reduce the seismic design loads to a level which allows the benefits offered by the energy dissipation capability of each structure to be availed of, while still ensuring that the imposed ductility demand does not exceed the available supply. In this, it is assumed that the total response, including both elastic and plastic deformations, is no greater than that implied by a linear elastic analysis under the unreduced loads. For a particular response period, the structural behaviour factor, q, as employed in Eurocode 8 l, is the ratio of the

q : (Sa) el d ](Sa)din,

(l)

where, as shown in Figure 1, (Sa)d is the design spectral

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707

Design,

collapse

and yield acceleration

spectra

Seismic response of composite frames--II: A. S. Elnashai and B. M. Broderick

708

acceleration and the superscripts 'el' and 'in' refer to its elastic and inelastic values, respectively. In Eurocode 8, maximum allowable q-factor values are specified for a range of structural forms and construction materials. These values reflect the ability of each type of structure to undergo stable oscillations in the inelastic range. They are also intended to represent lower bounds on the actual ductility supply of individual structures, thus it should be expected that qcode ~< q', where q' is the ultimate value which relates, not the elastic and inelastic design spectra of equation ( 1 ), but the response spectra corresponding to the ground motion intensitities which produce structural collapse and yield, viz,

q'= (Sa)~'/(S,)~,',

(2)

where, the subscripts c and y denote collapse and yield, respectively. Comparison of equations (1) and (2) shows that the design code behaviour factors correspond to the case where collapse is imminent under the loading defined by the elastic design spectrum and yield is equally imminent with the conditions of the inelastic design spectrum. In contrast, Figure 1 illustrates the actual ground motion dependence of these conditions. For a given ground motion, however, the collapse intensity will be uniquely defined; in which case by combining equations (1) and (2) it is possible to further define the behaviour factor of an individual structure as ~1/~~,S aid. ~in q , D : t~S a/c

(3)

This definition has been employed by Kappos 2 in the investigation of the behaviour of reinforced concrete buildings. While it has the advantage that it relates the intensity of loading at collapse to the design loads, it fails to include for the disparity between the ground acceleration at yield - which will vary with ground motion, structural design and response period - and that related to the inelastic design spectrum. By assuming a constant dynamic acceleration amplification, the ratios in equations (2) and (3) can be represented by the peak ground accelerations corresponding to each of the spectra of Figure 1. Thus,

ag(collapse)/ag(yield)

(4)

q'D = ag( collapse)/ [ ag( dcsign)/ q ],

(5)

q'

=

where ag(collapse) and ¢2g(yield) are the peak ground accelerations at which collapse and yield occur, respectively, and ag(de~ign~ is the design value of the ground acceleration, denoted as ad in Figure 1.

Analysis of composite frames To date, no systematic investigation of the characteristic behaviour factors of composite frames has been performed, with the result that Eurocode 8 employs the same values as are applied to the design of steel structures. To obtain more rational values for use in design, the seismic response of 20 moment-resisting composite frames varying in dimension and member type were analysed using the nonlinear dynamic analysis program ADAPTIC. To include a realistically wide range of earthquake loads, six different ground motion records were employed; the selection and scaling

of which is described in a companion paper 3. Each frame was designed according to the requirements of the structural Eurocodes, so that the identified response and behaviour could be assumed to be typical of practical structures. By limiting the range of the frames to those which fulfil Eurocode requirements, the variability in structural response which arises due to the differences between individual designs is somewhat reduced. It is then hoped that the degree of variation between each of the structures analysed is sufficient to cover the majority of the response features which arise in realistic composite frames. Thus, a comprehensive assessment of the demands imposed upon composite frames and the effects of seismic loading on their capacities may be assessed. For each flame, the structural behaviour factors are identified by defining those ground motion intensities sufficient to cause yield and collapse. In this regard, collapse may be represented by the attainment of one of a number of failure criteria, defined in the companion paper, corresponding to a set of conditions at either member or storey levels 3.

Frame designs The range of composite frames investigated is described in Table 1. In all, 20 frames were analysed, consisting of 10 frames employing bare steel columns and 10 with partiallyencased composite columns possessing cross-sections of the form shown in Figure 2. These members have been observed to possess significant rotation ductility capacities, even with high section slendernesses and axial loads. In Table 1, each frame is distinguished by the number of storeys and bays which it possesses. Thus, Frame S2S2B-A is a two-storey, two-bay frame with steel columns and C2S2B-A is an equivalent frame employing composite columns. The trailing character distinguishes between frames possessing similar architectural layouts, but which are significantly different in some other feature. Two, three, six and 10-storey frames are included, possessing either three or five bays. Storey heights are either 3.6 or 3.0 m with beam spans of either 8.0 or 5.0 m. The characteristic imposed load also varies, from 3.5 to 5.5 kN m 2. Characteristic material strengths offy = 275 N mm -~ for structural steel, fr = 4 0 0 N mm -2 for reinforcing steel, and J~k = 30 N mm 2 for concrete were employed throughout. The frames are designed in accordance with the provisions of the structural Eurocodes, with member capacity design being based on the provisions for steel and composite building frames contained in Eurocode 8. It is assumed that all beam-column joints are fully rigid and possess resistances which are sufficiently large in comparison with their connected members to prevent the occurrence of yield. Connection flexibility is therefore not taken into account. The controlling design criterion for each frame was the need to limit interstorey drift to the maximum code-allowed value. The resulting member dimensions are detailed in Table 2 in terms of the steel sections employed in both beams and columns, the slab thickness and the area of longitudinal reinforcement. Only commercially available steel sections and reinforcing bars were considered, and only column arrangements which resisted the imposed loading about their major axes were employed. The external and internal columns in each frame are of equal dimension, hence irregularity effects are not included. In taller frames, smaller beam dimensions were employed in the upper storeys wherever this did not imply maximum larger interstorey drifts at lower levels. In these cases, the member dimen-

Seismic response of composite frames--II: A. S. Elnashai and B. M. Broderick

709

Table 1 Dimensions, imposed loads and column types of frames analysed Frame dimensions, loads and column types Frame reference

No. of storeys

No. of bays

Storey height (m) Bay width (m)

Live load (kN m -2) Column type

S2S2B-A C2S2B-A

2 2

2 2

3.6 3.6

8.0 8.0

3.5 3.5

Steel Composite

S2S2B-B C2S2B-B

2 2

2 2

3.0 3.0

8.0 8.0

3.5 3.5

Steel Composite

S3S3B-A C3S3B-A

3 3

3 3

3.6 3.6

8.0 8.0

3.5 3.5

Steel Composite

S3S3B-B C3S3B-B

3 3

3 3

3.0 3.0

8.0 8.0

3.5 3.5

Steel Composite

S3S5B-A C3S5B-A

3 3

5 5

3.0 3.0

8.0 8.0

3.5 3.5

Steel Composite

S3S5B-B C3S5B-B

3 3

5 5

3.0 3.0

5.0 5.0

5.5 5.5

Steel Composite

S6S3B-A C6S3B-A

6 6

3 3

3.0 3.0

8.0 8.0

3.5 3.5

Steel Composite

S6S3B-B C6S3B-B

6 6

3 3

3.0 3.0

8.0 8.0

5.5 5.5

Steel Composite

$6S5B C6S5B

6 6

5 5

3.0 3.0

8.0 8.0

3.5 3.5

Steel Composite

S1OS5B C10S5B

10 10

5 5

3.0 3.0

8.0 8.0

3.5 3.5

Steel Composite

Figure2 Partially-encased composite beam-column section with flange buckling inhibitors sions given in Table 2 relate to those in the lower storeys. In all frames, the stiffness of the roof beams was reduced from those employed in the lower storeys. The most practical method of limiting lateral drift in composite frames is through the use of the largest beam members permitted by the requirements of capacity design 4. This principal is applied in the majority of the designs as described in Table 2. The first three frames listed therein, however, were designed so that a proportionally greater contribution to stiffness is provided by their column members. Hence, the influence of both of these design approaches on the seismic performance of the resulting structures may be assessed. Failure criteria. Table 2 also lists the failure states for each of the structural members employed 3. Inspection of the column member designs employed and their resulting

rotation ductility capacities shows that the greater bending moment capacities of composite columns allowed proportionally larger beam members to be employed than in the case of frames employing bare steel columns. When combined with the contribution to stiffness and strength of the concrete component, this led to lighter steel sections being employed in partially-encased members. The higher b/t ratios of these lighter members reduced the advantages offered by the increased rotation ductility capacity of partially-encased columns to the extent that in some instances designs with steel columns possess less severe column failure criteria. Generally, however, the rotation ductility capacity of the composite columns is significantly higher than that of their bare steel equivalentst The critical flange stresses for the beam members display no obvious trends with the other design features of the frames. This is due to the large number of factors contributing to both their design and failure conditions. In particular, the critical stresses are highly sensitive to increased web depths. Hence, wherever greater stiffness is achieved through the use of deeper sections, as in Frame S10S5B, a more stringent failure criterion results. On the whole, however, the critical stresses of the beam members are very similar across the range of frames investigated. The relative economy of frames employing partially-encased and steel beams will depend on the respective material costs of steel and concrete and on any additional fabrication costs incurred by the composite option. However, the tendency of the composite columns to allow larger beam members to be employed will lead to more economical designs.

S e i s m i c response o f c o m p o s i t e f r a m e s - - I I : A. S. Elnashai a n d B. M. Broderick

710

Table2 M e m b e r dimensions and critical states Frame member dimensions and critical states Column

Frame reference

UC section

S2S2B-A C2S2B-A S2S2B-B C2S2B-B S3S3B-A C3S3B-A S3S3B-B C3S3B-B S3S5B-A C3S5B-A S3S5B-B C3S58-B S6S3B-A C6S3B-A S6S3B-B C6S3B-B S6S5B C6S5B Sl0S5B C10S5B

254 x 254 x 203 x 203 × 203 x 203 x 203 x 203 x 305 x 305 x 305 x 305 x 254 x 254 x 254 x 254 × 254 x 254 x 254 x 254 x 203 x 203 x 203 x 203 x 305 × 305 x 305 x 305 x 305 x 305 x 305 x 305 x 305 x 305 x 305 x 305 x 356 x 368 x 356 x 368 x

132 60 71 71 158 137 89 73 89 73 71 60 118 97 137 118 137 118 177 153

Beam

Rotation ductility capacity /~.c 8.1 7.7 7.0 8.9 6.7 7.6 5.7 5.5 5.7 5.5 7.0 7.7 5.0 4.5 5.8 7.0 5.8 7.0 4.9 5.7

UB section

Slab depth (ram)

Longitudinal reinforcement (mm 2)

Critical flange stress (N mm 2)

203 x 203 x 203 x 203 x 203 x 203 x 254 x 254 x 203 x 254 x 203 x 203 x 305 x 305x 305 x 305 x 305 x 305 x 305 x 305 x

140 140 140 140 140 140 140 140 140 140 120 120 125 125 150 150 140 140 150 150

1570 1570 1570 1570 1570 1570 2945 2454 2945 2945 1005 1570 2945 2945 2945 2945 2945 2945 2945 2454

336 336 337 337 336 336 331 331 336 331 337 337 337 335 335 335 337 335 317 328

133 x 30 133 x 30 102 x 23 102 x 23 133 x 30 133 x 30 102 x 28 102 x 28 103 x 30 102 x 28 102 x 23 102 x 23 127 x 48 127 x 4 2 127 x 42 127 x 42 127 x 48 127 x 42 165 x 46 165 x 54

Modelling of frames

column connection and two further elements connected at mid-span. These short elements are necessary not only to reflect the high degree of plasticity expected in these regions, but also to ensure that the length of the negative moment region, which can vary considerably with loading, is accurately modelled. As no verification of the multi-surface steel plasticity model has been performed for composite beam elements, the more conventional bilinear model is employed to represent the material response in the steel section and reinforcing bars of these members. Strain hardening moduli of 1% for structural steel and 0.5% for reinforcing steel are employed. The mass of the structure contributing to the response of the frame is determined by assuming a frame spacing normal to the direction of loading of 4.0 m. The calculation of the mass of each structure is based on the thickness of the floor slabs employed, with further allowance being made

A typical ADAPTIC model of the analysed flames is shown in Figure 3, while the cross-sections of the beam and column elements are shown in Figure 4. Four cubic elements are employed within each column length, including two short elements at either end. This ensures that there are three Gauss sections within each potential plastic hinge zone, allowing the spread of plasticity across each section and along each member to be captured. For both partiallyencased and bare steel columns, a multi-surface plasticity model was employed to represent the inelastic cyclic response of the steel components 6, while a uniaxial cyclic model allowing for variable confinement represented the behaviour of the concrete components 7. A similar assembly of beam elements is used, with four cubic elements employed in each span. These also consist of two short elements, of length 500 mm, in the region of the beam-

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711

Seismic response of composite frames--I~: A. S. Elnashai and B. M. Broderick L.

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i

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(b) S t e e l I - S e c t i o n

(c) PartiaUy-Encased Section

Figure 4 ADAPTIC composite beam and column sections for other significant masses due to internal and external walls or cladding. An accurate prediction of these values is not possible due to their dependence on individual building types, hence a uniform correction is applied throughout by increasing the mass of the structural frame and slab by 15%. Allowances are also made with respect to the contribution of the imposed loads stipulated by Eurocode 8, and the increased mass of the composite columns over their bare steel equivalents. Analytical

results

The composite frames described above were analysed to determine their response to each of the selected earthquake ground motions. A number of analyses were conducted for each frame-earthquake combination in which the ground motions were scaled to identify the intensity of loading at which yield and the various failure criteria of Table 2 occurred. In all, over 500 dynamic analyses were performed.

Illustrative frame response The results obtained from the analysis of Frame C6S3B-B are presented in Figures 5-8. These allow the response of the various members of the structure to be compared, in which respect, the behaviour of this frame is typical of the collection of analysed frames as a whole. Storey displacements. The displacement response of Frame C6S3B-B to each of the earthquake ground motions is illustrated in Figure 5. The results shown are those at which the maximum interstorey drift index reaches the failure criterion of 3%. As indicated in Figure 5a, maximum

interstorey drifts most commonly occur in the second storey of each frame. For some ground motions, however, maximum drift response occurs in higher storeys, as in the response due to the Friuli earthquake. In this case, maximum drift occurs in the uppermost storey, with much smaller relative displacements being observed at lower levels. This irregular response is also observable in Figure 5b which illustrates the envelope of the maximum displacement responses of each storey. For all ground motions except the Friuli earthquake, similar maximum displacement distributions are displayed, with a linear variation in the lower storeys decreasing somewhat towards the top of the structure. Much smaller displacements are observed for the Fruili earthquake, indicating that the maximum interstorey drift coincides with movement in opposing directions of adjacent storeys, indicating higher mode response. Across the entire range of frames analysed, the response due to the Friuli earthquake was significantly different to that caused by the other five ground motions, demonstrating the desirability of considering a wide selection of seismic loads in analyses of this type.

Member rotations. Figure 6 illustrates the maximum beam rotations and column rotation ductilities experienced in each storey of Frame C6S3B-B when the seismic loads have been scaled to produce a maximum interstorey drift of 3%. The values shown represent the local rotation demands which the capacities of the individual members should exceed to ensure adequate seismic performance. Figure 6a shows the maximum column rotation ductility demand experienced at the lower end of each storey, from which maximum values of 2.5-3.5 are observable. With the exception of the response due to the Loma Prieta EW earth-

Seismic response of composite frames--II: A. S. Elnashai and B. M. Broderick

712 6--

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100

200

300

400

Maximum Storey Displacement (mm) Co)

Inter-Storey Drift Index (%) (a)

Figure 5 Relative displacements of storeys in frame C6S3B-B expressed in terms of interstorey drift index and maximum displacement relative to ground for each ground motion (scaled at maximum interstorey drift = 3.0%)

6 - '\

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u

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0.03 0.06 0.09 Rotation (rads) (c)

1.5 2 0 Rotation Ductility (b)

0.12

M a x i m u m Beam Rotation in Each Storey

Column Rotation Ducfilty at Top of Each Storey

Figure 6 Maximum column rotation demands and maximum beam rotations experienced by frame C6S3B-B for each ground motion (at maximum interstorey drift = 3.0%)

6_

i I

E1 Cent~o

i

L. Prieta EW

I

..........

L. Prieta NS

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.......

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Plastic Hinge Lth (mm)

1K

1

2000 4000 0 200 400 0 Plastic Hinge Lth (rnm) Plastic Hinge Lth (mm)

(a)

(b)

(c)

M a x i m u m Column Plastic Hinge Length at Bottom of Each Storey

M a x i m u m Column Plastic Hinge Length at Top of Each Storey

M a x i m u m Beam Beam Plastic Hinge Length in Each Storey

Figure 7 Maximum estimated plastic hinge lengths exhibited by frame C6S3B-B for each ground motion (at maximum interstorey drift = 3.0%)

Seismic response of composite frames--II: A. S. Elnashai and B. M. Broderick 6 7~..~ \

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Figure 8 Energy dissipated through inelastic rotations in (a) column members and (b) beam members of frame C6S3B-B for each ground motion (at maximum interstorey drift = 3.0%) quake, the maximum value observed outside of the first storey is less than 1.5, with ductilities lower than 1.0 indicating elastic behaviour. The idiosyncratic response caused by the Friuli earthquake is again observable. The rotation ductility demands occurring at the upper ends of the column members are ilustrated in Figure 6b. While capacity design procedures are intended to ensure that column hinging takes place only at their bases, the combined effects of strainhardening in beams and the irregular distribution of forces arising during the dynamic response of such structures implies that some amount of inelasticity will occur at higher locations. The rotation ductilities experienced, however, are not large, indicating that only small excursions into the inelastic range take place. Hence, so long as a complete column collapse mechanism does not form, this column hinging will not threaten the stability of a structure, implying that no added precautions are required within the design procedure. Generally, more column hinging is observed in the case of composite columns than in their steel equivalents. This is attributable to the greater difference between their yield and plastic moments and the use of proportionally larger beam members than in frames with bare steel columns. As described in the companion paper, the local deformations occurring in beam members are not expressed in terms of ductilities, but in terms of the absolute rotation demands imposed in the potential plastic hinge zones. These rotations, which are determined from beam curvature distributions, are indicated in Figure 6c. These distributions show that demand is greatest in the lower stories, decreasing at higher levels, but increasing again in the roof members due to the reduction in member dimensions.

Member plastic hinge lengths. The plastic hinge lengths occurring in individual members are important in that they define the extent to which members should be detailed to ensure adequate resistance to local inelastic instability and the proportion of each member in which energy dissipation occurs. Figure 7 indicates the longest platic hinge lengths occurring in each storey. In comparison with steel columns, the spread of plastic is slightly greater at the base of composite columns due to their greater plastic moment to yield moment ratios. While the longest column plastic hinges observed approach h J4, where h~ is the height of the storey, those occurring in the beam members

exceed L/3, where L is the span of the beam. This is due to the comparatively low yield moment which a composite beam can possess in comparison with its ultimate resistance, and the influence of strain hardening in longitudinal reinforcement.

Energy dissipation in beams and columns. The inelastic deformations shown in Figures5-7 indicate the locations where seismic energy is dissipated as irrecoverable strain energy. The greater plastic hinge lengths occurring in beams allow more energy to be dissipated in these members. Moreover, the capacity design procedures employed cause the inelastic deformations to be much greater at these locations. Figure 8 compares the cumulative energy dissipation occurring in the beam and column members in each storey of Frame C6S3B-B, where the energy dissipated in the beam members is seen to be far greater than that in the columns. Moreover, while this dissipation occurs largely in members in the lower half of each structure, ground-motion dependence is noticeable in the distributions due to the Friuli and Gazli earthquakes. In the case of the Friuli record, more energy is dissipated in the upper, as opposed to lower, storeys of the frame, while a significant proportion of the total energy dissipated during the Gazli event occurs in the column members. This energy dissipation distribution implies that a significant level of column inelasticity in the higher storeys arises due to the high frequency content of the ground motions which excite the higher modes of vibration to a greater extent than in other earthquakes. The consequent irregular distribution of forces between the structural members leads to the observed increase in column hinging. Frame natural periods and overstrengths Table 3 lists the values of two important properties for each of the frames investigated in the present study: the fundamental natural periods and the lateral resistance overstrengths for each frame. The fundamental periods were obtained from eigenvalue analyses of the ADAPTIC models of each frame. A significant variation in period with the number of storeys in each frame is, as would be expected, observable. The influence of the number of bays is not as strong, as all frames are designed to equal lateral stiffnesses irrespective of the number of members employed• Moment-

Seismic response o f composite frames--II: A. S. Elnashai and B. M. Broderick

714

Table3

Fundamental

periods and lateral resistance over-

strengths Natural periods and overstrengths

Frame Reference

Fundamental natural Lateral resistance period overstrength 7-1 (s) a~= ~o/c~

S2S2B-A C2S2B-A S2S2B-B C2S2B-B S3S3B-A C3S3B-A S3S3B-B C3S3B-B S3S5B-A C3S5B-A S3S5B-B C3S5B-B S6S3B-A C6S3B-A S6S3B-B C6S3B-B $6S5B C6S5B S10S5B C10S5B

0.66 0.72 0.60 0.59 0.67 0.70 0.74 0.76 0.73 0.77 0.79 0.81 1.11 1.18 1.13 1.16 1.12 1.16 1.25 1.28

1.14 1.20 1.29 1.27 1.18 1.19 1.33 1.41 1.35 1.41 1.36 1.36 1.29 1.40 1.11 1.24 1.18 1.25 1.25 1.33

au = ultimate lateral resistance of frame, c~1= lateral resistance of frame at yield

resisting frames of the type being considered here generally possess longer natural periods than are displayed by similar structures employing alternative lateral load resistance systems, e.g. braced frames. The fundamental periods of Frames S3S3B-A and C3S3B-A are significantly shorter than those of Frames S3S3B-B and C3S3B-B despite the taller storey heights used in the former cases. This is a result of the relatively stiffer columns and more flexible beams employed in the first pair of frames than in the latter two. In all but one of the pairs of frames listed in Table 3, the response period of the frame employing partiallyencased columns is longer, usually by 2-4%, than that of the frame designed with bare steel columns. While some of the benefit which this implies in terms of design seismic actions is offset by the increased mass of the partiallyencased members, on the whole frames with composite columns were required to resist lower base shears. The overstrength of the structural system employed to resist the imposed seismic loads, a~, is defined in Eurocode 8 as ai -

Ogtl OLI

,

(6)

where a, is the ultimate lateral resistance which the structure can provide and cq is the lateral resistance at which yield occurs. The design value of the structural behaviour factor to be employed for each moment resisting frame is directly proportional to this value. In the determination of the values of o~ given in Table 3, a~ relates to the base shear in each structure at which the first instance of column yielding is observed and a, is the maximum lateral resistance provided by each frame prior to the attainment of a maximum interstorey displacement of 3%. These definitions differ from those given in Eurocode 8, in which a~ relates to the formation of a hinge in any member and a,

relates to the ultimate lateral resistance of the frame. In composite frames, however, the formation of plastic hinges in the negative moment regions of composite beams does not lead to an appreciable decrease in overall frame stiffness as in steel beams. Similarly, the greater resistance of composite beams in negative bending causes the lateral resistance of the frame to continue to increase, even at large storey drifts, prohibiting a rational evaluation of %. As a result, the literal application of the provisions of Eurocode 8 can lead to oq of 20 and more, as confirmed elsewhere ~. In contrast, the definitions of cq and au employed here not only relate to realistic yield and ultimate states, but also lead to a~ values close to those of steel frames. From Table 3, frames with composite columns achieve higher a~ values than do their counterparts with steel columns. The average difference in this regard is approximately 5%, indicating that the value suggested by EC8 could be increased somewhat when partially-encased columns are employed. However, while no consistent variation in o~ with structural redundancy is noticeable, frames possessing larger beam elements possess significantly higher overstrengths than those in which lateral resistance is primarily contributed by the column members. Ground acceleration at yield Equation (4) indicates how the true behaviour factor of an individual structure may be evaluated in terms of the relative ground accelerations which cause yield and failure to occur. In terms of the earthquake ground motions employed here, this ground acceleration ratio is equal to the ratio of the factors applied to scale the accelerograms to the levels which produce each of these conditions. The scaling factors at which first yield was identified in each frame are given in Table 4. As this property is highly ground motion dependent, values for each earthquake-frame combination are presented in terms of the ratio agy. This relates the ground acceleration at yield to the design values of ground acceleration and behaviour factor:

agy =

ag(y ield) ~ ] qdesign" \t~g(design)/

(7)

in equation (7), ag(yield) is the peak ground acceleration when the ground motions are scaled to cause first yield, ag(design) is the peak value in the accelerogram scaled to the Eurocode 8 design spectrum 1, and qde~g, is the behaviour factor employed in the design of each frame. In all cases, a qdesign value of 6.0 was employed. The value of agy may be interpreted as the ratio between the ground motion intensity at which yield occurs for the earthquake under consideration and the intensity at which yield is implied by the peak ground acceleration and behaviour factor employed in the design process. In Table 4 therefore, values of agy less than 1.0 imply that yield occurred with ground motions scaled below their design values, while values greater than 1.0 indicate that yield occurred at intensities greater than this. The values listed in Table 4 show much variation, which may be attributed to a number of factors, including the fact that in the design of each frame, interstorey drift requirements were more critical than those relating to structural strength. Hence the margin between yield resistances and member design forces varied considerably across the range of frame designs. In fact, as indicated by the mean agy

715

Seismic response of composite frames--II: A. S. Elnashai and B. M. Broderick Table 4

Ground acceleration at first yield for each frame by ground motion Relative peak ground acceleration at first yield (agy)

Frame reference

El Centro

L. Prieta EW

L. Prieta NS

Spitak

Gazli

Friuli

S2S2B-A C2S2B-A S2S2B-B C2S2B-B S3S3B-A C3S3B-A S3S3B-B C3S3B-B S3S5B-A C3S5B-A S3S5B-B C3S5B-B S6S3B-A C6S3B-A S6S3B-B C6S3B-B $6S5B C6S5B S 10S5B C 10S5B

0.85 0.85 0.79 0.82 0.94 0.97 0.98 1.02 1.02 1.05 1.03 1.15 1.30 1.30 1.02 1.16 1.14 1.16 1.05 1.13

0.91 0.77 0.84 0.83 0.91 0.87 0.96 0.91 0.98 0.90 0.83 0.76 0.78 0.78 0.77 0.74 0.73 0.73 0.74 0.73

1.60 0.94 0.91 0.92 1.12 0.99 1.55 1.52 1.70 1.57 1.22 1.13 1.16 0.94 0.98 0.94 0.94 0.86 0.92 0.96

0.90 0.82 0.67 0.67 0.90 0.89 1.30 0.78 0.98 0.80 0.78 0.65 1.07 1.18 1.27 1.27 1.12 1.24 1.22 1.28

0.89 0.94 0.99 0.96 1.02 1.00 1.85 1.49 1.44 1.34 1.49 1.10 1.60 1.90 1.62 1.69 1.48 1.63 1.72 1.64

4.41 5.88 4.63 4.82 5.41 5.94 3.51 3.66 3.85 3.90 5.95 5.96 3.16 3.20 3.11 3.39 4.28 4.38 4.06 3.92

Mean (aeym) Minimum Maxim u m agym(steel) agym(comp)

1.04 0.79 1.30 0.96 1.06

0.83 0.73 0.98 0.85 0.80

1.15 0.86 1.60 1.21 1.09

0.99 0.65 1.30 1.02 0.96

1.39 0.89 1.85 1.41 1.37

4.37 3.11 5.96 4.24 4.50

where, ag(yield) is the ground acceleration at yield, ag(yield ) is the design ground acceleration = 0.25g and qaesign is the design behaviour factor = 6.0.

agy = [ag(yie~d)/ag(deslgn)]xqdesig n

values, yield generally occurred with base excitations greater than that implied by the design parameters. However, significant variation is displayed in the results, even within those relating to the same ground motion. This is best exemplified by the collection of results due to the Gazli earthquake. Furthermore, as the occurrence of yield is usually related to the effects of a single ground acceleration pulse, the variation between the maximum ground accelerations in each of the scaled ground motions employed3 becomes especially relevant, in particular contributing to the low agy values produced by the Loma Prieta EW and Spitak records. The interaction of the frequency content of the individual ground motions and the natural response periods of the structures is observable in both the relative responses of the frames to different earthquakes, and the various effects of the same earthquake on different frames. For example, the effects of the Gazli and E1 Centro earthquakes, which possess the shortest periods of maximum amplification (0.15-0.60 s), are more severe for the more squat structures than in the case of the taller, more flexible frames. The good correlation observed in this regard is due to the largely linear elastic nature of the response prior to yield. Due to the capacity design procedures employed, yield will occur in the negative moment regions of beam members before it occurs in columns. In the case of those frames in which lateral resistance is provided primarily by the column members, as is the case in the first six rows of Table 4, the smaller beam designs lead to yield occurring at lower agy values. With the exception of those relating to the E1 Centro ground motions, the average agy values for frames with composite columns are lower than those for frames with steel columns. While the difference in these mean values is not large, significant variations occur within

individual pairs of frames. The values of agy relating to the response of the frames to the Friuli earthquake are much greater than those observed for the other ground motions. This can be attributed to the failure of the single large ground acceleration response cycle contained in this record to produce a displacement response commensurate with its amplitude. As a result, it is the effects of the smaller peaks in the accelerogram which control the response, requiring greater scaling for the yield state to be attained.

Member rotation demands The maximum deformation of individual members likely to occur during the response of a structure to seismic loading should be known if proper guidelines are to be provided to ensure that sufficient local rotation capacity is available in each case. These maximum deformations will vary with loading intensity, ground motion characteristics and structural form. As a rational basis on which to define the demands imposed on members of composite frames, the maximum column rotation ductilities and beam rotations occurring in each frame, at a maximum interstorey drift of 3% are given in Table 5. The maximum compressive flange stresses occurring in the beam members are also given. For each frame, the earthquake ground motions which impose these maximum demands on the beam and column members are identified. In comparison with the member failure states presented in Table 2, the column rotation ductility demands given in Table 5 are everywhere less than the available supplies. With the exception of Frame C3S3B-B, this also applies in relation to beam flange stress. Thus, the local member failure criteria are seen to be less stringent than storey failure criteria. Of these, the criterion relating to the 3% interstorey drift limit employed was invariably

716

TaMe5 A~of 3%

Seismic response of composite frames--II: A. S, Elnashai and B. M. Broderick M a x i m u m column rotation ductility,/~oc beam rotation, Oband beam flange stress ~%f, demands at an interstorey drift index

Local member rotation demands at A i = 3% M a x i m u m column rotation ductility demand M a x i m u m beam rotation demand

Frame reference

Ductility /~

Ground motion

Rotation 0b (radians)

(rbf~.... ) (N mm 2)

Storey

Ground motion

S2S2B-A C2S2B-A S2S2B-B C2S2B-B S3S3B-A C3S3B-A S3S3B-B C3S3B-B S3S5B-A C3S5B-A S3S5B-B C3S5B-B S6S3B-A C6S3B-A S6S3B-B C6S3B-B $6S5B C6S5B S10S5B C1OS5B

1.96 3.00 3.44 3.50 2.59 2.77 4.21 4.15 4.20 4.29 3.33 3.78 3.79 3.70 3.60 3.55 3.75 3.72 3.59 3.72

Gazli L. Prieta EW L. Prieta EW Spitak L. Prieta NS El Centro Spitak El Centro Gazli El Centro Gazli Gazli L. Prieta NS L. Prieta NS Spitak L. Prieta NS Gazli Gazli L. Prieta NS L. Prieta NS

0.160 0.157 0.134 0.158 0.167 0.169 0.113 0.116 0.139 0.105 0.094 0.093 0.132 0.127 0.122 0.110 0.129 0.125 0.112 0.105

319 323 324 323 323 331 320 335 321 317 314 320 315 314 323 321 322 325 308 311

1 1 1 1 3 3 3 3 3 3 1 1 6 6 1 1 1 1 3 3

Gazli L. Prieta EW L. Prieta EW Gazli Gazli Gazli El Centro El Centro El Centro El Centro El Centro El Centro Gazli Friuili Spitak L. Prieta EW Gazli L. Prieta EW El Centro L. Prieta NS

Mean, /x Maximum /~(Steel) /~(Comp)

3.53 4.29 3.45 3.61

-----

0.129 0.169 0.130 0.129

320 335 319 321

the first to occur. Of the other criteria 3, a 10% loss of lateral resistance and stability indices greater than 0.3 were never observed. It should be noted, however, that for taller structures, increased P-A effects may increase the relevance of both of these criteria. In relation to the formation of storey collapse mechanisms, while hinging may occur at both ends of the internal columns, this never occurred concurrently in both external members, hence the formation of a column mechanism was never observed. Thus, it was the exceedance of the maximum allowable interstorey drift which almost exclusively constituted the critical failure criterion. Given the flexible nature of the structures under investigation here, this observation should not be surprising. The rotation ductility demand imposed on composite columns is generally seen to be greater than that imposed on their bare steel equivalents. This is due to the smaller member sizes which apply in the case of composite columns, which results from the contribution of the concrete components and the larger beam members with which they are often employed. In addition, while frames with composite columns possess longer natural periods and hence, are designed to lower base shears, the seismic loads imposed by the individual earthquakes within the selection employed here do not necessarily decrease accordingly. Moreover, the added mass of the composite columns is likely to lead to increased loads, resulting in larger deformations. These effects do not appear to carry over to significantly affect the rotation demands imposed on the beam members. As was observed in Table 4, there is a noticeable difference in the behaviour of the frames which employ stiff columns and those which were designed with optimum beam stiffnesses. In the former case, much greater beam rotations

m

m

m

m

m

m

were observed, however, this did not produce comparable increases in maximum beam stresses. In all other cases, the imposed rotations were comfortably within the capacities experimentally identified for members whose cross-sections meet the code requirements for plastic design 9. The ground motion dependence of the maximum member rotation demands is clearly observable, in that the critical earthquake varies, not only between frames, but also between the beam and column responses in the same frame. Indeed, each of the selected ground motions impose the maximum demand on either beams or columns for at least one frame. Maximum beam rotations are most commonly observed in the first or third storey beams, including some instances where these third storey beams correspond to the roof members. In Frames S6S3B-A and C6S3B-A, the critical beam response occurs in the sixth, or uppermost, storey, suggesting that these frames displayed significant higher mode responses. The fact that the critical earthquakes causing this behaviour (Gazli and Friuli records) have previously been seen to excite such a response supports this observation.

Behaviour factors for composite frames Evaluation procedure Equation (4) describes how the behaviour factor of an individual structure could be evaluated from the peak ground accelerations required to cause collapse and yield, while Table 4 presented the ground accelerations causing yield in each of the analysed frames. In the definition of the ground acceleration at collapse, use is made of the individual failure criteria defined in the companion paper 3. Thus, for each frame, there will exist different values of ag(collapse), not only

Seismic response of composite frames--II: A. S. Elnashai and B. M. Broderick for each ground motion, but also for each failure criterion. To reduce the number of variables involved, it is assumed that allowable interstorey drift is the controlling failure criterion at individual storey level. This criterion is assessed along with the local failure criteria which define the limits of response for beam and column members. In total therefore, q' values are evaluated for all combinations of these three failure criteria and six earthquake ground motion records. Comparison of the member rotation demands and supplies presented in Tables 5 and 2, respectively, indicated that the 3% failure criterion for interstorey drift was invariably reached at a lower ground acceleration than failure due to local member deformations. However, this does not necessarily imply that the drift criterion will always lead to the lowest q' values, as the variability in yield ground acceleration between the various frame-earthquake combinations observable in Table 4 must also be included. To evaluate behaviour factors for member failure criteria, the peak ground accelerations causing failure to occur in both beams and columns are determined for each frameearthquake combination. These values are then employed with the ground accelerations at yield, as represented by agy in Table 4, to give the q" values relating to critical beam flange stress (q',~b) and column rotation ductility capacity (q',o~). Comparison of these values, along with that due to drift, (q'~rm), allows the minimum behaviour factor displayed by each frame and ground motion combination to be identified.

Evaluation of qtdrift. In the evaluation of the behaviour factors due to member failure criteria, the yield state may be simply represented as the ground acceleration at which initial member yield occurs. However, for the evaluation of q'dm, through equation (4), no unique definition of an equivalent yield state, ay(drifl) is available. For instance, the application of the yield accelerations given by agy would give rise to behaviour factors which are dominated by the interaction of the elastic properties of the structure under consideration and the frequency characteristics of the earthquake record. Hence, the inelastic response characteristics of the structural form would not be properly reflected in the evaluated q'dm, values. To overcome this difficulty, the yield acceleration may be defined in terms of the design ground acceleration and the q-factor employed in the design, or ay(drin) =

ag¢de~ign)[q.

(8a)

In this case, the value of q'drift will be that given by equation (5). While this approach is practicable, it eliminates the ground motion dependence of the drift of the structure completely. A correction factor is therefore applied to the definition of ay(drift) given by equation(8a) which allows for the variation in drift, Ai(design), which occurs under each of the selected ground motions scaled to their design values. As the servicability limit state design requirements of Eurocode 8 required that each frame was designed to a maximum interstorey drift under the design ground acceleration of 1.5%, the ratio A~(ae~gn]0.015 may be applied as a correction factor to allow for the ground motion dependence of the displacement response observed in each frame analysis. This correction is employed to define a value of the ground acceleration which can be used to represent the yield state in the evaluation of q'drift as

ag(design) ay(drift) -- Ai~de~ign)/0.015

717 (8b) "

The value of ay(drift) determined from equation (8b) may be employed in equations (4) and (5) with the ground acceleration at which the 3% interstorey drift limit is reached, ag(A~ = 3%), to give ,

(ag(A~= 3%) )

q drift ~- \

ay(drift)

(9)

qdesign

or, .

q d~i~'t= \

0.015

X

ag(design)

qdesign-

(10)

In Table 6, the scaling factor applied to the accelerograms is denoted by A~, where A~= 1.0 represents the design ground acceleration. The ground motion scaling factor at which the 3% drift limit is reached, A~(A~= 3%), may be employed in equation (10) with the value of qdesign used in the design of the frames (6.0) to give

q'drift = 400(Ad Ai =

3%))(Ai(de.~ign))"

( 11)

Equation (l l) allows the behaviour factor associated with the interstorey drift failure criterion to be determined from the maximum drift experienced due to the design acceleration and the ground motion scaling factor required to cause a drift of 3%.

Evaluated behaviour factors, q" Behaviour factors due to drift, q'dr~ The expression for q'drm provided in equation ( 11 ) is applied to the results of the analyses of each frame-earthquake combination. For each frame, the relevant values ofAdA~ = 3%) and A~de~ig,~, corresponding to the earthquake record producing the lowest q'drm values are presented, with these q'drm values, in Table6. Also indicated are the storeys in which the maximum drift is displayed and the critical earthquake ground motion record. The results show that the evaluation procedure ensures that while considerable variation occurs in both the drifts experienced under the design loads and the scaling factors applied to the accelerograms to invoke the failure criterion, this is not reflected in the calculated q'dr~ft values. Hence, the behaviour factors computed reflect more accurately the characteristics of composite frames as a whole, rather than the particular response of individual structures and ground motions. The calculated q'~rm values vary from a minimum of 9.15 to an upper limit of 14.04, and may be compared with the value used in the design of the frames of 6.0. This increase is to be expected as the frames were designed to an interstorey drift of 1.5%, while the failure criterion was defined to be twice this. In any event, in so far as drift control is concerned, the use of different behaviour factors will not affect the design of a structure as, Eurocode 8 requires that the design displacements, dr, be determined as dr = qde

(12)

where de is the elastic displacement due to the design loads ~. Therefore, any reduction in the design loads, and

Seismic response o f composite frames--II: A. S. Elnashai and B. M. Broderick

718

Table 6 Calculation of behaviour factor corresponding to the attainment of a m a x i m u m interstorey drift of 3% in each frame Behaviour factor for maximum allowable interstorey drift Response at design ground acceleration (As = 1.0)

(q'drift)

Response at m a x i m u m allowable drift (Ai = 3.0%)

Frame reference

z-~i(%)

Storey

As

Storey

Behaviour factor qtdrif t

Critical earthquake

S2S2B-A C2S2B-A S2S2B-B C2S2B-B S3S3B-A C3S3B-A S3S3B-B C3S3B-B S3S5B-A C3S5B-A S3S5B-B C3S5B-B S6S3B-A C6S3B-A S6S3B-B C6S3B-B $6S5B C6S5B S10S5B C10S5B

1.86 0.57 1.43 1.78 1.35 2.11 1.05 1.46 1.37 1.42 1.25 1.63 0.58 1.70 1.51 1.50 1.51 1.51 1.54 1.52

2 2 2 2 2 2 2 3 2 2 2 2 6 3 2 2 2 2 2 2

1.50 5.30 1.60 1.41 2.00 1.32 2.22 1.92 2.18 1.84 1.90 1.64 6.05 1.92 2.00 1.99 2.03 1.96 2.03 2.01

2 2 2 2 3 3 2 2 2 2 2 1 6 3 3 3 3 3 3 3

11.16 12.08 9.15 10.03 10.80 11,14 9.32 11.22 11.95 10.62 9.51 10.69 14.04 13.06 12.08 11.94 12.24 11.84 12.50 12,20

Spitak Friuli L. Prieta EW Spitak Gazli Spitak Gazli Gazli Gazli L. Prieta NS Gazli Gazli Friuli Spitak Spitak Spitak Spitak Spitak Spitak Spitak

Figures shown are for the input motion producing the lowest qPdrift value, indicated in the right-hand column

hence d~, achieved through an increase in q will be offset in the calculation of dr in equation (12). Nevertheless, the values of q'drin given in Table 6 are important as they indicate that so long as the behaviour factors corresponding to other failure criteria are also in excess of the code values, then the conservatism of the design procedures can be confirmed. Table 6 also shows that while the greatest interstorey drift due to the design earthquakes generally occur in the second storey of the frame, for increased loads the maximum drift is often located in a higher storey.

Behaviour factors due to all criteria. Table 7 presents the values of q' evaluated for each frame-earthquake combination. The values therein relate to the failure condition producing the lowest q' value, hence they are the minimum of q ' ~ , q'j,o~ and q'drirt, and can be interpreted as the behaviour factors displayed by the individual frames under the particular earthquake concerned. The critical earthquake ground motion for each frame is indicated by italics. From here, a minimum value of 8.48 and the maximum value in excess of 20 are identified. These results demonstrate the extent to which behaviour factors can vary both for individual structures exposed to different ground motions and for different structures excited by the same earthquake. The application of the El Centro record, for instance, results in a q' value of 12.13 for Frame S3S3B-A, but 15.77 for Frame S6S3B-B, while the corresponding figures for the Spitak earthquake are 13.57 and 10.93. Overall, there seems to be an increase in q' with the number of members in the structure, most probably due to the ability of the larger structures to redistribute member forces more successfully. However, it is not possible to discern a definite relationship in this regard, especially as this increase may also be related to the period of vibration of the various structures. In comparison with the behaviour factor of 6.0 suggested in Eurocode 8 for moment-resisting composite frames, the

lowest identified value of q' is more than 40% greater. The importance of the structural overstrength, c~, in the definition of behaviour factors for moment-resisting frames was discussed previously. To evaluate q'/c~ for each frame-earthquake combination, Table8 combines the values of q' given in Table 7 with the values of c~ identified for each frame in Table 3. The values given range from a minimum of 6.96 to a maximum of 15.98. This minimum value of q'/c~, is approximately 40% greater than the code recommended behaviour factor 5a~, agreeing with the margin identified for q' above, in which the code q-value of 6.0 was obtained using the recommended value for oq of 1.2. To identify more clearly those factors controlling the actual behaviour factor for each structure, Table 9 presents the lowest values of q ~,o~, q o-b and q d~m identified for each frame from the entire set of earthquake ground motions. The values obtained are presented both with and without allowance for ai. The failure criterion giving rise to the lowest q' and q'/cq values are identified. While the limiting drift criterion was identified in Table 5 as being the most onerous of the failure criteria, the inclusion of the yield state in the evaluation of q' leads to values of q'dr~r, which are often greater than those of q'~eo and q ~0~. In fact, for the majority of frames, the maximum allowable beam stress constitutes the controlling criterion which determines the behaviour factor. It should also be noted however, that the values of q'dr,-t are usually not much greater, hence it is unlikely that any improvement in beam rotation capacity would offer much benefit in terms of increased behaviour factors. While in most cases, the failure criterion relating to available column rotation ductility is not critical, it is possible, as indicated by the behaviour of a couple of frame pairs, that this feature can constitute the limiting condition. In particular, the minimum q'~o~/Cq value observed of 7.37 is only 6% greater than the lowest value relating to beam failure of 6.96. It is also noteworthy that the single pair of t

t

p

p

Seismic

response

of composite

f r a m e s - - I ~ : A . S. E l n a s h a i

719

a n d B. M . B r o d e r i c k

Table 7 Analytically identified behaviour factors, q', for each frame, by ground motion accelerogram Behaviour factors (q') for each ground motion record Frame reference

El Centro

L. Prieta EW

L. Prieta NS

Spitak

Gazli

Friuli

Mean

S2S2B-A C2S2B-A S2S2B-B C2S2 B-B S3S3B-A C3S3B-A S3S3B-B C3S3B-B S3S5B-A C3S5B-A S3S5B-B C3S5B-B S6S3B-A C6S3B-A S6S3B-B C6S3B-B $6S5B C6S5B S 10S5B C10S5B

11.79 15.05 14.95 15.42 12.13 13.05 14.74 14.65 14.11 12.75 14.10 12.42 13.20 12.78 15.77 15.04 15.79 14.18 15.99 15.60

12.33 15.76 9.15 10.57 21.29 16.31 10.09 14.51 13.35 13.97 13.34 13.79 15.71 17.51 17.74 18.31 18.40 18.40 19.45 19.34

13.90 14.58 11.47 10.73 16.56 16.97 12,04 11.10 10. 15 9.84 14.59 11.33 11.58 13.08 12.73 12.31 13.90 13.03 15.36 14.75

11.16 13.76 9.70 10.03 13.57 11.14 9.92 12.04 12.50 10.87 13.26 11.57 14.98 13.06 10,93 11.72 12.24 11.76 12.50 12.22

14.56 14.60 10.59 11.00 10.80 12.71 9.32 9.90 10.49 10.29 9.51 10.69 11.86 10.44 11.68 11.90 13.37 13.34 13.58 14.12

9. 10 8.77 8.98 9.08 9.27 8.48 10.39 10.17 13.46 11.00 10.55 10.00 14.04 13.92 12.98 13.71 11.34 11.28 12.49 13.66

12.14 13.75 10.81 11.14 13.94 13.11 11.08 12.06 12.34 11.45 12.56 11.63 13.56 13.47 13.64 13.83 14.17 13.67 14.90 14.95

Mean Minimum

14.18 11.79

14.97 9. 15

13.00 9.84

11.95 9.70

11.74 9.51

11.13 8.48

12.83 10.81

Table 8 Analytically identified behaviour factors c/'/~i for each frame, by ground motion accelerogram Behaviour factors (q'/~xi) for each ground motion record

Frame reference

El Centro

L. Prieta (E-W)

L. Prieta (N-S)

Spitak

Gazli

Friuli

Mean

S2S2B-A C2S2B-A S2S2B-B C2S2B-B S3S3B-A C3S3B-A S3S3B-B C3S3B-B S3S5B-A C3S5B-A S3S5B-B C3S5B-B S6S3B-A C6S3B-A S6S3B-B C6S3B-B $6S5B C6S5B S 10S5B C10S5B

10.34 12.54 11.59 12.14 10.28 10.97 11.08 10.39 10.45 9.04 10.37 9.13 10.23 9.13 14.21 12.13 13.38 11.34 12.79 11.73

10.82 13.13 7.09 8.32 18.04 13.71 7.59 10.29 9.89 9.91 9.81 10.14 12.18 12.51 15.98 14.77 15.59 14.72 15.56 14.54

12.19 12.15 8,89 8.45 14.03 14.26 9.05 7.87 7.52 6.98 10.73 8.33 8.98 9.34 11.47 9.93 11.78 10.42 12.29 11.09

9.79 11.47 7.52 7.90 11.50 9.36 7.46 8.54 9.26 7.71 9.75 8.51 11.61 9.33 9.85 9,45 10.37 9.41 10.00 9.19

12.77 12.17 8.21 8.66 9.15 10.68 7. 01 7.02 7.77 7.30 6.99 7.86 9.19 7.46 10.52 9.60 11.33 10.67 10.86 10.62

7.98 7.31 6.96 7.15 7.86 7. 13 7.81 7,21 9.97 7.80 7.76 7.35 10.88 9.94 11.69 11.06 9.61 9.02 9.99 10.27

10.65 11.46 8.38 8.77 11.81 11.02 8.33 8.55 9.14 8.12 9.24 8.55 10.51 9.62 12.29 11.16 12.01 10.93 11.92 11.24

Mean Minimum

11.17 9.04

12.23 7.09

10.29 6.98

9.40 7.46

9.29 6.99

8.74 6.96

10.19 8. 12

Italics denote critical ground motion for each frame

frames (S6S3B-A and S3S6B-B) for which column ductility is the most critical feature is also that in which a significant proportion of the response occurs in the higher modes of vibration has already been identified. Table 10 identifies the earthquake ground motions which produce the lowest q'.oc, q'o-b and qtdrif t values for each frame. For the first three frame pairs, which were designed with relatively stiff columns, it is the response due to the Friuli earthquake which results in the lowest q" values for

the member failure criteria. This ground motion does not, however, constitute the critical case for the storey drift criterion. For the longer period structures, the Spitak ground motion has most effect overall, while the Gazli and Loma Prieta earthquakes are most critical in the intermediate range. For a given frame, a different ground motion may be critical for each of the three failure criteria. Furthermore, these ground motions are not necessarily those whose periods of maximum amplification are closest to the funda-

720 Table 9

Seismic

response

of composite

frames--II:

A . S. E l n a s h a i

a n d B. M . B r o d e r i c k

Analytically identified behaviour factors, q' and q'/ei, by failure criterion Behaviour factors by failure criterion Column rotational capacity

Beam critical stress

Interstorey drift

/~,c

~rcr

Ai

Frame reference

q"

q'/c~i

q"

S2S2B-A C2S2B-A S2S2B-B C2S2B-B S3S3B-A C3S3B-A S3S3B-B C3S3B-B S3S5B-A C3S5B-A S3S5B-B C3S5B-B S6S3B-A C6S3B-A S6S3B-B C6S3B-B $6S5B C6S5B S10S5B C10S5B

16.53 12.00 10.55 12.87 18.11 16.66 9.92 10.39 10.15 14.14 11.51 13.64 11.58 10.44 11.29 14.06 13.70 14.23 13.54 13.33

14.50 10.00 8.18 10.13 15.35 14.00 7.46 7.37 7.52 10.03 8.46 10.03 8.98 7.46 10.17 11.34 11.61 11.38 10.83 10.02

9. 10 8.77 8.98 9.08 9.27 8.48 9.40 9.90 10.71 9.93 9.86 10.00 12.31 10.61 10.93 11.72 11.34 11.28 12.49 13.02

Mean, /z V= o-//~ Minimum Maximum

12.93 0.17 9.92 18. 11

10.24 0.22 7.37 15.35

10.36 0.09 8.48 13.02

q'/c~i

q"

q'/~xi

7.98 7.31 6.96 7. 15 7,86 7. 13 7.07 7.02 7.93 7.04 7.25 7.35 9.54 7.58 9.85 9.45 9.61 9.02 9.99 9.79

11.16 12.08 9.15 10.03 10.80 11.14 9.32 11.22 11.95 10.62 9.51 10.69 14.04 13.06 12.08 11.94 12.24 11.84 12.50 12.22

9.79 10.07 7.09 7.90 9.15 9.36 7.01 7.96 8.85 7.53 6.99 7.86 10.88 9.33 10.88 9.63 10.37 9.47 10.00 9.19

8.14 0.14 6.96 9.99

11.38 0.11 9. 15 14.04

8.97 0.14 6.99 13.08

Italics denote critical failure criterion for each frame Table 10 Critical earthquake for each frame by failure criterion

Critical earthquakes by failure criterion

Frame reference

Column rotational capacity /Z,c

Beam critical stress O-cr

~i

Interstorey drift

S2S2B-A C2S2B-A S2S2B-B C2S2B-B S3S3B-A C3S3B-A S3S3B-B C3S3B-B S3S5B-A C3S5B-A S3S5B-B C3S5B-B S6S3B-A C6S3B-A S6S3B-B C6S3B-B $6S5B C6S5B S10S5B C10S5B

Friuli Friuli Friuli Friuli Friuli Fruili Spitak Gazli Loma Prieta - - EW Friuli Gazli Friuli Loma Prieta - - EW Gazli Spitak Gazli Gazli Spitak Spitak Spitak

Friuli Friuli Friuli Friuli Friuli Friuli Gazli Gazli Gazli Loma Prieta - - EW Gazli Friuli Loma Prieta - - EW Gazli Spitak Spitak Friuli Friuli Friuli Spitak

Spitak Friuli Loma Prieta - - NS Spitak Gazli Spitak Gazli Gazli Gazli Loma Prieta - - NS Gazli Gazli Friuli Spitak Spitak Spitak Spitak Spitak Spitak Spitak

Italics denote critical failure criterion for each frame

mental period of vibration of the structure. These observations confirm the need to include a wide range of accelerograms, selected in a rational manner, in a series of analyses of this type. Only then may it be concluded that the results of the analyses are indicative of the general response of each structure to seismic loads. Of particular

note is that the El Centro record, one of the ground motion records most widely employed in seismic analyses, is not critical for any failure criterion in any of the frames. To compare the performance of the frames employing composite and steel columns, Table 11 presents the ratios of the q' values for each pair of frames employing these

721

S e i s m i c r e s p o n s e o f c o m p o s i t e f r a m e s - - I I : A. S. E l n a s h a i a n d B. M. B r o d e r i c k Table 11 Ratio of behaviour factors for frames with composite and steel columns Bare steel and partially-encased columns: comparative behaviour factors Failure criterion Column rotational capacity

Beam critical stress O'cr(beam)

JLLoc

Interstorey drift A i : 3%

Mean

Frame reference

It( .... ]/ [ q'steel]

[ q'/czicompl/ [ qt/O/isteel]

[ q'comp]/ [ qtsteel]

q'/crlcomp ]/ [ q~//(3~i..... ]

[q(comp]/ [#steel]

[ q'/°qcompl/ [ q2/oListeel]

[ q'comp]/ [ qt ..... ]

2S2B-A 2S2B-B 3S3B-A 3S3B-B 3S5B-A 3S5B-B 6S3B-A 6S3B-B 6S5B 10S5B

0.73 1.22 0.92 1.05 1.39 1.19 0.90 1.25 1.04 0.98

0.69 1.24 0.91 0.99 1.33 1.19 0.83 1.12 0.98 0.93

0.96 1.01 0.91 1.05 0.93 1.01 0.86 1.07 0.99 1.04

0.92 1.03 0.91 0.99 0.89 1.01 0.79 0.96 0.94 0.98

1.08 1.10 1.03 1.20 0.89 1.12 0.93 0.99 0.97 0.98

1.03 1.11 1.02 1.14 0.85 1.12 0.86 0.89 0.91 0.92

0.92 1.11 0.95 1.10 1.07 1.11 0.90 1.10 1.00 1.00

Mean Minimum Maximum

1.07

1.02

0.98

0.94

1.03

0.99

1.03

0.73 1.39

0.69 1.33

0.86 1.07

O.79 1.03

0.89 1.20

0.85 1.12

0.90 1.11

Italics denote critical failure criterion for each frame

different column members, but which otherwise possess equal design descriptions. On average, frames with composite columns possess higher q',0~ values, but lower q'o-b values, while the values relating to drift are similar. Overall, the behaviour factors, q', determined for frames with partially-encased columns are an average of 3% greater. However, when allowance is made for the overstrength ratios, c~, the difference between the behaviour factors observed with both types of column reduces to an insignificant level. While overall the values of q' with composite and steel columns are similar, for some frame pairs the difference, especially in q'~o~, is significant. What is important, therefore, is not the type of structural member employed, but that each member is designed and detailed to ensure adequate rotation ductility. If so, the traditional benefits of composite columns such as added fire resistance and more economical stiffness and strength can be retained in earthquake resistant structures. However, due to the significance of other criteria - such as those relating to beam instability and interstorey drift - the use of composite columns will not, on their own, lead to higher behaviour factors.

Summary of evaluated behaviour factors. To provide an overview of the range of behaviour factors identified for the composite frames investigated herein, Figure 9 presents the minimum q'/e~ values with respect to column failure, beam failure and interstorey drift identified for all frames. These values are rounded to the first decimal place and classified in increments of 0.5. The number of frames for which behaviour factors were identified in each of these increments is plotted in Figure 9. It is shown that no frame failed with a q'/a~ value below 7.0, while the most common range in which frames failed was 7.0 <~ q'/c~ < 7.5. Most of the frames in this range experienced the earliest failure in their beams. With progressive increases in q'/c~, less frames fail in each increment, mainly due to the lower instance of beam failure. An exception in this regard is the range 9.5 ~< q'/c~ < 10.0 where a cluster of beam failures

12[ ] drift

I0-

~8-

[] column .

~6Z 4-

" - -

2-



~, o r<

06 ~ ~

o6 c5 06 q'/~tiValue Range

Figure 9 No. of frames possessing q-factors (q'/c~) within a number of value ranges of increment 0.5

are observed. When the behaviour factor due to drift is the critical value, it is most likely to occur in the range 9.0 ~< q'/a~ < 10.5, while column failures predominate for 10.0 ~< q'/a~. In general, however, q' values may be identified for each criterion at any point above q ' = 7.0.

Recommended behaviour factors The use in Eurocode 8 of the same behaviour factors for composite and steel structures means that the inherent robustness and ductility which composite moment-resisting frames possess cannot be fully availed of in the design process. This situation has arisen because no previous comprehensive studies into the seismic response of composite frames have been performed, hence it has not been known whether features such as increased ductility demand and varying natural response periods could diminish the advantages offered by composite structures in other directions. The results from the dynamic analyses of the seismic

Seismic response of composite frames--II: A. S. Elnashai and B. M. Broderick

722

response of moment resisting composite frames described herein can be used to recommend more appropriate behaviour factors. As no previous research has been conducted in this regard, it is not possible to compare the results achieved with an independent work. However, it is suggested here that the behaviour identified in this study is typical of that of moment-resisting composite frames as a whole; a suggestion which is based on the following rationale: (1) As any quantification of behaviour factors, or force reduction factors in general, are code-dependent, the structures employed in this quantification should fulfil the requirements of the design codes under consideration. Additionally, the design of these structures should not be over-conservative, leading to unrepresentatively high values of q'. Both of these conditions apply in this instance. (2) A wide range of structural designs have been included in the analyses, including frames with composite and steel columns, and frames which possess varying column to beam stiffness ratios. (3) To complement the number of frames analysed, six separate earthquake ground motions, selected to possess a meaningful range of characteristics, were applied in each case. Hence, a comprehensive assessment of the response to general seismic loading can be assumed from the results of the analyses. (4) The structural Eurocodes employ a limit state, partial safety factor design philosophy. This is mirrored in the procedure employed in the assessment of behaviour factors, where separate failure criteria based on the limiting behaviour of each structural element and storey are defined. To include for any uncertainties in the behaviour of individual structures, slightly conservative assessments of each failure criterion have been employed. In addition, the scaling of the earthquake loads is such as to impose more severe demands than those required by the code. With this approach, there is no need to provide an additional global allowance for uncertainties in behaviour. (5) In each instance, structural collapse is assumed when one of the failure criteria is exceeded. This is plainly a conservative assumption as it is likely that local failure will need to occur in more than one area before overall collapse is experienced. Eurocode 8 defines the behaviour factors of moment resisting frames as qcod~ = 5 C~.

(13)

O/1

This value was universally exceeded by the behaviour factors identified in the analytical studies presented above. As the minimum amount by which these identified values exceeded that given in equation (13) was 40% of the code value, it is recommended that a more accurate value for Eurocode 8 to employ would be q.

. . =. 7. .au al

(14)

The 40% increase in behaviour factors suggested by equation (14) would cause the design seismic actions for

moment-resisting composite frames to be reduced by nearly 30%, hence allowing the benefits described above to be availed of. A more conservative increase in the factor in equations(13) and (14) from 5 to 6 would reduce the design loads by over 16%, allowing some advantage to be gained from the benefits of composite frames, without altering the present code provisions too greatly. It is felt, however, that the expression in equation (14) gives the most accurate value, without resorting to undue refinement or conservatism.

Comparison of bare steel and composite frames. Given the above recommended behaviour factors for composite frames, it is worthwhile considering whether the results of this study suggest that the Eurocode 8 behaviour factors for bare steel frames are also conservative. No significant difference was observed between the behaviour factors evaluated for frames employing bare steel columns and those employing partially-encased columns. The principal reason for this, however, was that column rotation ductility demand rarely constituted the critical failure criterion for a frame, with local beam instability and interstorey drift limitations predominating. In the present study therefore, where the effects of beam-to-column connections are neglected, differences between composite and bare steel frames reduce to those attributable to the beam members. In those frames which displayed the lowest behaviour factors, local instability in beam members in negative bending was the predominant failure mode. As the local stability of steel sections is highly dependent on the web depth, it is likely that this failure condition will be more critical in the case of steel beams where deeper webs are required to provide given levels of stiffness and strength. Whereas no net axial force will exist in steel beams, the need to equilibriate the tensile force acting in the longitudinal reinforcement in negative moment regions of composite beams will give rise to axial compression in the steel joists of such members, with consequent detrimental effects on rotation ductility capacity. However, Eurocode 4 j° caters for this feature by explicitly placing more severe requirements on flange and web b/t ratios. A further implicit reduction in the maximum values of these limits is also imposed by requiring the depth of the web in compression to be included in section slenderness classifications. While the behaviour of steel beams is normally identical in negative and positive bending, composite beams display significant variations in stiffness and strength between these regions. However, in composite beams, the difference between positive and negative plastic moments leads to their behaviour under seismic loads being dominated by that displayed under positive moment 4. Hence, significant benefit in terms of energy dissipation is derived from the highly stable response, which is available in the positive moment regions of properly designed composite beams. Combined with the influence of tensile strain-hardening in the steel joist and the consequent growth in the concrete flange compression block, this leads to greater post-yield increases in bending resistance being provided by composite beams in positive bending than is the case for their bare steel equivalents. As a result, the lateral resistance of composite frames increases monotonically, even when large lateral displacements are applied. Consequently, in the dynamic analyses described in this chapter, failure criteria defining the maximum allowable degradation of resistance with displacement were never invoked. Steel frames,

Seismic response of composite frames--II: A. S. Elnashai and B. M. Broderick on the other hand, have been seen to display significant degradation in lateral resistance under increasing displacements due to seismic actions. Hence, this failure criterion may become significant, reducing the conservative lower bound on the behaviour factor. These overstrengths in bending resistance displayed by composite beams in positive bending increase the likelihood of column hinging. However, the asymmetric response of these beams also makes it less likely that such hinging will occur in column members connected to negative moment regions, especially in the case of exterior members. Hence, the simultaneous existence of sufficient plastic hinges to form a collapse mechanism is less likely. In contrast, the more uniform force distribution in steel frames implies that such simultaneous hinging may occur.

Conclusions A series of dynamic analyses have been performed to determine the response of moment-resisting composite frames to a selection of earthquake ground motions. Structural behaviour factors evaluated from the demands determined for seismic events of various intensities were found to be significantly greater than those recommended by Eurocode 8. While interstorey drift was commonly the most severe response parameter, when the variability caused by the elastic response of individual structures to different earthquake loads is taken into account, the inelastic rotation of composite beams under negative moment more usually determined the identified behaviour factors. Sufficient differences in the seismic behaviour of composite and steel frames have been identified to justify the use of separate behaviour factors in either case, and as such, the code provisions for composite structures can be amended to reflect the more accurate behaviour factors identified here. Furthermore, in contrast with the provisions for the design of steel frames, the recommended behaviour factors should not be related to the ratio of the frame resistance at beam yielding, which has little influence on the global frame response, and ultimate lateral resistance, which has little practical meaning in composite frames. In the design of composite frames to resist gravity loading, a large proportion of the negative beam moments are redistributed to positive moment regions. However, as seismic design is normally based on elastic analysis, this is not possible when earthquake loads are to be resisted. To prop-

723

erly reflect the characteristics of composite frames, plastic design procedures should be employed. The use of local behaviour factors to reduce the design forces in selected locations may allow this to be achieved without contradicting current seismic design philosophies. Overall, the enhanced rotation ductility capacities of composite members in general and the asymmetric behaviour of composite beams in particular, greatly improves the energy dissipation capabilities of moment-resisting composite frames over that of their bare steel equivalents; leading directly to the identified higher behaviour factors. While the work detailed here constitutes a comprehensive assessment of the class of structure under investigation, it would nevertheless be enhanced through comparison with similar studies on both steel frames and composite frames with different lateral resistance systems (such as braced frames). In this manner, the identified characteristics which most affect the specific behaviour of moment-resisting composite frames under seismic actions could be confirmed and the suggestions for improved design guidance given here extended to a wider range of structures.

References 1 Eurocode 8, Structures in Seismic Regions, Commission of the European Communities, ENV 1989, 1994 2 Kappos, A. J. 'Analytical prediction of the collapse earthquake for R/C buildings: suggested methodology', Earthquake Engng Struct. Dyn. 1991, 20, 167-176 3 Broderick, B. M. and EInashai, A. S. 'Seismic response of composite frames. Part 1: response criteria and input motion', Engng Struet. 1995 4 Broderick, B. M. Seismic testing, analysis and design of composite frames. PhD thesis, Imperial College, University of London, 1994 5 Elnashai, A. S. and Broderick, B. M. 'Seismic resistance of composite beam-columns in multi-storey structures. Part 1: experimental studies', J. Const. Steel Res. 1994, 30, 201-230 6 Broderick, B. M. and Elnashai, A. S. 'Seismic resistance of composite beam-columns in multi-storey structures. Part 2: analytical model and discussion of results', J. Const. Steel Res. 1994, 30, 231-258 7 Madas, P. J. and Elnashai, A. S. 'A new passive confinement model for the analysis of concrete structures subjected to cyclic and transient dynamic loading', Earthquake Engng Struct. Dyn. 1992, 21,409-431 8 Amadio, C., Benussi, F., Noe, S. and Spanghero, F. 'Semi-rigid composite frames under seismic actions', Proc. lOth European Conf. Earthquake Engineering, Vienna, Austria, 1994 9 Climenhaga, J. J. and Johnson, R. P. 'Local buckling in continuous composite beams', Struct. Engnr 1972, 50, 367-374 10 Eurocode 4, Design of Steel and Concrete Structures - Part I- 1: general rules and rules for buildings, Commission of the European Communities, ENV 1994-1-1, 1992