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Floor Response Spectra for the Design of Acceleration

Sensitive Light Nonstructural Systems in Buildings

J. F. Velásquez ROSE SCHOOL

– Istituto Universitario di Studi

Superiori. University of Pavia, Italy

J. I. Restrepo Department of structural EngineeringUniversity of California, San Diego-USA

C. A. Blandón Escuela de Ingeniería de Antioquia, Colombia

SUMMARY:

Using data collected from the full-scale test of a 7-story reinforced concrete bearing wall building slice testedon the NEES-UCSD Large High-Performance Outdoor Shake Table of the University of California at San

Diego, this paper compares the design requirements for acceleration-sensitive nonstructural componentscontained in the Colombian seismic code NSR-10, the European seismic code EUROCODE 8 and U.S. seismic

code ASCE/SEI 7-10.

The building was subjected to four historical ground motions recorded in Southern California, representing

seismic demands for different hazard levels, including a test representing the design basis earthquake as isdefined in the United States. The building experienced extensive nonlinear response during the design basis

earthquake.

Elastic and inelastic floor response spectra were computed from the total floor accelerations recorded in the

building during each of the tests. Assuming the nonstructural components and the main structure are fully

decoupled, the study identifies those main parameters that affect the demands, such as modal periods andstrength and ductility of the supporting structure and element location, as well as its own natural period,

ductility in the nonstructural component and damping.

It is concluded that the current seismic codes may not adequately address the design of acceleration-sensitive

nonstructural components.

Keywords: Floor Response Spectra; Nonstructural Components; Seismic Codes; Shake Table Testing

1. INTRODUCTION

In recent years, building owners, lessees, territorial authorities, architects, mechanical and structuralengineers have become more aware that satisfactory seismic building performance is not onlyconfined to the performance of the structural system but also of the nonstructural subsystems andcontents. By definition, nonstructural systems are those systems and elements housed or attached tothe floors, roofs, and walls of a building or industrial facility that are not part of the main load bearingstructural system. Those systems may also be subjected to large seismic forces and must depend ontheir own structural characteristics to resist these forces (Villaverde, 1997). In this work, thosesystems will be referred as nonstructural components [NSCs].

A slice of the prototype building was designed for lateral forces obtained from a displacement-baseddesign methodology (Panagiotou and Restrepo, 2011) built at full-scale and tested on the large high- performance outside shake table [LHPOST] of the University of California at San Diego, see Figure 1.

The building test was subjected to four historical earthquakes (Panagiotou et al., 2011), recorded inSouthern California. This study makes use of the floor acceleration recordings taken during the





Figure 2. Acceleration Time Histories and Response Spectra as Reproduced on the LHPOST (Panagiotou etal., 2011)

3. BUILDING RESPONSE

3.1. Floor Acceleration Time Histories for Phase I

The response of the structure to the EQ1 input motion was practically linear, for motions EQ2 andEQ3 the response was moderately nonlinear, with maximum tensile strains in the longitudinalreinforcement reaching 1.8% and a roof drift ratio of about 0.8%. For motion EQ3 the response washighly nonlinear, with strains in the longitudinal reinforcement reaching 2.9% and a roof drift ratio of

2.1% (Panagiotou et al., 2011). Table 1 lists the maximum absolute acceleration on each floor in thedirection of shaking (east-west), for each earthquake. It can be seen in this table that (i) flooraccelerations increase with an increase in the intensity of the ground motion, (ii) floor accelerationsgenerally tend to increase with height, and that (iii) the relative base/upper level floor accelerationincrease is more pronounced in the low intensity ground motion EQ1 than in the strong intensityground motion EQ4. These observations will be discussed in more detail in the following section.

Table 1. Maximum Values of Building Response for Phase I Maximum Absolute Floor Acceleration (g)

Floor EQ1 EQ2 EQ3 EQ4

7 0.42 0.59 0.73 1.08

6 0.35 0.49 0.53 0.72

5 0.31 0.40 0.42 0.664 0.27 0.34 0.40 0.79

3 0.20 0.31 0.39 0.78

2 0.17 0.32 0.36 0.77

1 0.15 0.26 0.33 0.86

Platen 0.15 0.26 0.34 0.91

3.2. Variation of the Period with Shaking Intensity

The variation of the building first and second translational periods identified from WN vibration testsis plotted in Figure 3. At the beginning of the test program for Phase I, the building had a fundamental

period of 0.51 sec. After testing with the EQ1 motion, the fundamental period lengthened to 0.65 sec.After tests to motions EQ2 and EQ3, the fundamental period lengthened to 0.82 sec. and 0.88 sec. Thefundamental period lengthening was primarily the result of the loss of tension stiffening across the



cracked concrete. Finally, the fundamental period was 1.16 sec. after test EQ4. It can be also seenfrom Figure 3 that the second mode period, remained practically constant throughout testing at around0.1 sec.

Figure 3. Variation of the First and the Second Mode Periods with Shaking Intensity for Phase I (adapted fromPanagiotou et al., 2011)

3.3. Normalized Total Floor Accelerations

Figure 4 plots the envelopes of the total floor accelerations normalized by the peak ground

acceleration (PGA) for Phase I of testing. It can be seen in Figure 4 that floor accelerations weregreater than PGA for records EQ1 to EQ3. However, for EQ4, when significant nonlinear responseoccurred, the roof acceleration tended towards PGA, and most floors experienced accelerations belowPGA, indicating saturation of the response.

Figure 4. Total Floor Acceleration Normalized by PGA

4. FLOOR RESPONSE SPECTRA

It is recognized that NSCs are difficult to analyze accurately. It is always possible to consider them inconjunction with the analysis of their supporting primary structures, but a combined nonlinear primary- nonlinear secondary system generally is, at this point, only practical in academia. The

method of analysis used herein for the purpose of analyzing NSCs is through the constant ductilityresponse spectra [CDS] (Chopra, 2001), termed herein the constant ductility floor response spectra

0

1

2

3

4

5

6

7

0.0 1.0 2.0 3.0

S t o r y

Normalized Total Acceleration ,

a/agmax

EQ2

EQ1

EQ3

EQ4

PHASE I



[CDFRS] because it uses the total accelerations recorded in various floors during the tests. TheCDFRS considers that the NCS and the structure are fully decoupled. The advantage of usingexperimental data like the one obtained from the 7-story building test, is that there is no uncertaintyregarding the nonlinear response of the primary structure, including its inherent damping.

The CDFRS discussed in this paper were computed using the Clough hysteretic rule (Clough, 1966)

as the restoring term in the equation of motion for the NCS. These spectra were calculated assuminga damping ratio of 2.5%; a post-yield to initial stiffness ratio equal to 2.5%; and nonstructuralcomponent ductility p = 1.5, and 6.0. More details of the computational program are presented byVelásquez (2011).

Figure 5 shows CDFRS (pseudo-acceleration and displacement) obtained for the roof level motions.The envelope of each set of spectra is also shown. It is seen that the envelopes are controlled by EQ4,which was the design earthquake for the test building. It is noted that CDFRS for EQ3 and EQ4 arenot very dissimilar, despite these motions correspond to different ground motion intensities.

Figure 5. Roof Level CDFRS for EQ1-EQ4 and Envelopes

From analysis of the various CDFRS, not shown here, the post-yield to elastic stiffness ratio wasfound to have a minor effect on the response. Furthermore, the roof displacement response spectraclearly indicate that displacement demands are sensitive to the ductility p of the NSC. In general,and for up to 0.4 sec., as p increases, the displacement demands on the NSC increase.

Figure 6 plots the spectral displacement envelopes for various values of p obtained for the roof level

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

P s e u d o - a c c e l e r a t i o n

( g )

Period, T p (s)

= 2.5%

r =2.5%

Story: 7

Phase I

Elastic

EQ4

EQ1

EQ3

EQ2

Envelope

0.00

0.05

0.10

0.15

0.20

0.25

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

D i s p l a c e m e n t ( m )

Period, T p (s)

= 2.5%

r =2.5%

Story: 7

Phase I

Elastic

EQ4

EQ1

EQ3

EQ2

Envelope

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

P s e u d o - a c c e l e r a t i o n

( g )

Period, T p (s)

= 2.5%

r =2.5%

Story: 7

Phase I

p= 3.0

EQ4Envelope

EQ1EQ2

EQ3

0.00

0.05

0.10

0.15

0.20

0.25

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40


Period, T p (s)

= 2.5%

r =2.5%

Story: 7

Phase I

p= 3.0

EQ3

EQ4

Envelope

EQ2

EQ1

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

P s e u d o - a c c e l

e r a t i o n ( g )

Period, T p (s)

= 2.5%

r =2.5%

Story: 7

Phase I

p= 6.0

EQ4

Envelope

EQ1EQ2

EQ3

0.00

0.05

0.10

0.15

0.20

0.25

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

D i s p l a c

e m e n t ( m )

Period (s)

= 2.5%

r =2.5%

Story: 7

Phase I

p= 6.0

EQ3EQ4

Envelope

EQ1

EQ2



motions. This figure clearly shows the dependency of spectral displacement with p and NSC period. There is, however, a period where an inversion occurs and spectral displacements for thelarger component ductility become smaller than even those for elastic response. Such inversionoccurs at a period short of the predominant period of response of the primary structure and is notshown in Figure 6. Since this period is greater than the period considered for NSCs it will not beaddressed further in this paper.

Figure 6. Roof Level Displacement Response Spectra Envelopes for EQ1-EQ4 for Various Ductilities

Another way to post-processed the data is to obtain R p-T p- p relationships, where R p is the forcereduction factor for the design of of the NSC. Such relationships are plotted Figure 7 for the rooflevel motions and for p = 3 and 6. The average value R p computed for the four test motions is alsoshown in Figure 7. It is important to note in Figure 7 that R p and p are not of the same order, with R p being smaller than p, and that R p increases somewhat with an increase in p. In design codesvalues of R p are usually derived on the basis of engineering expert opinion assuming R p and p aresimilar. Finally, it can be also seen in Figure 7 that there the values computed for R p are stronglyinfluenced by the ground motion.

Figure 7. R p -T- p Relationships Computed for the Roof Level Input Motions EQ1-EQ4

The results of the analyses can also be investigated from a displacement perspective adapting thedisplacement coefficients C defined by Miranda (2001). In the context of this study suchcoefficients are termed C p because they are derived as the ratio between the displacement demandsfor a component with a given period and ductility to the displacement demand of an elasticcomponent with the same period and damping ratio. Figure 8 plots the average C p ratios obtainedfrom the 7-story building roof level motions during tests EQ1-EQ4. The C p ratios obtained areductility and period dependent. In the period range shown in Fig. 7, coefficients C p are greater thanone. At periods close to but greater than the predominant period of the primary structure suchcoefficients can reach values less than one.

0.00

0.05

0.10

0.15

0.20

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40


Period, T p (s)

= 2.5%

r =2.5%

Story: 7

Phase I p= 6.0

p= 3.0

p= 1.5

p= 1.0

1.0

1.5

2.0

2.5

3.0

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

R e d u c t i o n f a c t o r , R p

Period, T p (s)

EQ4

EQ2

= 2.5%

r =2.5%

Story: 7

Phase I

p= 3.0

EQ3

EQ1

Average

1.0

2.0

3.0

4.0

5.0

6.0

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

R e d u c t i o n f a c t o r , R p

Period, T p (s)

EQ4

EQ2

= 2.5%

r =2.5%

Story: 7

Phase I

p= 6.0

EQ1

EQ3 Average



Figure 8. Average C p Ratios for EQ1-EQ4 for Different Ductilities Calculated for Phases I

5. COMPARISON OF THE FLOOR RESPONSE SPECTRA TO SEISMIC CODES EXAMINED

Nonstructural components typically have fundamental periods equal or less than 0.4 sec. It isassumed that nonstructural components with periods less than 0.2 sec. are “rigid ”; whereas, thosewith periods equal or greater than 0.2 sec. are “flexible ”.

The requirements for the design of NSCs specified by NSR-10 (2010), EUROCODE 8 (2003) andU.S. seismic code ASCE/SEI 7-10 (2010) are examined. It is assumed, as an example, the building issubjected to EQ4 ground motion in Phase I of the testing three different NSCs are considered, eachone of them with a damping ratio of 2.5% and the post yielding to initial stiffness ratio of 2.5%.

Example NSC (1) is an electrical equipment, considered rigid, with a period of T p =0.1 sec. Examples NCS (2) and NCS (3) are considered flexible, and having periods T p =0.2 sec. and T p =0.4 sec. piping

system (2), respectively.

The normalized horizontal seismic force, well-known as the seismic coefficient, S a /g , acting on NSCs, for each seismic code, is listed in Table 2. The seismic coefficient for Colombian code isobtained by Equation (5.1). For more detailed of the computation of the seismic coefficient, thereader is referred to NSR-10 (2010).

Where x: the acceleration on the support of the NSC.

p: the dynamic amplification of the NSC.

p: the energy dissipation capacity in the inelastic range of the NSC. I : the importance factor. Aa: the effective peak acceleration.

For EUROCODE 8 and ASCE/SEI 7-10, the seismic coefficient is given by Equations (5.2) and(5.3), respectively.

Where a: the seismic coefficient applicable to NSC.a: the importance factor of the NSC.

a: the behavior factor of the NSC.

For more detailed of the computation of the seismic coefficient for the European code, the reader is

1.0

2.0

3.0

4.0

5.0

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

C

p

Period, T p (s)

= 2.5%

r =2.5%

Story: 7

Phase I

= 6.0

= 3.0

= 1.5



referred to EUROCODE-8 (2003).

(

)

Where

DS : the spectral acceleration at short period which is equal to

.

MS : the mapped considered earthquake spectral response acceleration for short periodsadjusted for site class effect.

p: the component amplification factor to account for flexibility of the NSC, which variesfrom 1.0 to 2.5. The coefficient is assigned for equipment generally regarded asrigid (fundamental period <0.06 s) and rigidly attached, is for equipmentgenerally regarded as flexible (fundamental period >0.06 s) and flexibly attached.

p: the component importance factor that varies from 1.0 to 1.5. p: the component response modification factor that varies from 1.00 to 12.: the height of point of attachment of NSC with respect to the base.: the average roof height of structure with respect to the base.

For more detailed of the computation of the seismic coefficient by American code, the reader should be referred to ASCE/SEI 7-10 (2010).

Table 2 also lists the relative slab-component displacement demand computed from the motionsrecorded at the roof level. The procedure to compute the displacement demand on the NSCs for the NSR-10 seismic code will be discussed below. This procedure also applies for the other codesexamined.

Table 2. Value of the Seismic Coefficient acting on NSCs and its respective displacement, for each SeismicCode Examined

NSR-10 EUROCODE-8 ASCE/SEI 7-10

S a /g S d [m] S a /g S d [m] S a /g S d [m]

NSC (1) 0.60 >0.013 0.86 >0.013 0.70 >0.013

NSC (2) 1.50 0.023 0.86 >0.053 0.97 0.053NSC (3) 1.50 0.115 0.86 0.18 0.97 0.15

NSC (1): Electrical equipment

NSC (2): Piping system (1)

NSC (3): Piping system (2)

For T p = 0.1 sec., and F p /W p = 0.6 we look at the component ductility demand that satisfies thiscondition on the envelopes of the pseudo-acceleration response spectrum for Phase I shown on theleft column of Figure 5. For a component ductility of p = 6 and T p = 0.1 s we need F p /W p = 1.03,which is greater than the value required by the code. This implies that the component will besubjected to a ductility level greater than 6. Now looking at the spectral displacement plots in Figure5 for T p = 0.1 s and p = 6 we determine that the spectral displacement in Phase I is 0.013 m. That is,such component will likely experience a relative slab-component displacement greater than 0.013 m.

Whether such component can resist several inelastic cycles to 0.013 m is the question. If inelasticdeformations take place on the bolts anchored to the slab, such displacement demands seem large butcould be acceptable as long as life-safety is not compromised. If the equipment hangs, failure of thefastenings could be life-threatening. However, if the equipment is installed above the slab failurewould not be necessarily be life-threatening.

For the piping system NCS (1), a value of F p /W p = 1.5 is required by the Colombian code. Now, weinvestigate in Figure 5 what component ductility p has S a /g = 1.5 for T p =0.2 sec. We find that forPhase I, S a /g = 1.5 when p is approximately equal to 1.5. It is very interesting to see that in this particular example, the demand is governed by EQ3, which was not the strongest intensity motionand had a greater probability of exceedance than the strong intensity motion EQ4. The spectraldisplacement demand for this component is from Figure 5 equal to 0.023 m. Such demand is at the

effective length of the pipe subsystem. Effective length is used here in a similar context as the termeffective height is used in a building. Greater relative slab-pipe displacement may occur in locations



in the pipe subsystem away from its effective length depending on the boundary conditions. Whatmay be important to note is that the displacement demands could be tolerated by the piping systemand could be considered acceptable for life-safety, and even for immediate operation.

Finally, for the piping system NCS (3), the code requires F p /W p = 1.5. Looking at the value ofcomponent ductility which has S a /g =1.5, we find that this value is approximately half way between

the envelopes computed for p = 1.5 and for p = 3. The spectral displacement for this component,from Figure 5, for p = 1.5 is 0.102 m and for p = 3 is 0.128 m. Taking the average for these valueswe can approximate the solution to 0.115 m, which could be considered high and, most likely,unattainable by a piping system.

6. CONCLUSIONS

1. The motions recorded at the roof level during the testing of a 7-story bearing wall building lsicewere analyzed to obtain constant ductility floor response spectra that could be used to comparecurrent design recommendations for the design of nonstructural components in buildings.

2. The roof displacement response spectra clearly indicate that displacement demands are sensitiveto the ductility of the nonstructural component. In general, and for periods up to 0.4 sec., as thedisplacement ductility increases, the displacement demand on the NSC increases.

3. Data reduction of the floor response spectra for the short period range shows that the relationship between the component displacement ductility and the component force reduction factor Rpratios are period dependent and can be quite different from the ductility of the component. Thisis not currently reflected by any of the codes examined. Furthermore, codes make very littleemphasis, if any, on the displacement demands that components will be subjected to. Thisresearch work has highlighted that displacement demands in components designed followingthree codes may be large and, in some cases, quite difficult to attain.

AKCNOWLEDGEMENT

The authors sincerely thank the Englekirk Board of Advisors, at University of California, San Diegoindustry group supporting research in structural engineering. They also thank the Charles PankowFoundation, the Portland Cement Association, and UC-Mexus who provided financial support fordifferent parts of the project. Finally, the authors thank Prof. Marios Panagiotou of UC Berkeley forhelping with data interpretation.

REFERENCES

ASCE - American Society of Civil Engineers. (2010). Minimum Design Loads for Buildings and Other

Structures, ASCE/SEI 7-10. Virginia.

Chopra, A. (2001). Dynamics of Structures: Theory and Applications to Earthquake Engineering, 3rd. New

Jersey.Clough, R.W. (1966). Effect of Stiffness Degradation on Earthquake Ductility Requirements. Technical Report

SESM 66-16 , Department of Civil Engineering, University of California, Berkeley CA 94720.

Eurocode 8. (2003). Design of Structures for Earthquake Resistance - Part 1: General Rules, Seismic Actions

and Rules for Buildings. Brussels.

Hoehler, M.S., Panagiotou, M., Restrepo, J.I., Silva, J.F., Floriani, L., Bourgund, U. and Gassner, H. (2009).

Performance of Suspended Pipes and Their Anchorages During Shake Table Testing of a Seven-Story

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Story Full-Scale Building Slice Tested on the UCSD-NEES Shake Table. Journal of Structural Engineering

137(6), pp. 705-717. NSR-10. (2010). Reglamento Colombiano de Construcción Sismo Resistente. Bogotá D.C., Colombia.

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Phase I: Rectangular Wall. Journal of Structural Engineering 137(6), pp. 691-704.

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