Preliminary Analytical Findings for Floor Inertia Force Limiting Anchorage System Under

Preliminary Analytical Findings for Floor Inertia Force Limiting Anchorage System under

Earthquake Loading

ABSTRACT

An innovative floor anchorage isolation system that reduces inertial forces during major earthquakes is being developed through a multi-university NSF/NEES research project. Different than floor isolation systems proposed previously that isolate an entire story of the structure, the isolating effect is introduced between the primary (vertical) elements of the lateral force resisting system and the gravity load resisting system. This isolation effect achieved by placing a ductile anchorage connector between the lateral force resisting system and the floor diaphragm has potential to reduce the diaphragm acceleration and inertia force and further reduce the seismic demand on the lateral force resisting system. This paper presents a preliminary analytical study for the floor anchorage isolation system focusing on the sensitivities of several design and modeling parameters on the structure seismic response. A trail design space for a 12-story shear wall structure using the isolation system has been proposed. 1. INTRUDCTION

An innovative floor anchorage isolation system that reduces inertial forces during major earthquakes is being developed through a multi-university NSF/NEES research project. In this system, different than floor isolation systems proposed previously that isolate an entire story of the structure, the isolating effect is introduced between the primary (vertical) elements of the lateral force resisting system (LFRS), e.g. cores, shear walls, braced or moment frames, and the gravity load resisting system (GLRS), i.e. the floor system and gravity columns. The idea of separating the LFRS and the GLRS is attractive since nearly all of the building’s mass originates in the GLRS, in particular within the floor systems, and hence is the source of most of the inertial forces acting during a seismic event.

An anchorage connector is introduced to isolate the floor system and the primary LFRS elements.

The connector is initially stiff and strong, and intended to transfer the ground motion excitation to the structure without relative movement of the floor under service level earthquake. However, at a predefined force level, e.g. design basis earthquake (DBE) level, the primary transfer mechanism “cuts-off”. At this point, the anchorage, responding as a ductile connector, dissipates energy through the relative motion

(sliding) of the floor to the primary LFRS elements. This “cuts-off” mechanism limits the transmissibility of accelerations from the LFRS to the floor system. The seismic forces carried by building structures originate almost entirely from the inertia of the floor system mass. Therefore, a reduction of the transmissibility of accelerations from the LFRS to the floor system has the potential to reduce most responses associated with seismic excitation, including (1) seismic demands in the primary vertical LFRS elements; (2) inertia forces in the floor diaphragm; and (3) floor accelerations that could lead to nonstructural damage.

The floor anchorage isolation system needs to control the relative movement between the floor system and the primary LFRS within a manageable range (in an order of 10cm or less) while it is still able to reduce the structure seismic demands for two reasons: (1) large relative movement requires special considerations for mechanical and architectural elements (cladding, full-height partitions, conduits, etc.), and substantial gaps and expansion joints; (2) large relative movement might result in an excessive gravity column drift.

As a first step of the research project, relationships between the floor anchorage connector yield

(“cut-off”) strength and the seismic responses of structures have to be developed. These relationships are used to establish a design space for the floor anchorage isolation system which is able to reduce the structure seismic demand without excessive relative movement between the floor system and the primary

LFRS. This paper presents the preliminary results and findings of an analytical study for developing these relationships for several sensitive parameters such as number of stories, anchorage connector properties and gravity system participation. A trail design space for the floor anchorage isolation system is proposed based on these results and findings.

2. BACKGROUND

Floor Isolation System

Floor isolation systems have been proposed previously to reduce seismic response including:

(1) by isolating single or multiple stories e.g. for system response reduction using the roof

(Villaverde and Mosqueda 1999) in a manner similar to that desired of a tuned-mass damper (Villaverde et al. 2004), the middle story of a high rise (Tsuneki et al. 2008), single floors distributed at key locations in the structure (Ryan and Earl 2010), or by segmenting the building into independent regions (Pan et al. 1995). The typical isolation system adopts the vibration absorber consisting of mass, spring (linear and nonlinear) and damper (viscous and hysteretic), e.g. elastic rubber bearing plus viscous damper (Villaverde and Mosqueda 1999), elastic rubber bearing plus hysteretic damper (Tsuneki et al. 2008) and nonlinear steel oval damper (Villaverde et al. 2004). The seismic response of the structure can be significantly reduced by using the vibration absorber at single or multiple stories (Ryan and Earl 2010) though the isolation system usually incurs large sliding response (40-65cm).

(2) for precious non-structural equipment (e.g. computers, emergency generators, or hazardous material) by placing a restoring device (typically elastic springs) between the equipment and the structure (Kondo 1987) (Ishida and Fujita 1983) (Kurabayashi et al. 1983).

The isolation devices are designed to store the seismic energy in the elastic springs and damp the forces transmitted to the equipment.

(3) isolating the LFRS and GLRS using elastic springs and viscous dampers (Mar and

Tipping 2007) or nonlinear hysteretic connection (Crane 2004) between the LFRS and GLRS.

The structure inertial forces can be significantly reduced through the isolation system between

LFRS and GLRS and the seismic energy can be dissipated through viscous or hysteretic dampers. By placing the GLRS columns on sliders at the lowest story, Mar and Tipping (2000) demonstrated through simulation that an isolated GLRS could significantly reduce inertial forces, and by introducing a system of elastic spring devices and viscous dampers as the connection between the isolated GLRS and fixed base LFRS, could reduce the sliding displacements relative to a traditional base isolation system, while also avoiding costly special detailing in the foundation.

Characteristics of Floor Anchorage Connector

The floor anchorage connector needs to possess the following characteristics: (1) initially stiff and strong to prevent the relative movement between the floor and LFRS under service level earthquake; (2) large deformation capacity to accommodate the large relative movement; (3) energy dissipation capability; (4) self-centering or partial self-centering capability to minimize the residual relative movement. Three distinct types of devices (See Fig. 1) are able to achieve the required characteristics for the anchorage connector along or in combination: (1) Hysteretic energy dissipation devices to provide initial stiffness/strength and energy dissipation; (2) Elastic restoring devices to provide secondary stiffness and self-centering; and (3) passive damping devices to provide supplemental damping for energy dissipation.

Force Force Force

Relative Relative Relative displacement displacement displacement

Fig.1. Anchorage connector: (a) Hysteretic energy dissipation; (b) Elastic resorting; (c) passive damping. 3. STUDY DESCRIPTION

Prototype Structure

Prototype structure being evaluated in this paper is a perimeter shear wall residential building. As seen in plan view of Figure 2, the structure has a footprint of 180’ x 100’. The floor- to-floor height is 10.5’ for the typical floor and 16’ at the 1st story. The floor slab thickness is 8”.

The lateral force resisting system (LFRS) is perimeter RC wall at each face of structure. The typical floor mass is 135psf. The column spacing is 33’. Structure heights of 5, 12 and 16 stories are being evaluated.

Fig. 2. Plan of PS#1 for the 12-story structure.

The prototype structure seismic design is based on ASCE 7 (2005). The seismic design site

is Berkeley (CA): SDC E and soil class C (Ss=2.08, S1=0.92). The seismic-resistant system is

special reinforced concrete (RC) shear wall (R=6, o=2.5, Cd=5). As an example, the Equivalent

Lateral Force (ELF) procedure for the 12-story structure (Cs=0.122, T=1.09 sec) appears in Table

1. The shear wall design is based on ACI (2008). Inelastic action is assumed to be limited to the base. The final design section example for the 12-story structure at shear wall base is shown in Fig. 3.

Table 1. Calculations of Equivalent Lateral Forces for the 12-story structure

k Stor hx (ft) Wx (kips) Wx hx Cvx Fx (kips) Fpx (kips)* V M (k-ft) y (kips) 12 131.5 2430 1338944 0.168 599 674 599 6286 11 121 2430 1202290 0.151 538 674 1136 18215 10 110.5 2430 1069078 0.134 478 674 1614 35164 9 100 2430 939537 0.118 420 674 2034 56523 8 89.5 2430 813934 0.102 364 674 2398 81703 7 79 2430 692594 0.087 310 674 2708 110135 6 68.5 2430 575909 0.072 257 674 2965 141270 5 58 2430 464378 0.058 208 674 3173 174585 4 47.5 2430 358647 0.045 160 674 3333 209583 3 37 2430 259607 0.033 116 674 3449 245801 2 26.5 2430 168575 0.021 75 674 3525 282810 1 16 2430 87765 0.011 39 674 3564 339832 Sum 29160 7971258 1 3564

* Note: Fpx is controlled by lower bound value (0.2SDSWx)

65' 1'

12#18 2#4 @ 14"

Fig. 3. Wall section detailing at base for the 12-story structure.

Study Parameters

Several parameters which might be sensitive to the structure seismic response using the floor anchorage isolation system are considered in the study. These parameters include: (1) number of story; (2) gravity system participations including gravity system modeling, P- effect and column base condition; (3) secondary slope (post-yielding stiffness, K2) of the anchorage

connector quantified as the ratio between post-yield stiffness and initial stiffness (Ki); and (4) adding viscous damper. A full list of the parameter combination used for each set of analysis is shown in Table 2. As noticed in Table 2, most analyses are performed with the 12-story structure and only a limited set of analyses are performed with the 5 and 16 story structures. Therefore the trial design space proposed in this paper is established only for the 12-story structure.

Table 2. Analytical study parameter combinations

Analysis Set # of GLRS participation Anchorage connection

stories GLRS model P-D Base BC Type Secondary Strength slope distribution

1 Effect of 5 Cantilever column Yes Pinned Hysteresis 0% constant

building 12 Cantilever column Yes Pinned Hysteresis 0% constant

height 16 Cantilever column Yes Pinned Hysteresis 0% constant

2 Effect of 12 No column No - Hysteresis 0% constant

GLRS 12 Cantilever column No Pinned Hysteresis 0% constant

modeling 12 Cantilever column Yes Pinned Hysteresis 0% constant

12 Gravity frame Yes Pinned Hysteresis 0% constant

3 Effect of 12 Gravity frame Yes Pinned Hysteresis 0.4% constant/varying

column 12 Gravity frame Yes Fixed Hysteresis 0.4% constant base BC

4 Effect of 12 Cantilever column Yes Pinned Hysteresis 0%, 0.4% constant

secondary 12 Gravity frame Yes Pinned Hysteresis+ Varying constant slope Elastic

5 Effect of 12 Cantilever column Yes Pinned Hysteresis+ 0% constant viscous damping

damper 12 Gravity frame Yes Pinned Hysteresis+ 0.4% varying damping

Study Procedure

Each set of analyses with the different parameters listed in Table 2 is performed for the structures with different anchorage connector strengths. As shown in Table 3, the anchorage

connector strength is normalized by the current code diaphragm force Fpx at top floor (see Table

1) and has a constant distribution along building height. Since current code uses a load factor

E=1.0, an overstrength factor (for shear walls) o = 2.5 applied to collectors, and a strength reduction factor,  =0.75, current code design strength is indicated as 2.5/0.75 = 3.33. The anchorage connector strength changes proportionally with the strength since its yield deformation is approximately set as 0.045” based on cyclic shear test results for the dowel anchorage bars (Naito et al. 2006).

Table 3. Anchorage connector strength and stiffness.

2FY/Fpx* Connector strength (FY) Initial Stiffness (Ki) [kips] [k/in]

0.03Fpx 11 248

0.33Fpx 113 2476

0.67Fpx 226 4961

1.01Fpx 339 7442

1.34Fpx 453 9922

1.68Fpx 566 12403

2.35Fpx 792 17364

3.35Fpx 1132 24805 Elastic Elastic 24805 * Two connectors per floor (one connector per each shear wall)

The analyses are conducted using earthquake simulations under maximum considered earthquake (MCE). For each earthquake simulations, the following maximum structure responses are measured: (1) LFRS responses including base plastic rotation, inter-story drift and internal force demand; (2) GLRS responses including floor acceleration, inter-story drift and internal force demand; and (3) anchorage connector responses including force, deformation and residual deformation. These measured maximum structure responses are used to developed the relationships between the floor anchorage yield (“cut-off”) strength and the seismic responses of structures and further to establish the trial design space for the floor anchorage isolation system as mentioned in previous section.

Ground Motion

A suite of 10 ground motions selected from the historical earthquakes is used for the analytical study. The ground motion information is listed in Table 4. The ground motions have been scaled using the factors shown in Table 4 to match the 5% damping design spectrum for

Berkeley, CA (see Fig.4) at DBE level. For MCE level simulations, the scaled ground motions have been further scaled by a factor of 1.5. The analytical results presented in this paper are the mean values of the 10 ground motions.

Table 4. Selected ground motion information # Earthquake Magnitude Date PGA (g) Scaling factor EQ1 Chi Chi 7.6 9/20/1999 0.53 0.88 EQ2 Chi Chi 7.6 9/20/1999 0.69 1.67 EQ3 Erzincan, Turkey 6.7 3/13/1992 0.68 1.38 EQ4 Imperial Valley 6.5 10/15/1979 1.04 1.73 EQ5 Loma Prieta 7.0 10/17/1989 0.41 0.72 EQ6 Loma Prieta 7.0 10/17/1989 0.69 2.14 EQ7 Northridge 6.7 1/17/1994 0.69 0.82 EQ8 Northridge 6.7 1/17/1994 0.50 1.06 EQ9 Superstition Hills (B) 6.7 11/24/1987 0.67 1.76 EQ10 Tabas, Iran 7.4 9/16/1978 0.78 0.93 3 Average Design

2 ) g (

0 0 1 2 3 T (s)

Fig. 4. Response spectrum with 5% damping.

Analytical Modeling

Four two-dimensional (2D) models were created using OPENSEES for the analytical study: Model A (no gravity system); Model B (with gravity system); Model C (with gravity system and P- effects); and Model D with the gravity frame action included (and P- effects) as shown in Figure 5. The intent of evaluating these models is to broadly determine the sensitivity of response to inherent gravity system stiffness, P- effects, and gravity system frame action. The LFRS is modeled as elastic beam column element with base hinge (nonlinear rotational spring) representing the behavior of a reinforced concrete shear wall. For the anchorage connector, the hysteretic device is modeled as a nonlinear spring with variable post-yield stiffness; the elastic restoring device as an elastic spring; and the supplemental damping device as a viscous material element. The gravity columns in model B and C are modeled as a single 2D elastic beam column element (Icr=0.7Ig) with sum of the stiffness and area of all columns in the structure and pinned connected to the base and at each floor. For model D with gravity frame action, each column in the frame model represents the sum of the columns in the same column line, i.e. 4 columns for exterior column and 5 columns for interior column. The floor slab is modeled as elastic beam element with 8” thickness and sum of six floor strip effective width (L/4=100”). The crack section properties are used for column

(Icr=0.7Ig) and floor slab (Icr=0.25IgTwo types column base conditions are considered in the analysis: (1) one is pinned connection as shown in Fig. 5; (2) the other is fixed connection. The gravity load applied in model C and D is dead load plus 25% of live load. The P- effect is included. 2% Rayleigh damping is used in the earthquake simulation. The damping coefficients are determined from a modal analysis with the 2% critical damping anchoring at 1st and last significant model (the accumulative mass participation is larger than 99%). Force Floor mass P=1.0DL+0.25LL

Nonlinear Anchorage Ki spring Connection Sliding

Moment

Gravity Rotation Base hinge column LFRS Model A Model B Model C

Floor: Elastic beam Exterior Floor Strip column A

Interior B column A A L

Model D Fig.5. 2D Models used for the analytical study.

4. ANALYTICAL RESULTS

Analytical results are presented in two sections. First, the general system seismic behaviors are reported based on the results from the analysis set of 2a which uses the simplest model (Model A) and the elastic-perfect plastic hysteresis model for the anchorage connector. Second, the parameters sensitivities on the seismic responses of the structure with anchorage floor isolation system are discussed.

4.1 General Results

Figure 6 shows the maximum shear wall seismic responses vs. the anchorage connector strength: (a) base flexural plastic rotation; and (b) base shear force. As seen in Fig.6, generally shear wall seismic responses reduces with the decrease of the anchorage connector strength. Also noticed in Fig. 6 that the anchorage connector elastic force demand is about 7 times of the

diaphragm design force Fpx. This high force demand is caused by the structural higher modes responses (Rodriguez et al. 2002) since the floor force demand due to 1st mode response is

limited close to design level (Fpx) by the yielding of shear wall base. It has been pointed out by other researchers (Eberhard and Sozen 1993) that the shear wall base flexural plastic rotation response is controlled by the 1st mode response while the shear wall base shear and diaphragm force are controlled by higher modes. Therefore the shear wall base flexural plastic rotation response does not reduce until the anchorage connector strength is lower than the diaphragm

st design force Fpx which is based on the structure 1 mode response. On the other hand, the shear base shear force immediately starts to reduce as the anchorage connector strength decreases from elastic state.

0.025 4 3.5 )

d 0.02

a 3 r (

e Current n 2.5

0.015 d , o

i Elastic w t

s 2 Design a t V / o 0.01 Current r

Elastic s c i

Design V t 1 0.005s a l 0.5 P 0 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 2FY/Fpx 2FY/Fpx

Fig.6. Shear wall responses: (a) base plastic rotation; (b) base shear force.

Figure 7 shows the maximum diaphragm acceleration vs. the anchorage connector strength. Because the diaphragm acceleration is controlled by the inertia force which can be transferred to the shear wall, it proportionally reduces with the decrease of the anchorage connector strength.

2 Current ) g (

Design

n 1.5 o i t a r e

l 1 e c c A 0.5 r

o Elastic o l F 0 0 1 2 3 4 5 6 7 2FY/Fpx

Fig.7. Diaphragm acceleration response.

Figure 8a shows maximum structure inter-story drift and Figure 8b shows the maximum relative displacement between the shear wall and diaphragm, i.e. anchorage connector deformation. As seen in Fig. 8a, the maximum shear wall inter-story drift follows the response trend of the shear wall base flexural plastic rotation and only starts to reduce as the anchorage

connector strength is lower than Fpx. Also noticed in Fig.8, the GLRS drift and the relative

displacement significantly increases as the anchorage connector strength is lower than Fpx.

15 ) 30

Current n Elastic i Current ( ) Elastic

25 t % 12 Design Design ( n

i 20 m r

9 e d LFRS c a y

l 15 r Max p o

t 6 s GLRS i s - d 10

r Residual e e t

3 v n i

t 5 I a l 0 e 0 R 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 2FY/Fpx 2FY/Fpx

Fig.8. Structure responses: (a) Inter-story drift; (b) Relative displacement. Figure 9 shows a 5% damping floor acceleration response spectra for top and 1st floor. As seen, the floor diaphragm acceleration response significantly reduces as the strength of connector decreases especially in short period range (0.1~0.3sec). This reduction is benefit for reducing the demand on the non-structural member.

1 0 6 0 . 0 3 F p x 0 . 0 3 F p x 0 . 3 3 F p x 5 0 . 3 3 F p x 8 0 . 6 7 F p x

0 . 6 7 F p x ) ) g ( g

1 . 0 1 F p x 1 . 0 1 F p x

n n 6 1 . 3 4 F p x o 1 . 3 4 F p x i o i t t a

a 1 . 6 8 F p x r 3 1 . 6 8 F p x r e e l l 2 . 3 5 F p x e 4 e 2 . 3 5 F p x c 3 . 3 5 F p x c c c 2 3 . 3 5 F p x A 6 . 0 7 F p x A 6 . 0 7 F p x 2 1

0 0 0 0 . 5 1 1 . 5 2 0 0 . 5 1 1 . 5 2 P e r i o d ( s ) P e r i o d ( s ) Fig.9. Floor response spectra: (a) top floor; (b) 1st floor.

The above discussed behaviors indicate that using the floor anchorage isolation system: (1) the reduction of the structure higher modes controlled responses (shear wall shear force and diaphragm acceleration) can be achieved without increase of the seismic responses in the other part of structure; (2) the reduction of the structure 1st mode controlled responses (shear wall base flexural rotation and inter-story drift) in the floor anchorage isolation system requires significant demand increase in the GLRS inter-story drift and the anchorage connector deformation.

Therefore, the trial design space developed in this paper is to identify the balanced design strengths of the anchorage connector with desirable structure seismic responses reduction but without significant increase of the other structure seismic responses. Several parameter sensitivities are examined for developing the design space as discussed in the following section.

4.2 Parameter Sensitivities 4.2.1 Effect of Building Heights

The study of building height effect is performed using the model C with the stiffness participation of gravity column and P- effect. Figure 10 shows the maximum shear wall seismic responses vs. the anchorage connector strength: (a) base flexural plastic rotation; and (b) base shear force for three different building heights. As seen, the short building (5-story) has the highest shear wall base flexural plastic rotation demand before the rotation demand starts to reduce with the decrease of the connector strength. This observation is because the short building has more mass participation in 1st mode response than the taller buildings and the 1st mode response is related to the shear wall base flexural plastic rotation response. However after the

connector strength is lower than Fpx, the reduction of the shear wall base plastic rotation is faster than taller buildings. On the other hand, the tall building (16-story) has the highest shear wall base shear force demand because it has more mass participation in the higher modes response compared to shorter buildings. However the reduction of the shear wall base shear force demand is faster in the taller buildings and the shear force demands of three buildings are similar when

the anchorage connector strength is much lower than Fpx.

0.03 4 5-story 12-story 0.025 3.5 16-story

a 0.02 s r 2.5 e ( d

n 0.015 V 2 / o i w t s

a 5-story 1.5 t 0.01 V o 12-story Current Current R 16-story 1 0.005 Design 0.5 Design 0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4 2FY/Fpx 2FY/Fpx Fig.10. Shear wall base responses for different heights: (a) plastic rotation; (b) shear force.

Figure 11a shows maximum GLRS inter-story drift and Figure 11b shows the maximum relative displacement for three different building heights. As seen, the short building has higher demand in the GLRS while lower demand in the anchorage connector deformation as compared to the taller buildings.

6 5-story 10 5-story ) n

12-story i 12-story ( )

5 16-story

t 8 16-story

% Current ( n

t 4 Design f m i 6 r e Current c d

3 a l y Design r p

s 4 o i t 2 s - D

t 2 1 v i n t I a l

0 e 0 R 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4 2FY/Fpx 2FY/Fpx Fig.11. Structure responses for different building heights: (a) Inter-story drift; (b) Relative displacement.

Figure 12 shows the maximum inter-story drift profile for GLRS. As seen, the GLRS maximum demand profile is more uniform in lower building than the higher building.

5 1 2 1 5 1 0 1 2 4 0 . 0 3 F p x 8 1 0 0 . 3 3 F p x 1 0 y y r 0 . 6 7 F p x y r r o t 3 o 8 o t 6

t 1 . 0 1 F p x S S S y r 1 . 3 4 F p x o 4 t 6

S 5 2 . 3 5 F p x 2 3 . 3 5 F p x 2 4 6 . 0 7 F p x 1 0 2 0 2 3 4 5 6 1 2 3 4 5 6 0 2 4 6 In t e r - s t o r y D r i f t ( % ) I n t e r - s t o r y D r i f t ( % ) 0 In t e r - s t o r y D r i f t ( % ) 0 2 4 6 Fig.12. Max GLRS inter-story drift profile: (a) 5-story; (b) 12-story;I n t e r -(c) s t o r y16-story. D r i f t ( % )

4.2.2 Effect of Gravity System Participation The effect of gravity system participation has been examined in two aspects by: (1) using different GLRS models from the no column model to the gravity frame model; and (2) applying different boundary conditions (pinned or fixed) at column base.

Figure 13 shows the maximum structure demands vs. the anchorage connector strength: (a) inter-story drift; and (2) relative displacement between LFRS and diaphragm for different models

(Model A: no column; Model B: single column without P-; Model C: single column with P- and Model D: gravity frame with P-). As seen in Fig.13 (a), the gravity system participation has little effect on the LFRS demand while it has a significant effect on the GLRS demand. The

GLRS inhere stiffness provides reduction in its drift and delays onset of drift amplification. The

P- effect counteracts the added benefit of GLRS stiffness and makes the system unstable when

the connector strength is less than 67% Fpx. The gravity frame action incurs smaller GLRS drift demand compared to the single column modeling case. As seen in Fig.13 (b), the gravity system participation reduces the relative displacement demand and the gravity frame model provides the best reduction.

10 Model A Current 20 Current Model B ) ) 9 n

i Design

Design ( % Model C t ( 8

15 n t

f Model D

7 e i Model A r m

d 6 e Model B c y r 5 a 10 Model C GLRS l o t 4 p s

s Model D - i r

n 2 v I i t

0 e 0 R 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4 2FY/Fpx 2FY/Fpx

Fig.13. Structure maximum demand for different GLRS modeling: (a) inter-story drift; (b) relative displacement.

Figure 14 shows the maximum GLRS inter-story drift profile along building height for

different models with the anchorage connector strength at 1.68Fpx, 1.0Fpx and 0.6Fpx. As seen, the gravity system inherent stiffness has a significant effect on the GLRS inter-story drift distribution. This effect increase as the anchorage connector strength reduces. For the case without gravity column (model A), the drift demand is concentrated at 1st floor. The single column models (Model B and Model C) produce a cantilever shape and the gravity frame model

(Model D) reduces the drift demand at top level through frame action.

1.68 Fpx 1.0 Fpx 0.67 Fpx 1 2 1 2 1 2

1 0 1 0 1 0

8 8 M o d e l A 8 M o d e l B y y y r r M o d e l C r o o o

t 6 t 6 S S M o d e l D S 4 4 4

0 0 0 1 2 3 4 1 2 3 4 1 2 3 4 D r i f t ( % ) D r i f t ( % ) D r i f t ( % )

Fig.14. Gravity column inter-story drift for: (a) 1.68Fpx, (b) 1.0Fpx; and (c) 0.67Fpx.

As discussed above, the gravity frame model generates the largest contribution from the

GLRS inherent stiffness to the structure system seismic response. However, it is necessary to check if the internal force demands in the gravity system remain elastic as assumed in the model.

Figure 15 shows the column internal forces profile for Model D. As seen, the column internal force demands are increase with the decrease of the anchorage connector strength but are all less than the design strengths.

1 2 1 2 1 2 0 . 0 3 F p x 0 . 0 3 F p x 0 . 3 3 F p x 0 . 3 3 F p x 1 0 1 0 1 0 0 . 6 7 F p x 0 . 6 7 F p x 1 . 0 1 F p x 8 1 . 0 1 F p x 8 8 1 . 3 4 F p x 1 . 3 4 F p x y y y r r 1 . 6 8 F p x 1 . 6 8 F p x r o o o

t 6 t 6 t 6 S S 2 . 3 5 F p x 2 . 3 5 F p x S 4 3 . 3 5 F p x 4 3 . 3 5 F p x 4 6 . 0 7 F p x 6 . 0 7 F p x 2 2 2

0 0 0 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 - 4 0 0 0 - 3 0 0 0 - 2 0 0 0 - 1 0 0 0 0 C o l u m n M o m e n t ( k - f t ) C o l u m n S h e a r ( k ) C o l u m n A x i a l ( k ) Fig.15. Column internal force profile for Model D: (a) Moment; (b) Shear; (c) Axial.

Also noticed in Fig. 14(c), the gravity frame model produces the maximum GLRS drift at 1 st floor due to the pin connected column base condition. Figure 16 shows the maximum structure response profiles: (a) inter-story drift; and (b) relative displacement for pin and fixed column base boundary conditions using gravity frame model (Model D). As seen, the fixed column base case significantly reduces the GLRS drift demand at 1st floor and moves the maximum demand into the middle height of the structure. Further, the fixed column base case increases the maximum relative demand at top floor. 1 2 1 2 L F R S G L R S 1 0 1 0

8 8 y y r r o o t 6 t 6 S S

Pin 2 2 M a x Fix R e s i d u a l 0 0 1 2 3 0 5 1 0 D r i f t ( r a d ) D i s p l ( i n )

Fig.16. Profiles for different column base BCs: (a) inter-story drift; (b) relative displacement. For the structures with a gravity column base boundary condition close to pin connection, the excessive GLRS inter-story drift demand observed at the lower floor can be reduced by increasing the anchorage connector at lower floors. As seen in Fig. 17, the constant anchorage connector strength profile was increased at 1st three floors by introduction a strength increasing factor .

Fpx Fpx e l i f o r P

h t g n e r t S

n o i th t 4 Floor c e n n o C

Fpx Constant Profile Varied Distribution

Fig.17. Anchorage connector strength distribution along building height. Figure 18 shows the maximum structure demands vs. the anchorage connector overall strength (: (a) inter-story drift; (b) relative displacement; and (c) diaphragm forces for different

. As seen, changing the connector strength does little change the LFRS drift and only slightly changes the relative displacement: deceases for lower overall connector strength cases and increases for higher overall connector strength cases. However increasing the connector strength at lower floors significantly reduces the GLRS drift demand (See Fig. 18a).Although diaphragm maximum force demand increases as the connector strength increases at lower floor, it is still significantly lower than the rigid connector case (See Fig. 18c).

GLRS Constant 20 Constant b=1.5 4 b=1.5 6 b=2.0 ) b=2.0 n Constant b=2.5 i ( b=2.5 5 Rigid 15

b=3.0 t b=2.0

3 n b=3.0 Max x ) e p 4 b=1.5 F % m

( b=2.5 e /

t 10 c x f

i 2 a a 3 b=3.0 l r m p D s F Rigid i 2 1 D 5 Residual a=2FY/Fpx 1 LFRS a=2FY/Fpx a=2FY/Fpx 0 0 0 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8

Fig.18. Structure maximum demand for : (a) inter-story drift; (b) relative displacement; (c) diaphragm force. 1 2 1 2 1 2 1 2

b = 1.0 1 0 b = 1.5 1 0 1 0 1 0 b = 2.0 b = 2.5 8 b = 3.0 8 8 8 y y y y r r r r o o o o t t t 6 6 t 6 6 S S S S

4 4 4 4

2 2 2 2

0 0 0 0 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 I n t e r - s t o r y D r i f t ( % ) I n t e r - s t o r y D r i f t ( % ) In t e r - s t o r y D r i f t ( % ) In t e r - s t o r y D r i f t ( % )

Fig.19. Gravity column inter-story drift with different  for =: (a) 0.33Fpx, (b) 0.43Fpx; (c)

0.53Fpx, and 0.67Fpx.

Figure 19 shows the maximum GLRS drift profile for different  and . As seen, increasing the connector strength () at lower floors deceases the GLRS drift at lower floors but increases it at upper floors, which results in a reduction of the GLRS drift because the maximum GLRS drift demand occurs at 1st floor. However this reduction becomes less effect when the maximum

GLRS drift demand shift from 1st floor to the mid-height of the structure. For different overall connector strength (a), an optimized  can be identified to achieve the lowest GLRS drift demand (indicated as solid dots in Fig. 19).

Figure 20 shows the maximum relative displacement between the LFRS and diaphragm profile for different  and . As seen, increasing the connector strength () at lower floors deceases the GLRS drift at lower floors but increases it at upper floors. This observed change results in a reduction of the relative displacement for lower  cases but an increase for higher  cases.

1 2 1 2 1 2 1 2

b= 1.0 1 0 b= 1.5 1 0 1 0 1 0 b= 2.0 b= 2.5 8 b= 3.0 8 8 8 y y y y r r r r o o 6 6 o o t t 6 6 t t S S S S

4 4 4 4

2 2 2 2

0 0 0 0 0 5 1 0 1 5 2 0 0 5 1 0 1 5 2 0 0 5 1 0 1 5 2 0 0 5 1 0 1 5 2 0 R e l a t i v e d i s p l a c e m e n t ( i n ) R e l a t i v e d i s p l a c e m e n t ( i n ) R e l a t i v e d i s p l a c e m e n t ( i n ) R e l a t i v e d i s p l a c e m e n t ( i n )

Fig.20. Relative displacement with different  for =: (a) 0.33Fpx, (b) 0.43Fpx; (c) 0.53Fpx, and

0.67Fpx.

4.2.3 Effect of Secondary Slope of the Anchorage Connector

The effect of secondary slope of the anchorage connector has been examined using two methods: (1) the first one is to study the effect of the secondary slope for the same connector yield strength; and (2) the other is to study the effect of the secondary slope for the same connector ultimate strength.

In the 1st study, two set of analyses have been performed with 0% and 0.4% secondary slope ratio for different anchorage connector strength. Figure 21 shows the maximum inter-story drift vs. the connector strength with different secondary slope ratio for: (a) LFRS; (b) GLRS. As seen in Fig.21(a), increasing the connector secondary slope does not change the maximum LFRS drift demand expect a slightly increase in the low connector yield strength case (0.33Fpx). However, the increase of the secondary slope significantly reduces the GLRS drift demands when the

connector strength is less than 1.0 Fpx.

) 2.5 ) 5 % % Current ( (

t t f f

i 2 i 4 Design r r d d

y 1.5 y 3 r Current r o o t t

s 0% s - 1 Design - 2 r r

e e 0% t 0.4% t n 0.5 n 1 I I 0.4% 0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4 2FY/Fpx 2FY/Fpx

Fig.21. Structure maximum inter-story drift demand for different secondary slope ratios: (a) LFRS; (b) GLRS.

Figure 22 shows the relative displacement between LFRS and diaphragm vs. the anchorage connector strength for: (a) maximum demand; (b) residual demand. As seen, increasing the secondary slope ratio reduces the relative displacement in maximum and residual demands.

Figure 23 shows the maximum diaphragm force vs. the connector strength for different secondary slope ratio. As expected, the system with 0.4% secondary slope ratio has a larger maximum force demand for the same connector yield strength compared to the system with 0% secondary slope ratio. 25 6 )

0% ) n i n (

i 5 Current Current (

n 0.4% n e Design 4 Design e m 15 m e e c 0% c a 3 l a l p 10 s p 0.4% i

s 2 i d

i 1 v t i t a l a l e 0 0 e R 0 0.5 1 1.5 2 2.5 3 3.5 4 R 0 0.5 1 1.5 2 2.5 3 3.5 4 2FY/Fpx 2FY/Fpx

Fig.22. Relative displacement for different secondary slope ratios: (a) Maximum; (b) Residual.

1500 )

s 0% p i 1200 k (

0.4% e c

r 900 o F

g Current a r

h 300 Design p a i

D 0 0 0.5 1 1.5 2 2.5 3 3.5 4 2FY/Fpx

Fig.23. Diaphragm maximum force demand for different secondary slope ratios

nd In the 2 study, both the connector yield strength (FY), initial stiffness (Ki) and the secondary

slope (K2) are varied to achieve the same strength (1.0Fpx) at a pre-defined deformation of 4” as illustrated in Fig. 24 and Table 5. As seen, these variations are achieved by combined hysteretic device with 0% secondary slop and the elastic restoring device. Force 1.0Fpx

K Combined FY 2

FYsys Hysteresis Ki

Elastic restoring Relative Kelas displacement 4"

Fig.24. Illustration of the connector properties.

Table 5. Connector property variation for secondary slop study.

F @ 4" FY (k) Ki (k/in) K2 (k/in) K2/Ki FYsys (k) Kelas (k/in) 339 339 7461 0 0.0% 339 0 339 305 6723 8 0.1% 305 8 339 272 5986 17 0.3% 271 17 339 238 5248 25 0.5% 237 25 339 205 4511 34 0.8% 203 34 339 171 3773 42 1.1% 170 42 339 138 3035 51 1.7% 136 51 339 104 2298 59 2.6% 102 59 339 71 1560 68 4.3% 68 68

6 0 0 6 0 0

4 0 0 4 0 0

2 0 0 2 0 0 ) ) s s p p i 0 i k 0 k ( (

4 . 3 % F - 2 0 0 F 1 . 7 % - 2 0 0 - 4 0 0 0 . 8 % 0 . 3 % - 4 0 0 - 6 0 0 0 % - 6 0 0 - 1 0 - 5 0 5 1 0 - 1 0 - 5 0 5 1 0 D i s p l ( i n ) D i s p l ( i n )

Fig.25. Anchorage connector hysteresis response under EQ9: (a) 4th floor; (b) Top floor. Figure 25 shows one example hysteresis response for the anchorage connector at 4th and top floor for EQ9 (See Table 4). As seen, as the secondary slope ratio increases and the yield strength reduces, the energy dissipated by the connector reduces for the cycle with the same peak relative displacement and therefore the maximum relative displacement demand increases. The maximum and residual relative displacement demands vs. the secondary slope ratio are shown in

Fig. 26. As seen, although the larger secondary slope ratio and lower yield strength increase the maximum relative displacement, they reduce the residual displacement demand.

) 8 n i (

e Max c a l 4 p Residual s i d

v 2 i t a l e

R 0 0% 1% 2% 3% 4% 5% Secondary Slope Ratio

Fig.26. Relative displacement demand vs. connector secondary slope ratio.

4 LFRS 0.8 )

) GLRS g (

( Current design n 0.7 t o f i i

3 t r a d r

e y l 0.6 r e o c t c s - a

2 r r e t

o 0.5 n o I l F 1 0.4 0% 1% 2% 3% 4% 5% 0% 1% 2% 3% 4% 5% Secondary Slope Ratio Secondary Slope Ratio

Fig.27. Structure maximum responses for different secondary slope ratios: (a) inter-story drift; (b) diaphragm acceleration.

Figure 27 shows the maximum structure responses vs. the connector secondary slope ratio for: (a) inter-story drift; and (b) diaphragm acceleration. As seen in Fig. 27, the GLRS inter-story drift and the diaphragm acceleration increases with the increase of the secondary slope ratio. The influence of the secondary slope ratio on the LFRS drift demand is secondary: with the increase of the secondary slope ratio, the LFRS drift demand initially reduces but starts to increase around

0.9% secondary slope ratio.

4.2.4 Effect of Viscous Damper

The effect of viscous damper is examined using two analyses: (1) adding viscous damper with different critical damping ratio at every floor; and (2) adding viscous damper at selected floors to the anchorage connector. A linear viscous damper material is used in the analysis.

st The 1 analysis is performed for the anchorage connector strength at 1.0Fpx. The critical damping ratio of the added viscous damper varies from 2% to 50%. Figure 28 shows the maximum inter-story drift profile for different viscous damping ratios: (a) LFRS; and (b) GLRS.

As seen, the viscous damper increase the LFRS drift demand but deceases the GLRS drift demand. 1 2 1 2

1 0 1 0 0 % 8 8 0 % 2 % y y r r 2 % 5 % o o

t 6 t 6

5 % S S 1 0 % 4 1 0 % 4 1 5 % 1 5 % 2 0 % 2 2 0 % 2 5 0 % 5 0 % 0 0 1 . 9 5 2 2 . 0 5 2 . 1 2 . 1 5 2 . 2 1 . 5 2 2 . 5 3 3 . 5 I n t e r - s t o r y D r i f t ( % ) I n t e r - s t o r y D r i f t ( % ) Fig.28. Maximum inter-story drift: (a) LFRS; (b) GLRS. Figure 29 shows the maximum response profile: (a) relative displacement between LFRS and diaphragm; and (b) viscous force. As seen, the viscous damper decreases the relative displacement demand but generate a fairly large viscous force at each floor, which in turn cause the increase of the LFRS drift demand (see Fig. 28a). 1 2 1 2

1 0 1 0 0 % 0 % 8 2 % 8 2 %

y 5 % y r

5 % r o o

t 6 1 0 % 1 0 % S S 1 5 % 1 5 % 4 4 2 0 % 2 0 % 5 0 % 2 5 0 % 2

0 0 0 2 4 6 0 1 0 0 2 0 0 3 0 0 S l i d i n g ( i n ) F o r c e ( k i p s ) Fig.29. Maximum response profile: (a) Relative displacement; (b) Viscous force.

The 2nd analysis is performed for four different anchorage connector strengths which are below 1.0Fpx. The viscous damper with 50% critical damping ratio has been added at selected floors, where the relative displacement demand is significant (refer to Fig. 20): (1) 9th floor; (2) 9th and top floors; and (3) 6th, 9th and top floors. Figure 30 shows the structure maximum response vs. the anchorage connector strength: (a) LFRS inter-story drift; and (b) relative displacement between LFRS and diaphragm. As seen, adding viscous damper at selected floors significantly reduces the relative displacement demand but increases the LFRS drift demand. The benefit and side-effect of adding the viscous damper seems cancel each other: 0.67Fpx case with no damper generates similar LFRS drift and relative displacement demand as the 0.33Fpx case does. This observation implies that to reduce the excess relative displacement demand in 0.3Fpx case, adding three viscous damper or increase the anchorage strength to 0.67Fpx is equivalent. 2.5 20 No Damper Rigid 1 Damper ) n

i 2 Dampers (

2 ) t 15 3 Dampers n % e (

t m f e i 1.5 r c

a 10 D l

p y s r

1 i o t D

e 5 r v e

i Rigid

t 0.5 t n a l I e 0 0 R 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 2FY/Fpx 2FY/Fpx

Fig.30. Maximum response vs. connector strength: (a) LFRS drift; (b) Relative displacement. 5. PROPOSED TRAIL DESIGN SPACE

Based on the sensitivity studies discussed in section 4, trail design space is developed for the

12 story structure. The trial design space is over a range of connector design strength from

0.33Fpx to 0.67Fpx as intent to reduce the LFRS flexural demands (shear wall base hinge rotation or inter-story drift) controlled by 1st model response. Within the design space, the maximum seismic structure demands are showing in Fig. 31 and Fig. 32. These demands are obtained the earthquake simulation using the GLRS frame model (model D) with 0.4% secondary slope ratio for: (1) no viscous damper; (2) one 50% viscous damper at 9th floor; and (3) two 50% viscous damper at 6th, 9th and top floor.

As seen in Fig. 32(a), all LFRS inter-story drift demands are reduced in the design space compared to the current design. However some design points result in a relative displacement larger than a possible acceptable value of 8” (See Fig. 32b). These points are not recommended for the design of the structure. 15 2.5 Current design ) n i (

t ) 2 n e % 10 Acceptable: 8" (

m t e f i

1.5 c r a l D p s y i r 1 5 o No Damper D t

s e - v r

1 Damper i Current design e 0.5 t t a l n I 3 Dampers e 0 0 R 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 2FY/Fpx 2FY/Fpx

Fig.31. Connector design strength vs. structural maximum demand: (a) LFRS inter-story drift; (b) Relative displacement.

As expected, the diaphragm acceleration demands are significantly reduced compared to the current design in the proposed design space (See Fig. 32a) as they are controlled by the higher modes responses. An increase of GLRS inter-story drift demands is observed in the design space compared to the current design. However the drift demands are less the maximum allowable drift in current design code (ASCE 7 2005) under MCE.

2 Current design 4 MCE limit 1.5 No Damper ) % ) (

One Damper t 3 ( f

o Three Dampers i 1 D t

a y r r e l o

t 2 e s

c 0.5 - r c Current design e t A n I 0 1 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 2FY/Fpx 2FY/Fpx

Fig.32. Connector design strength vs. structural maximum demand: (a) diaphragm acceleration; (b) LFRS inter-story drift.

6. CONCLUSION

An innovative floor anchorage isolation system is being developed through a multi-university

NSF/NEES research project. This system is able to reduce inertial forces during major earthquakes and further reduce the seismic demand on the LFRS. This paper presents a preliminary analytical study on the structure seismic behavior using the floor anchorage isolation system. The following conclusions are made through this study:

(1) The structure demands, such as LFRS demand and diaphragm acceleration under earthquakes can be reduced by lowering the strength of the floor anchorage connector. However these reductions come with the increase of the relative displacement between LFRS and diaphragm and the GLRS demands.

(2) The 1st mode driven structure demands, such as shear wall flexural base plastic rotation and LFRS inter-story drift, can only start to reduce after the floor anchorage connector strength is

lower than 1.0Fpx. Therefore this reduction also requires significant relative displacement between LFRS and diaphragm.

(3) The higher modes driven structure demands, such as shear wall base shear force and diaphragm acceleration, can immediately reduce once the floor anchorage connector strength starts to reduce from the maximum force reached in elastic model. Therefore this reduction does not require significant relative displacement between LFRS and diaphragm.

(4) The participation of GLRS is benefit to the overall structure seismic response and is able to change the structure seismic response vertical distribution. The GLRS frame model provides the best results for reducing the structure seismic demand using the isolation system. For a structure with a pin connection, an excessive GLRS inter-story drift can be concentrated at 1 st floor. This excessive GLRS drift can be mitigated by increasing the anchorage connector strength at bottom floors.

(5) The secondary slope of the anchorage connector can stabilize the gravity system and reduce the residual relative displacement. However an anchorage connector with significant secondary slope will increase the maximum relative displacement due to a decrease in energy dissipation per cycle.

(6) Adding viscous damper to the hysteretic device in the anchorage connector can reduce the relative displacement demand but increase the LFRS inter-story drift demand at the same connector yield strength level. The benefit and side-effect of adding the viscous damper seems be cancelled by each other.

(7) A trial design space for the floor anchorage isolation system is proposed for a 12-story shear wall structure.

7. ACKNOWLEDGE

This research was supported by the Network for Earthquake Engineering Simulation

(NEES) and National Science Foundation (NSF) under Grant CMMI-1135033. The authors are grateful for this support. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NEES or National Science Foundation.

8. REFERENCE

ACI 318-08 (2008). Building Code Requirements for Structural Concrete and Commentary, ACI committee 318.

ASCE/SEI 7 (2005). Minimum Design Loads for buildings and other Structures. ASCE

Standard.

Crane, S.T. (2004). Influence of energy dissipation connection between floors and the lateral force resisting system. Master Degree Thesis, University of California at San Diego.

Eberhard MO and Sozen MA. (1993). Behavior-based method to determine design shear in earthquake-resistant walls. ASCE Journal of Structural Engineering 119:619-640.

Ishida, J. and Fujita, T. (1983). Earthquake isolation floor. The United Sates Patent 4,371,143.

Kondo, H. (1987). Floor system for seismic isolation. The United Sates Patent 4,662,133.

Kurabayashi H., Sakaba and K. Fujita, T. (1983). Earthquake isolation floor. The United Sates

Patent 4,402,483 Mar, D. and Tipping, S. (2000) Smart frame story isolation system: a new high-performance seismic technology. Internal report of Tipping Mar associates, Berkeley, CA.

Naito, C., Peter, W. and Cao, L. (2006). “Development of a seismic design methodology for precast diaphragms - phase 1 summary report”. ATLSS Report No.06-01, ATLSS Center, Lehigh

University, PA.

Pan, T.C., Ling, S.F. and Cui, W. (1995). Seismic response of segmental buildings. Earthquake

Engineering and Structural Dynamics, 24: 1039-1048.

Ryan, K.L. and Earl, C.L. (2010). Analysis and design of inter-story isolation systems with nonlinear devices. Journal of Earthquake Engineering 14: 1044-1062.

Rodriguez, M., Restrepo, JI, and Carr, A.J. (2002). Earthquake induced floor horizontal accelerations in buildings. Earthquake Engineering & Structural Dynamics, 31:693-718.

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9. NOTATION

Cd, Cs = deflection amplification factor, seismic response coefficient;

Cvx = vertical distribution factor;

Fpx = diaphragm design force;

Fx = lateral seismic force;

FY =yield strength of the anchorage connector;

FYsys=yield strength of the hysteretic device;

hx = height at level x;

Ig, Icr = gross, cracked second moment of inertia of a concrete section;

Kelas = stiffness of elastic restoring device;

Ki, K2 = initial, post-yielding stiffness for the anchorage connector;

L = span of the floor strip;

M =story moment on LFRS;

R = response modification coefficient;

S1 Ss = mapped spectral acceleration for 1 second period, short period;

SDS = mapped design spectral acceleration for 1 second period, short period; T = structure design fundamental period;

V =story shear on LFRS;

Wx = weight at level x;

 = strength reduction factor for the anchorage connector;

 = strength increasing factor for the anchorage connector at bottom floors;

 = strength reduction factor;

0 = system overstrength factor.