MULTI-LEVEL FORTIFICATION INTENSITIES SEISMIC PERFORMANCE ASSESSMENT FOR REINFORCED CONCRETE FRAME- SHEAR WALL STRUCTURE WITH VISCOUS DAMPERS

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1 MULTI-LEVEL FORTIFICATION INTENSITIES SEISMIC PERFORMANCE ASSESSMENT FOR REINFORCED CONCRETE FRAME- SHEAR WALL STRUCTURE WITH VISCOUS DAMPERS Wenfeng Liu*, Jing Wang* * School of Civil Engineering, Qingdao Technological University, Qingdao 66033, China (lwf6688@sohu.com, wangjingnelly@63.com ABSTRACT Under the multi-level fortification conditions, the performance-based seismic design for frameshear-wall structure with viscous dampers is a challenging topic. Using Pushover Method, this paper pushes the frame shear-wall structure with viscous dampers, establishes the relationship between base shear and displacement and maps to a-single-degree-of-freedom structure. The relationship between the seismic coefficient (uivalent shear force and displacement is obtained and reflects the seismic performance. With the multi-level fruent earthquake and rare earthquake fortifications specified by the "Code for seismic design of buildings" in China, the seismic action will be adjusted according to the elastic-plastic state of the viscous damper structures. The seismic performance under the conditions of multi-level seismic fortifications will also be assessed. This paper establishes the performance-based seismic design of the frame-shear wall structure with viscous dampers under the multi-level fortification intensities. Studies have shown that: ( This is a new and effective performance-based seismic design method. A complete performance assessment may be conducted once for all under the multi-level seismic fortification intensities; ( Variable damping of viscous damper structures does not change the seismic capacity curve; (3 Obtain the intersection of the seismic action curve and the capacity curve under the multi-level fortification intensities. Determine whether the displacement angle limits set by the seismic code are met in the state of fruent earthquakes and rare earthquakes respectively. Evaluate the seismic performance of the frame-shear wall structure with viscous dampers under the multi-level fortifications; (4 The viscous dampers reduce the seismic action under the multi-level fortification intensities no matter whether in fruent or rare earthquake. Reduction at the elastic state is larger than that at the plastic state. The shock energy dissipation effect on the frame-shear wall structure with viscous dampers is verified. KEYWORDS Frame-shear structure with viscous dampers; Multi-level fortification intensities; Performancebased seismic design; Performance assessment; Seismic action curve and capacity curve; Reduction the seismic action. INTRODUCTION Energy dissipation structures refer to those containing energy dissipation devices (such as the dampers, viscoelastic materials, friction components, etc. in their local positions (such as the support, shear walls, nodes, links or connection joints, floor space, adjacent buildings, the main subsidiary structure, etc.. Through variable velocity and deformation, the energy dissipation devices provide additional damping to dissipate or absorb the earthquake energy input into the structure. They reduce the seismic response of the main structure to achieve the desired purpose of earthquake proofing. In the past three decades, the energy dissipation structure has been widely

2 used in engineering practice (Housner, et al, 997; Liu, 997; Zhou, 009. The "Code for seismic design of buildings" (GB500, 00 has extended the application of energy dissipation housing. In China, design and application of energy dissipation will become increasingly extensive and intensive. This paper focuses on frame-shear wall structure with viscous dampers. Performance-based seismic design is one of the future cores of seismic codes. The currently practical and feasible methods are the displacement coefficient method, recommended by FEMA- 73 (997 and FEMA-356 (000 and the capacity spectrum method recommended by ATC-40 (996 and FEMA-440 (005. In recent years, many scholars have adopted the performance-based thinking and conducted research on performance-based seismic design methods of the viscous damper structures (Liang, 0; Lin, 003. This paper, using Pushover Method, pushes the frame shear-wall structure with viscous dampers, establishes the relationship between base shear and displacement and maps to a-single-degree-offreedom structure. The relationship between the seismic coefficient (uivalent shear force and displacement is obtained and reflects the seismic performance. With the multi-level fruent earthquake and rare earthquake fortifications specified by the "Code for seismic design of buildings" in China, the seismic action will be adjusted according to the elastic-plastic state of the viscous damper structures. The performance-based seismic design of the frame-shear wall structure with viscous dampers under the multi-level fortification intensities is put forward in this paper. The seismic performance under the conditions of multi-level seismic fortifications will also be assessed. The characteristics and roles of the frame-shear wall structure with viscous dampers are discovered. PERFORMANCE-BASED SEISMIC DESIGN WITH MULTI-LEVEL FORTIFICATIONS Seismic performance of the structure. Seismic performance of the structure is usually calculated through the Pushover Method. The functional relation between the base shear force, the roof displacement can be expressed as: V = f (Δ roof-d ( Where, V is the base shear force; Δ roof-d is the roof displacement. The elastic mode of the structure is obtained through modal analysis. Considering the multi-modal effect, the elastic mode is then used to determine the generalized uivalent modal participation factor Γ and the generalized uivalent mass M in a MODF (multi-degree of freedom system. G = N å i= m N if å i= mf i N N ( å mif å mif i= i= M = (3 Where, m i is the mass of each story; Φ is the generalized uivalent mode, can be expressed as: m å f = (fijg j j= (4 Where, Φ ij is the horizontal displacement of i-th floor for j-th mode; Γ j is the participation factor for j-th mode. Map the functional relation of the base shear force and the displacement in a MDOF system onto the functional relation of the acceleration and displacement in a SDOF system. Express the result as the functional relation of the seismic effect coefficient and displacement: (

3 Sroof S = V a M gm G a = V G - d = D roof-d G (7 Where, S a is the spectral acceleration in a SDOF system; α is the uivalent seismic effect coefficient in a SDOF system; g is the acceleration due to gravity; S roof-d is roof uivalent displacement in a SDOF system. Seismic action under the elastic-plastic state Additional damping ratio of the frame-shear wall structure with viscous dampers. As the structure is imbedded with viscous dampers, this paper studies the additional damping ratio caused by the viscous dampers (GB500, 00; FEMA-74, 997: W z a =å j W /( 4pW cj W å s = (/ Fi ui cj = (p / T C j cos q j (0 Where, ζ a is the additional effective damping ratio of the energy dissipation structure; W c the energy consumption of all energy dissipation components completing one cycle under the expected displacement of the structure; W s is the total strain energy of the structure imbedded with energy dissipation devices under the expected displacement; F i is the horizontal force of i-th floor at u i by the Pushover Method; u i is the horizontal displacement of i-th floor by the Pushover Method; T is the basic vibration period of the energy dissipation structure; C j is the linear damping coefficient of the j-th viscous damper determined through test; θ j is the angle between the energy dissipation direction of the j-th viscous damper and the horizontal plane; Δu j is the relative horizontal displacement at both ends of the j-th viscous damper. Equivalent damping ratio caused by structural plasticity. Ma Yingzhan, Liu Wenfeng and Li Yi(008 pointed out that Kowalsky(995 uivalent linearization method shall be used to determine the plastic hysteretic damping ratio in order to have the best accuracy of the structural displacement. According to the principle of uality between the energy consumption of the viscous damping in the uivalent linear system and the hysteresis energy consumed in the nonlinear system, the hysteretic damping ratio in Kowalsky uivalent linearization method is expressed as: é ù z hyst = ê- (+ bm-b ú p êë m úû ( Where, β is the ratio of the yield stiffness and the initial stiffness; µ is the displacement ductility factor of the structure. Values of seismic action. According to "Code for seismic design of buildings" (GB500, 00, seismic action values are determined by the following formula: ì0.45a max + (0h a maxt 0 T 0.s ï ha max 0.s< T Tg a = í g ( ï ( Tg T ha max Tg < T 5Tg g ï î [ h0. -h( T - 5Tg ] a max 5Tg < T 6.0s g =.9+ (0.05-z (0.3+ 6z (3 s Du 0 h = 0.0+ (0.05-z /(4+ 3z (4 (5 (6 (8 (9

4 h = + (0.05-z ( z (5 Where, α max is the maximum seismic effect coefficient of an earthquake of rare or fruent intensity; γ is the power index of the curvilinear decrease section; T g is the characteristic period; η is the slope adjustment factor of the plummeting down segment; η is the damping adjustment factor; T is the natural vibration period of the structure; ζ is the uivalent damping ratio. Seismic action in elastic state When the frame-shear wall structure is in the elastic state, the viscous dampers cause additional damping. The uivalent damping ratio of frame-shear wall structure imbedded with viscous dampers is: z = z 0 + (6 z a Where, ζ 0 is the elastic damping ratio of the frame-shear wall structure. According to formula (- 6, calculate the seismic action of the frame-shear wall imbedded with the viscous dampers in elastic state. Seismic action in plastic state. When the frame shear-wall structure is in the plastic state, its period changes with the plastic state. Use the secant stiffness at maximum displacement to calculate the period of uivalent system. T = T0 m (- b + bm (7 When the frame-shear wall structure is in the plastic state, its damping ratio changes with the plastic state. At the same time, the viscous dampers cause additional damping. The uivalent damping ratio of the frame-shear wall structure imbedded with viscous dampers is: z = z 0 + z + z (8 a hyst According to the formula (-5 and formula (7-8, the seismic action of the frame-shear wall structure imbedded with the viscous dampers in plastic state. Seismic performance assessment of the frame-shear wall structure imbedded with viscous dampers under multi-level fortifications. Fruent intensity earthquake. For frame-shear wall structure, "Code for seismic design of buildings" (GB500, 00 provides that, in case of fruent intensity earthquake, the maximum elastic story displacement angle shall be /800. In most cases, the structure is in elastic state. And the seismic action shall be calculated in elastic state. The Pushover Method may generate a capacity curve from the uivalent seismic effect coefficient α and roof uivalent displacement S roof-d in a SDOF system. In a coordinate system composed of the seismic effect coefficient and the roof uivalent displacement, draw the α-s roof-d curve between the capacity and the seismic action at fruent intensity. Within the maximum elastic story displacement angle of /800, if the seismic action of the multi-level fruent earthquakes intersects with the capacity curve, this will be assessed as meeting the specified limit. When the seismic action of the multi-level fruent earthquakes cannot intersect with the capacity curves, this may be assessed as being unable to meet the specified limit. The calculation will discontinue. Thus, at fruent intensity, we have completed the seismic performance assessment, see fruent earthquake phases in Figure and Figure 3 (see below. Rare intensity earthquake. At rare intensity, the structure is in elastic state and shall be calculated accordingly. But in most cases, the structure will enter the plastic state and all calculations shall be done accordingly.

5 The Pushover Method may generate a capacity curve from the uivalent seismic effect coefficient α and roof uivalent displacement S drift-d in SDOF system In a coordinate system composed of the seismic effect coefficient and the roof uivalent displacement, draw the α-s roof-d curve between the capacity and the seismic action at rare intensity. With multi-level rare earthquakes, if the capacity curve intersects with the seismic action at rare intensity at elastic phase, the structure will be assessed as being in elastic state at rare intensity. If the capacity curve intersects with the seismic action at rare intensity at plastic phase and the maximum story displacement angle does exceed /00 (roof displacement angle of /8 in Figure and Figure 3, this will be assessed as meeting specified limit. When the maximum story displacement angle exceeds /00 (roof displacement angle of /8 in Figure and Figure 3, the seismic action of the rare earthquakes cannot intersect with the capacity curves. This may be assessed as being unable to meet the specified limit. The calculation will discontinue. Thus, at rare intensity, we have completed the seismic performance assessment, see rare earthquake phases in Figure and Figure 3 (see below. RESULTS AND DISCUSSION A 5-story frame-shear wall structure. The total height is 45m and width 4 meters. Concrete strength grade of the beam, slab and column is C30. Concrete strength grade of the shear wall at -5 story is C40. That at 6-5 story is C30. Column cross section at -5 stories is 0.8m 0.8m. That at 6-5 stories is 0.6m 0.6m. Shear wall thickness at -5 stories is 0.4m. That at 6-5 stories is 0.8m. The deep beam at -5 stories is 0.3m 0.5m. That at 6-5 stories is 0.5m 0.5m. The corridor beam is 0.5m 0.4m. The floor is reinforced concrete slab with a thickness of 0. m. The main reinforcement at beam cross-section is HRB335 grade steel reinforcement. The shear wall reinforcement is HPB35 grade steel reinforcement. Two side frames at each story are installed with two viscous dampers whose damping index is 0.5 and damping coefficient is 0000 KNs/m. The ground falls into category Ⅱ. The designed earthquake is in the second group. The site characterization period is 0.4s. Figure. Structural diagram (unit: m For the original frame-shear wall structure without viscous dampers, we assess its seismic performance. See Figure for the comparison the α-s roof-d curve between the roof uivalent displacement and the seismic action of multi-level fruent and rare earthquakes.

6 Figure. α-s roof-d compared with seismic action(original structure For the frame-shear wall structure with viscous dampers, we assess its seismic performance. See Figure 3 for the comparison the α-s roof-d curve between the roof uivalent displacement and the seismic action of multi-level fruent and rare earthquakes. Figure 3. α-s roof-d compared with seismic action(viscous damper In Figure -3, the first vertical line represents the maximum elastic story displacement angle of /800 at fruent intensity specified by "Code for seismic design of buildings". The area to the left of the first vertical is the fruent earthquakes phase. The second vertical line represents the maximum story displacement angle of /00 (roof displacement angle of /8 in Figure and Figure 3 at rare intensity specified by "Code for seismic design of buildings". The area between the first vertical and the second vertical line is the rare earthquake phase. Figure -3 show that, regardless of the earthquake intensity, the comparison between seismic performance and action at multi-level fortifications can be shown in one figure. Thus complete the seismic performance assessment at multi-level fortifications. Figure -3 show that, with 6-7 degrees fruent earthquakes, the capacity curve intersects with the seismic action of the frame-shear wall structure without dampers. This is assessed as meeting the specified limit specified maximum story displacement angle. When it falls within 8-9 degrees, no intersection can be found. The specified limit cannot be met. With dampers, an intersection can be found at 6, 7, 8 degrees. This is assessed as meeting the specified limit. At 9 degrees, no intersection can be found. The specified limit cannot be met. Figure -3 show that, with 6-7 degrees rare earthquakes, the capacity curve intersects with the seismic action of the frame shear-wall structure without dampers, with viscous devices. This is

7 assessed as meeting the specified limit specified maximum story displacement angle. When it falls within 8-9 degrees, no intersection can be found. The specified limit cannot be met. Figure -3 show that, with viscous dampers, the seismic action at a fruent earthquake of a frameshear wall structure at 6, 7, 8, 9 degrees decreases by %,.%,.%, 8.9% while that at a rare earthquake at 6, 7, 8, 9 degrees decreases by 4.7%, 4.6%, 4.6%, 4.7%. CONCLUSIONS For reinforced concrete frame-shear wall structure imbedded with viscous dampers, we have proposed a performance-based design method at multi-level fortifications. Our main conclusions are: ( This is an effective seismic design method. Performance assessment at multi-level fortifications may be completed once for all. This method may be used both for new and retrofitting frame-shear wall structure with viscous dampers design. ( We have obtained the intersection between the seismic action curve and the seismic performance curve at multi-level fortifications. The intersection is used to determine whether the displacement angle limit specified by the seismic code has been met both in fruent and rare earthquakes. We have evaluated the seismic performance of the frame-shear wall structure imbedded with viscous dampers at multi-level fortifications. (3 At multi-level fortifications, the dampers reduce the seismic action regardless of the earthquake scale. The reduction in elastic state is larger than that in the plastic state. ACKNOWLEDGEMENT This paper is funded by the National Natural Science Foundation of China under grant No , Natural Science Foundation of Shandong Province under grant No. Y008F58. REFERENCES FEMA 440 (005. Improvement of nonlinear static seismic analysis procedures. Federal Emergency Management Agency, Washington, D.C., USA. GB 500 (00. Code for seismic design of buildings. China Building Industry Press, Beijing, China. G W Housner, L A Bergman, T K Caughey, et al (997. Structural control: past, present and future. Journal of Engineering. Mechanics, 3 (9: Junfen Yang (009. Research on response modification factor and displacement amplification factor of concentrically braced steel frames. Ph D thesis, Xi'an University Of Architecture And Technology, Xi'an, China. Lin Y Y, Tsai M H, Hwang J S, et al (003. Direct displacement-based design for building with passive energy dissipation systems, Engineering Structure, 5(:5-37. Wenfeng Liu (997. Recent advances in structure control (Ⅰ, Ⅱ. World Information on Earthquake Engineering, 3 (3:9-6, 3 (4: 7~.

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