applied sciences Article
Seismic Damage Evaluation of Concrete-Encased Steel Frame-Reinforced Concrete Core Tube Buildings Based on Dynamic Characteristics Lei Zeng *, Yunfeng Xiao, Yiguang Chen, Siqian Jin, Wei Xie and Xianjie Li School of Urban Construction, Yangtze University, Jingzhou 434023, China;
[email protected] (Y.X.);
[email protected] (Y.C.);
[email protected] (S.J.);
[email protected] (W.X.);
[email protected] (X.L.) * Correspondence:
[email protected]; Tel.: +86-138-7235-9779 Academic Editors: Gangbing Song, Dimitrios G. Aggelis and Stefano Invernizzi Received: 8 December 2016; Accepted: 16 March 2017; Published: 23 March 2017
Abstract: To evaluate damage state and residual resistance of concrete-encased steel frame-reinforced concrete core tube buildings under earthquake actions, a criterion of damage assessment based on dynamic characteristics is proposed in this paper. Dynamic characterization experiments were conducted on a 10-story and 1/5 scaled building model using velocity sensors on each floor, and natural frequencies were obtained based on the measured data. Modal analysis was carried out using a nonlinear finite element program, and the simulation results of the dynamic characteristics agreed well with experimental ones. Then, the damage processes under different seismic wave inputs were revealed based on finite element analysis, and the max story drift angle was chosen to reflect the damage state and to quantify the degree of damage. A criterion of seismic damage assessment is proposed based on the relationship between the quantitative damage value and the dynamic characteristics, in which the higher order modes were considered. Moreover, influencing factors, including earthquake intensity and structural stiffness ratio, were analyzed, and the results indicated that the proposed damage index based on dynamic characteristics can account for the higher-order modes and provides an innovative approach to evaluate the seismic damage. Keywords: damage evaluation; earthquake; concrete encased structures; dynamic characteristics
1. Introduction Concrete-encased composite structures are widely used in high-rise buildings owing to their excellent seismic performance, high rigidity and low cost. The hybrid structural systems with concrete-encased composite frames and reinforced concrete core tubes have been adopted in many super high-rise buildings especially in the US [1], China [2] and Japan [3,4]. Many studies have been performed on hybrid structural systems by large-scale pseudo-static tests, pseudo-dynamic tests and shaking table tests to investigate the fundamental mechanisms and seismic behavior. The research objects included hybrid structural systems consisting of steel frames, concrete-encased steel frames, and concrete-filled steel tubes [5–10]. They attempted to understand the seismic response, seismic behavior and failure characteristics of the hybrid structural system. However, such tests are very expensive and even the largest shaking table in the world cannot simulate the damage process of full-scale super high-rise buildings. As an alternative, numerical simulations based on accurate models have been widely accepted as an important technique to study earthquake-induced structural behavior, by which the entire dynamical catastrophe processes from material damage and local failure to integral collapse can be replicated to a certain extent [11–15].
Appl. Sci. 2017, 7, 314; doi:10.3390/app7040314
www.mdpi.com/journal/applsci
Appl. Sci. 2017, 7, 314
2 of 18
The results of the above mentioned experiments and simulations indicated that a well-designed frame-core tube structural system possesses good seismic performance, but unfavorable failure mode can still occur in some states. As the two parts that resist lateral force, the frame and the core tube, cooperatively operate with different stiffness, an unequal distribution of shear in the two components is caused [16,17]. To effectively prevent earthquake-induced structural collapse, the damage stage and the residual bearing capacity of structures should be properly predicted in this structural system. A seismic damage model actually reflecting strength and stiffness degradation under cyclic loading is the basis of structural safety margin evaluation and post-earthquake restoration. Based on the initial strength criterion and deformation, seismic damage assessment models based on energy criteria were proposed [18,19]. Afterwards, the losses of motion stability and the loss of vertical bearing capacity were taken as criterions to judge the collapse of structures [20]. A stress wave-based active sensing method was also used to detect damage in concrete structures [21–27]. The piezoelectric smart aggregates were adopted for structural health monitoring [28–30]. However, the existing criterions cannot reflect the influence of loading amplitude and loading path on the cumulative damage of the structures. Since the damage and collapse of a structure is a complex dynamic instability problem, collapse criterion and damage evaluation index on the level of the overall structure should be developed and be applied to concrete-encased steel frame-reinforced concrete core tube structures. In this paper, a 1/5 scale and 10-storey concrete encased steel frame-reinforced concrete core tube building model was constructed according to the design code of China (GB50023-2009). The prototype structure was designed with 8 degrees of seismic fortification. The specimen was measured for a proposed criterion of seismic damage assessment. Dynamic characterization experiments were conducted using velocity sensors on each floor. The natural frequencies were obtained based on the experimental data. Modal analysis was also carried out using a nonlinear finite element program based on a fiber model in OpenSees. The modal analysis considered geometric nonlinearity and material nonlinearity. Then, the damage process under different seismic wave input was revealed based on finite element analysis, and the max story drift angle was chosen to reflect the damage state and to quantify the damage degree. The structural dynamic characteristics indexes such as vibration modes and frequencies can be well detected according to non-destructive structure. A criterion of seismic damage assessment was proposed based on the relationship between the quantitative damage value and dynamic characteristics. The author hopes to provide references for damage evaluation, structural health monitoring and post-earthquake restoration of concrete-encased steel frame-reinforced concrete core tube buildings. 2. Experimental Program 2.1. Details of Specimen The experimental specimen was constructed in the Civil Engineering Experimental Center of Yangtze University (Jingzhou, China). The specimen was a model of a concrete encased steel frame-reinforced concrete core tube built in an 8-degree seismic fortification intensity zone. The model was 1/5 reduced-scale of 10 stories with a total height of 8700 mm. To ensure experimental safety, the slab of the top floor was not constructed. The planar of specimen was a square with dimensions of 1800 mm × 1800 mm. The depth of the foundation, the first story and the rest of the stories were 500 mm, 1000 mm and 800 mm respectively. The specimen consisted of a concrete encased steel frame and a reinforced concrete core tube. The steel skeleton was pre-buried inside the foundation, as shown in Figure 1. The concrete-encased steel frame system consisted of 12 concrete-encased columns with cruciform section and 20 steel beams on each story. As shown in Figure 2, the longitudinal bars in columns were 4 mm in diameter. As shown in Figure 3a, steel beams were rigidly connected with columns and the substantial details of specimen were shown in Figure 3b.
Appl. Sci. 2017, 7, 314
3 of 18
The reinforced concrete core tube was 600 mm × 600 mm in square. The core tube in first two stories was 60 mm in thickness and for the rest it measured 40 mm. Two holes with 500 mm × 300 mm Appl. Sci. 2017, 7, 314 3 of 18 in dimension were set on each story to simulate the elevator doors. Double-layer meshed bars were set in the the holes asholes shown Figurein4a. The internal mesh reinforcement and the view set edge in theofedge of the asinshown Figure 4a. The steel internal steel mesh reinforcement and the of reinforced concrete core tube were shown in Figure 4b. Concealed columns were pre-buried in view of reinforced concrete core tube were shown in Figure 4b. Concealed columns were pre-buried thein corners of core tube, which improved the bearingthe capacity andcapacity was beneficial to the connection the corners of core tube, which improved bearing and was beneficial to the between beams and columns. The thickness of floor slabs is 30 mm. connection between beams and columns. The thickness of floor slabs is 30 mm. Premixed concrete waswas used. To To determine thethe average concrete compressive strength three Premixed concrete used. determine average concrete compressive strength three cylinders (150 × 300 mm) were tested. The measured concrete compressive strength was 41.5 MPa. cylinders (150 × 300 mm) were tested. The measured concrete compressive strength was 41.5 MPa. TheThe longitudinal barsbars andand hoop reinforcements used were 4 mm in diameter. TheThe results of the longitudinal hoop reinforcements used were 4 mm in diameter. results of the characterization tests are are shown in Table 1. 1. characterization tests shown in Table Table 1. Materials properties of steel. Table 1. Materials properties of steel. MaterialMaterial Φ4 bars Φ4 bars Steel plate Steel plate
Yield Strength fy Strength f u fu Yield Strength fy Ultimate Ultimate Strength 2) 2) (N/mm 2) 2) (N/mm(N/mm (N/mm 305 327
305 327
424424 463463
Elastic Es Es ElasticModulus Modulus 2 (N/mm (N/mm) 2) 5 5 2.1 × ×1010 2.1 5 2.0 × 10 2.0 × 105
According to Architectural Structure Standards (GB50009-2001) of live China, and dead According to Architectural Structure Load Load Standards (GB50009-2001) of China, andlive dead load 2 and 1.6 2 respectively, which took the weight of filler wall 2 2 load were considered as 2.0 kN/m kN/m were considered as 2.0 kN/m and 1.6 kN/m respectively, which took the weight of filler wall into into account. Appropriate combination of was the calculated loads was and calculated and bysandbags preloading account. Appropriate combination of the loads achieved by achieved preloading sandbags each floor.ofThe of the concrete-encased steel frame-reinforced core tube on each floor.on The design thedesign concrete-encased steel frame-reinforced concrete coreconcrete tube building building was governed by the earthquake actions. was governed by the earthquake actions.
(a)
(b)
Figure 1. Dimension of specimen: (a) cross section; (b) elevation (unit: mm). Figure 1. Dimension of specimen: (a) cross section; (b) elevation (unit: mm).
Appl. Sci. 2017, 7, 314 Appl.Sci. Sci.2017, 2017,7,7,314 314 Appl. Appl. Sci. 2017, 7, 314
4 of 18 4of of18 18 4 4 of 18
@ @ @
(a) (a) (a)
(b) (b) (b)
Figure2.2.(a) (a)Column Columnsection sectionand anddimension; dimension;(b) (b)dimension dimensionof ofsteel steelskeleton skeleton(unit: (unit:mm). mm). Figure Figure 2. (a) Column section and dimension; (b) dimension of steel skeleton (unit: mm).
(a) (a) (a)
(b) (b) (b)
Figure3.3.(a) (a)Beam Beamcross-section; cross-section;(b) (b)beam-column beam-columnconnection connection(unit: (unit:mm). mm). Figure Figure Figure 3. 3. (a) (a)Beam Beamcross-section; cross-section; (b) (b) beam-column beam-column connection connection (unit: (unit: mm). mm).
(a) (a) (a)
(b) (b) (b)
Figure4.4.(a) (a)Shear Shearwall wallwith withan anopening; opening;(b) (b)details detailsof ofShear Shearwall wall(unit: (unit:mm). mm). Figure Figure Figure 4. 4. (a) (a)Shear Shearwall wall with with an an opening; opening; (b) (b) details details of of Shear Shear wall wall (unit: (unit: mm). mm).
2.2.Test TestSetup Setupand andProcedure Procedure 2.2. 2.2. Test Setup and Procedure 2.2. Test Setup and Procedure The pulsation pulsation method method was was applied applied to to measure measure the the dynamic dynamic characteristics characteristics of of the the specimen. specimen. The The pulsation method was applied to measure the dynamic characteristics of the specimen. The pulsation method (China was applied to Institute measure of theNoise dynamic characteristics of the specimen. Vibration pickup sensors Orient & Vibration, Beijing, China) were Vibration pickup pickup sensors sensors (China (China Orient Orient Institute Institute of of Noise Noise & & Vibration, Vibration, Beijing, Beijing, China) China) were were Vibration Vibration pickup sensors (China Orient Institute of Noise & Vibration, Beijing, China) were installed installedon onthe thecenter centerof ofeach eachfloor, floor,which whichtook tookthe theearth earthpulse pulseas asthe thevibromotive vibromotivesource sourceas asshown shown installed installed on the center of each floor, which took the earth pulse as the vibromotive source as shown on the center of vibration each floor,pickup whichsensors took the earth pulse as the vibromotive source as shown in in Figure 5. The and signal acquisition system were shown in Figure 5d; in Figure Figure 5. 5. The The vibration vibration pickup pickup sensors sensors and and signal signal acquisition acquisition system system were were shown shown in in Figure Figure 5d; 5d; in Figure 5. The vibration pickup sensors andresults. signal The acquisition system were shown in Figurewith 5d; twomeasurements measurements weretaken takenfor for accurate sensorswere were applicable forstructures structures two were accurate results. The The sensors sensors applicable for with two measurements were taken for accurate results. were applicable for structures with two measurements were taken for accurate results. The sensors were applicable for structures with low low natural natural frequency frequency at at the the range range of of 22 Hz Hz to to 100 100 Hz. Hz. Due Due to to the the symmetry symmetry of of the the cross cross section, section, low low natural frequency at the range of 2 Hz to 100 Hz. Due to the symmetry of the cross section, natural frequency at the range ofhorizontal 2 Hz to 100direction Hz. Due were to themeasured. symmetry of the cross section, vibration vibration modes in only one As shown in Figure data vibration modes modes in in only only one one horizontal horizontal direction direction were were measured. measured. As As shown shown in in Figure Figure 6, 6,6,data data vibration modes in only one horizontal direction were measured. As shown in Figure 6, data collected from the collected from from the the sensors sensors indicated indicated aa resonance resonance phenomenon phenomenon at at f0 = 5.942 5.942 Hz, Hz, which which showed showed the the collected collected from the sensors indicated a resonance phenomenon at ff00 == 5.942 Hz, which showed the sensors indicated a resonance phenomenon at f = 5.942 Hz, which showed the primary frequency. 0 primary frequency. primary frequency. frequency. primary
Appl. Sci. 2017, 7, 314 Appl. Sci. 2017, 7, 314
5 of 18 5 of 18
Appl. Sci. 2017, 7, 314
5 of 18
Vibration pick-up instruments Vibration pick-up instruments
(a) (a)
(b)
(c)
(b)
(c)
(d) (d) Figure 5. 5. (a)(a)Arrangement instruments;(b) (b)the thesteel steelskeleton; skeleton;(c)(c) measurement Figure Arrangementofofvibration vibration pick-up pick-up instruments; measurement Figure 5. (a) Arrangement of vibration pick-up instruments; (b) the steel skeleton; (c) measurement instrument; (d)(d)details instrument; detailsofofthe theinstrument. instrument. instrument; (d) details of the instrument. 2.0 2.0
-1
velocity(mm*s -1)
velocity(mm*s )
Natural frequency frequency Natural 1.5 1.5
1.0 1.0
0.5
0.5
0.0
0.0 0 0
10
10
20 30 20 30 Frequency(Hz)
40
40
50
50
Frequency(Hz)
Figure 6. 6. Natural Figure Natural frequency. frequency. Figure 6. Natural frequency.
Furthermore, modal analyses of higher order frequencies based on the measured datas were Furthermore, modal analyses of higher higher order frequencies basedprogram. on the the measured datas were Furthermore, of order frequencies based on measured datasand were conducted by themodal Data analyses Acquisition and Signal Processing (DASP) The principle conducted by the Data Acquisition and Signal Processing (DASP) program. The principle and conducted by the Data Acquisition and Signal Processing (DASP) program. The principle and procedure are shown as the follows [31,32]. procedure are shown as the follows [31,32]. procedure are shown as the follows [31,32].can be expressed by the dynamic equation. Dynamic characteristics for structure Dynamic Dynamic characteristics characteristics for for structure structure can can be be expressed expressed by by the the dynamic dynamic equation. equation.
Appl. Sci. 2017, 7, 314
6 of 18
..
.
M x + C x + Kx = f (t)
(1) .
..
where M, C and K are matrices of mass, damping and stiffness, respectively; x, x and x are the response vectors of displacement, velocity and acceleration, respectively; f (t) is the vector of exciting force. Laplace transform method is applied on Equation (1). h
i Ms2 + Cs + K X (s) = F (s)
(2)
where s is a complex variable. The matrix of generalized impedance Z(s) can be expressed as: h i Z (s) = Ms2 + Cs + K
(3)
The matrix of frequency response H(s) can be expressed as: h i −1 H (s) = Ms2 + Cs + K
(4)
When s = j f , jf is column matrix of frequency at j-column. Equation (3) can be expressed as: Z( f ) = K − f 2 M + j f C
(5)
Matrix of vibration mode can be expressed as: Φ = [φ1 , φ2 , · · · , φn ]
(6)
where φn is the n-order of vibration mode. A symmetric matrix has weighting orthogonal characteristic, and M, C and K are respectively expressed as: .. . Φ T MΦ = (7) mr .. .
..
Φ T CΦ =
.
cr .. ..
Φ T KΦ =
(8)
.
.
kr ..
(9)
.
where mr , cr and kr are mass, damping and stiffness at r-order. According to Equations (7)–(9), Equation (5) can be expressed as: Z ( f ) = Φ−T
..
.
−1 Φ
zr
where zr = kr − f 2 mr + j f cr , jf is frequency at j-column.
..
.
(10)
Appl. Sci. 2017, 7, 314
7 of 18
The matrix of frequency response H(ω) can be expressed as: H ( f ) = Z ( f ) −1 N
Hij ( f ) =
∑
2 r =1 m r ( f r
(11)
φri φrj − f 2 + j2ϕr f r f )
(12)
kr mr cr ϕr = 2mr f r f2 =
(13) (14)
where ϕr , fr and φr are vibration mode at r-order mode, damping ratio and frequency, respectively; and mr , cr and kr are mass, damping and stiffness at r-order, respectively. H(f ) is actually linear superposition of frequency response from the vibration pickup sensors. The frequency values of the first five orders were calculated by the measured data through the theories above. The corresponding frequencies are shown in Table 2. Table 2. The frequency values of first five vibration modes. Vibration Mode
1
2
3
4
5
f (Hz)
5.942
18.981
25.130
37.935
50.034
3. Finite Element Analysis In this section, a finite element model of the concrete-encased frame-reinforced concrete core tube building is constructed based on fiber column element and layered shell element in OpenSees. OpenSees has the advantages of excellent nonlinear computation capacities and accurate simulation for elastic-plastic behavior of structures [33,34]. Reasonable constitutive relations and element types are respectively adopted and described as follows. The concrete and steel mechanical properties are related to the measured data. 3.1. Material Modeling The “Concrete02” material as uniaxial concrete material object with tensile strength and linear tension softening is described by the curve as shown in Figure 7. The modified Kent–Park uniaxial concrete model is adopted for the material properties. Both unconfined and confined concrete fibers in this constitutive model consider tensile strength with linear degeneration. The strain–stress constitutive relationship can be expressed in Equations (15)–(18) [35].
fc
h
2ε 0.002
−
2 ε 0.002
i
σ = f c [1 − Z (ε − 0.002)] 0.2 f c Z=
ε ≤ 0.002 0.002 ≤ ε ≤ ε 20 ε ≥ ε 20
0.5 ε 50u + ε 50h − 0.002
3 + 0.002 f c 0.002 f c − 1000 s 3 B ε 50h = ρs 4 sh
ε 50u =
(15)
(16) (17)
(18)
where σ is stress; ε is strain; f c is compressive strength; ρs is stirrup ratio; B is width of core concrete; and sh is stirrup spacing.
Appl. Sci. 2017, 7, 314 Appl. Sci. 2017, 7, 314
8 of 18 8 of 18
Stress Stress
where σ is stress; ε is strain; fc is compressive strength; ρs is stirrup ratio; B is width of core concrete; where σ is stress; ε is strain; fc is compressive strength; ρs is stirrup ratio; B is width of core concrete; and h is stirrup Appl. sSci. 7, 314spacing. 8 of 18 and sh is2017, stirrup spacing.
Elastic modulus modulus ofElastic unloading of unloading
Crushing Crushing strength strength
Compressive Compressive strength strength
Tension softening stiffness Tension softening stiffness Tensile strength Tensile strength
Strain Strain
Elastic modulus Elastic modulus
Stress–strain curve of concrete. Figure 7. Stress–strain Figure 7. Stress–strain curve of concrete.
The “Steel02”material materialis is in OpenSees, as uniaxial Giuffre–Menegotto–Pinto steel material The in as uniaxial Giuffre–Menegotto–Pinto steel material objects The“Steel02” “Steel02” material is OpenSees, in OpenSees, as uniaxial Giuffre–Menegotto–Pinto steel material objects with isotropic strain hardening are allocated to columns and beams. The von Mises yield with isotropic strain hardening are allocated to columns and beams. The von Mises yield criterion objects with isotropic strain hardening are allocated to columns and beams. The von Mises yield criterion usedThe for steel. The curve stress–strain exhibits two stages, elastic and iscriterion used forisissteel. exhibitscurve two stages, including elasticincluding and hardening stages, used forstress–strain steel. The stress–strain curve exhibits two stages, including elastic and hardening stages, as shown in Figure 8. The reinforcement element is embedded in concrete so that as shown in Figure 8. The reinforcement element is embedded in concrete so that the strain of the hardening stages, as shown in Figure 8. The reinforcement element is embedded in concrete so that the strain of theisreinforcement is compatible with that of concrete element [36]. Es is elastic modulus reinforcement compatible with that of concrete element [36]. E is elastic modulus of steel; f s y is the strain of the reinforcement is compatible with that of concrete element [36]. Es is elastic modulus of steel; f y is yield strength; and Ep is the strain-hardening ratio and takes the value of 0.001 [37]. yield strength; and strength; Ep is the strain-hardening ratio and takesratio the value of 0.001 [37]. The “Steel02” of steel; fy is yield and Ep is the strain-hardening and takes the value of 0.001 [37]. The “Steel02” material and “Concrete02” material take the properties which are with nonlinear material and “Concrete02” material take the properties which are with nonlinear stress–strain The “Steel02” material and “Concrete02” material take the properties which are with nonlinear stress–strain constitutive relations. constitutive stress–strainrelations. constitutive relations.
f fy y
Ep Ep
Es Es
0 0
Figure 8. Stress–strain curve of steel, steel, ffy:: yield yield strength; strength; Ep:: strain-hardening strain-hardening ratio; Es:: elastic elastic modulus modulus Figure 8. Stress–strain curve of steel, yfy: yield strength; Epp: strain-hardening ratio; Ess: elastic modulus of steel. of steel.
3.2. Elements of Component 3.2. 3.2. Elements Elements of of Component Component The nonlinear beam–column element is adopted, which considers the effects of P-Δ and large The The nonlinear nonlinear beam–column beam–column element element is is adopted, adopted, which which considers considers the the effects effects of of P-∆ P-Δ and and large large deformations, which P and Δ are static load and displacement, respectively [38]. The extra inner deformations, which P and ∆ are static load and displacement, respectively [38]. The extra inner deformations, which P and Δ are static load and displacement, respectively [38]. The extra inner forces will be transmitted to the surrounding elements of beam and column through the inner force forces forceswill willbe betransmitted transmitted to to the the surrounding surrounding elements elements of of beam beam and and column column through through the the inner inner force force redistribution. Therefore, reasonable material and element forms need to be selected. Columns and beams are simulated by “dispBeamColumn” element, which is a fiber element based on stiffness
Appl. Sci. 2017, 7, 314
9 of 18
Appl. Sci. 2017, 7, 314 Appl. Sci. 2017, 7, 314 redistribution. Therefore,
9 of 18
of 18 reasonable material and element forms need to be selected. Columns9 and redistribution. Therefore, reasonable material and element forms be selected. Columns and beams are simulated by “dispBeamColumn” element, which is aneed fibertoelement based on stiffness beams are simulated “dispBeamColumn” element,points; which the is aGauss–Lobotto fiber element based on stiffness method. Each elementby is divided into four integration quadrature rule is method. Each element is divided into four integration points; the Gauss–Lobotto quadrature rule is method. to Each element is divided into four integration points; rule is adopted integrate iteration as shown in Figure 9. Each pointthe hasGauss–Lobotto corresponding quadrature weight function ω adopted to integrate iteration as shown in Figure 9. Each point has corresponding weight function ω adopted to integrate iteration as shown Figure 9. Each point has by corresponding weight function ω and distribution of integral point ξ. The in beam section is assembled material stiffness and stress by and distribution of integral point ξ. The beam section is assembled by material stiffness and stress by and distribution of integral point ξ. The beam section assembled by material stiffness and different stress by fibers at local coordinate system as illustrated in is Figure 10 [39]; each fiber exhibits fibers at local coordinate system as illustrated in Figure 10 [39]; each fiber exhibits different constitutive fibers at local coordinate system as illustrated in Figure 10 [39]; each fiber exhibits different constitutive material models. material models. constitutive material models.
1=0.0 =1/6 11=0.0 1=1/6
3=0.7237 4=1.0 =1/6 44=1.0 =5/6 33=0.7237 4 =1/6 3=5/6
2=0.2763 =5/6 22=0.2763 2=5/6
Figure 9. Distribution of integral points and weighting function. Figure Figure 9. 9. Distribution Distribution of of integral integral points points and and weighting weighting function. function.
Y Y Z Z
Figure 10. Fiber distributions in section of steel beam. Fiber distributions in section of steel beam. Figure 10. Fiber
The shear wall is simulated by the “ShellMITC4” element. The “ShellMITC4” is a type of shell The shear wall the element. The isis athe of element program, which is by a bilinear isoparametric formulation to improve thin-plate The in shear wall is is simulated simulated by the “ShellMITC4” “ShellMITC4” element. The “ShellMITC4” “ShellMITC4” a type type of shell shell element in program, which is a bilinear isoparametric formulation to improve the thin-plate bending performance. It can account for the development of nonlinear membrane forces. The element in program, which is a bilinear isoparametric formulation to improve the thin-plate bending bending performance. It can forwall the fiber development of nonlinear membrane forces. The “LayeredShell” is adopted for the development shear section, which is based onThe the“LayeredShell” mechanics of performance. It can account foraccount the of nonlinear membrane forces. “LayeredShell” is adopted for the shear wall fiber section, which is based on the mechanics of composite materials. It considers the geometric nonlinearity of large deformations. A shell element is adopted for the shear wall fiber section, which is based on the mechanics of composite materials. composite It layers considers thethe geometric nonlinearity of deformations. A shell is divided materials. into along direction and each element layer is is endowed appropriate It considers the several geometric nonlinearity ofthickness large deformations. A large shell divided intoelement several is divided into several layers along the thickness direction and each layer is endowed appropriate material property to consider the coupling effect of bending and shear. The double-layer mesh layers along the thickness direction and each layer is endowed appropriate material property to material property to consider the coupling effect of bending and shear. The double-layer reinforcement of core tube is treated as the equivalent steel layer. In the computational process the consider the coupling effect of bending and shear. The double-layer mesh reinforcement ofmesh core reinforcement of tube treated the equivalent steel layer. In the computational the strain curvature the is core layer are obtained, other layers are strain calculated according tube isand treated ascore theof equivalent steelas layer. In the afterwards computational process the andprocess curvature strain and curvature of the core layer are obtained, afterwards other layers are calculated according to the plane section assumption. The stress at each layer is solved by the respective constitutive of the core layer are obtained, afterwards other layers are calculated according to the plane section to the plane section assumption. The is stress each layer isis solved by respective constitutive equation of material. Finally, the layer inner force ofatshell element educed by the numerical integration. The assumption. The stress at each solved by the respective constitutive equation of material. equation of material. Finally, the inner force of element is educed by numerical integration.layer The longitudinal and force transverse reinforcement is shell dispersed into theintegration. orthotropic reinforcement Finally, the inner of shell element is educed by numerical The longitudinal and longitudinal and transverse reinforcement is dispersed into the orthotropic reinforcement layer distributing uniformly in physical location, as illustrated in Figure 11 [40,41]. Table 3 shows the transverse reinforcement is dispersed into the orthotropic reinforcement layer distributing uniformly distributing uniformly in physicalinlocation, illustrated Figurethe 11 Component [40,41]. Table 3 shows the Component of model. in physical location, as illustrated Figure 11as[40,41]. Tablein 3 shows of model. Component of model. Z Z
X X
Y
Core concrete
Y
Core concrete Mesh reinforcement Mesh reinforcement Protective concrete layer Protective concrete layer
Schematic diagram of “LayeredShell”. Figure 11. Schematic Figure 11. Schematic diagram of “LayeredShell”.
Appl. Sci. 2017, 7, 314
10 of 18
Appl. Sci. 2017, 7, 314
10 of 18
Table 3. 3. Component Component of of model. model. Table
Item Item Node Node “dispBeamColumn” element “dispBeamColumn” element “ShellMITC4” element “ShellMITC4” element
Quantity Quantity 340 340 420 420 220 220
3.3. 3.3. Comparison Comparison between between Experimental Experimental Investigations Investigations and FEA Finite Finite element element modal modal analysis analysis is conducted on the experimental specimen. The The sections sections and and material aresame sameasasthe thetest test specimen. damping percentage is 0.05 according to material properties are specimen. TheThe damping percentage is 0.05 according to Code Code for Seismic of Buildings (GB50011-2001) China. The order first five order frequencies are for Seismic DesignDesign of Buildings (GB50011-2001) of China.ofThe first five frequencies are calculated, calculated, agreeexperimental well with experimental results as shown in Table 4.between Comparison which agreewhich well with results as shown in Table 4. Comparison finitebetween element finite test result indicatesofthe of the modal finite element modal analysis. resultelement and testresult resultand indicates the accuracy theaccuracy finite element analysis. Table Table 4. Comparison Comparison of of frequencies, frequencies, FEA: finite element modal analysis.
Order Order 1 1 22 33 4 55
Frequencies of Specimen (Hz) Frequencies of Specimen (Hz) 5.942 5.942 18.981 18.981 25.130 25.130 37.935 37.935 50.034 50.034
Frequencies of FEA (Hz) Frequencies of FEA (Hz) 5.864 5.864 18.126 18.126 23.974 23.974 36.469 36.469 48.433 48.433
Absolute Error (%) Absolute Error (%) 1.312 1.312 4.504 4.504 4.601 4.601 3.865 3.865 3.199 3.199
4. Seismic Seismic Damage Damage Evaluation Evaluation 4. 4.1. Structural Structural Damage Damage Analysis Analysis under under Earthquake Earthquake Action Action 4.1. The El-Centro selected as aasrepresentative ground motion input to investigate the damage The El-Centrowave waveisis selected a representative ground motion input to investigate the process. process. Acceleration–time history and elastic spectrumspectrum of El-Centro wave are wave shownare in damage Acceleration–time history andresponse elastic response of El-Centro Figure 12. The analysis time increment is 0.02 s to ensure the accuracy and convergence. Fundamental shown in Figure 12. The analysis time increment is 0.02 s to ensure the accuracy and convergence. period T0 of specimen in measured the above in experiment 0.169 s, theiscorresponding acceleration Fundamental period T0measured of specimen the aboveisexperiment 0.169 s, the corresponding in response spectrum is S = 0.67g, where g is acceleration of gravity. This intensity of earthquake a acceleration in response spectrum is Sa = 0.67g, where g is acceleration of gravity. This intensity of is appropriate to reflect dynamic characteristics of hybrid structure [42,43]. Specimen experiences earthquake is appropriate to reflect dynamic characteristics of hybrid structure [42,43]. Specimen different degree of stiffness degradation, eventuallywhich leads eventually to the increase of period. experiences different degree of stiffnesswhich degradation, leads to the Period-time increase of history curves for the first seven vibration modes are shown in Figure 13. period. Period-time history curves for the first seven vibration modes are shown in Figure 13. 4000
-2
Acceleration(mm*s )
3000 2000 1000 0 -1000 -2000 -3000 -4000 0
10
20
30 Time(s)
(a) Figure 12. Cont.
40
50
Appl. Appl. Sci. Sci. 2017, 2017, 7, 7, 314 314 Appl. 2017, 7, 314 Appl. Sci.Sci. 2017, 7, 314
11 11 of of 18 18 11 11 of of 18 18
Acceleration(mm*s ) -2 -2 Acceleration(mm*s Acceleration(mm*s) )
10000 10000 10000 -2
8000 8000 8000 6000 6000 6000 4000 4000 4000 2000 2000 2000 0 0 0 0 0 0
1 1 1
2 2 2 Period(s) Period(s) Period(s)
3 3 3
4 4 4
(b) (b)(b) Figure 12. (a) Time history curve of acceleration of El-Centro wave; (b) response spectrum. Figure Time history curve acceleration El-Centro wave; response spectrum. Figure 12.12. (a)(a) Time history curve of of acceleration of of El-Centro wave; (b)(b) response spectrum. Figure 12. (a) Time history curve of acceleration of El-Centro wave; (b) response spectrum. 0.4 0.4 0.4
T(s) T(s) T(s)
0.3 0.3 0.3 0.2 0.2 0.2
1 2 3 4 5 6 7
1 1 2 2 3 3 4 4 5 5 6 6 7 7
0.1 0.1 0.1 0.0 0.0 0 2 4 6 8 10 12 14 16 0.0 0 2 4 6 8 10 12 14 16 0 2 4 6 8Time(s) 10 12 14 16 Time(s) Time(s)
Figure 13. Time history curve of period for first seven vibration modes. Figure13. 13.Time Timehistory historycurve curveof ofperiod periodfor for the thefirst firstseven sevenvibration vibrationmodes. modes. Figure Figure 13. Time history curve of period for thethe first seven vibration modes.
Displacement-time history curves and acceleration-time history curves of the top node are Displacement-time historycurves curvesand andacceleration-time acceleration-time history curves ofthe thenode topnode node are Displacement-timehistory history curves and history curves of of the top are shown Displacement-time acceleration-time history curves are shown in Figures 14 and 15. Furthermore, the total shear resisted by the columns andtop the core wall at shown in Figures 14 and 15. Furthermore, the total shear resisted by the columns and the core wall at in Figures 14 and 15. Furthermore, the the total shear resisted byby thethe columns and the core atatthe shown in Figures 14 and 15. Furthermore, total shear and corewall wall the bottom are shown in Figure 16. At the initial stageresisted when t = 1.2 s, columns periods of allthe vibration modes the bottom are shown in Figure 16. At the initial stage when = periods 1.2 s, periods of all vibration modes bottom are shown in in Figure 16.16. At the initial stage when t = 1.2 of allofvibration modes remain the bottom are shown Figure At the initial stage t =t s, 1.2 s,bears periods allof vibration modes remain constant, no stiffness degradation occurs, andwhen the core wall 53.37% total shear. When remain constant, no stiffness degradation occurs, and the core wall bears 53.37% of total shear. When constant, no stiffness degradation occurs, and the core wall bears 53.37% of total shear. When t = 3.2 s, remain no stiffness occurs, and the core wall bears total shear. When t = 3.2constant, s, periods increase degradation in varying degrees. Concrete-encased steel53.37% frame of slightly damages and =3.23.2s, s,periods periodsincrease increase varyingdegrees. degrees. Concrete-encased steelframe frameslightly slightly damages andis periods increase in varying degrees. Concrete-encased steel frame slightly damages and shear t =tshear ininvarying Concrete-encased steel damages and is redistributed to core wall. Lateral displacement of specimen increases gradually and reaches shear redistributed to core wall. Lateral displacement specimen increases gradually and reaches redistributed to coretowall. Lateral displacement of specimen increases gradually and reaches maximum. shear is is redistributed core wall. Lateral ofof specimen increases gradually maximum. Subsequently when t = 4.8 displacement s, periods increase rapidly especially in theand firstreaches and the maximum. Subsequently when t = 4.8 s, periods increase rapidly especially in the first and the Subsequently when t = 4.8 s, periods increase rapidly especially in the first and the second vibration maximum. Subsequently t = 4.8 s, periods rapidly second vibration modes.when Core wall resists 77.36% increase of the total shear.especially in the first and the second vibration modes. Core wall resists 77.36% the total shear. modes. Core wall resists 77.36% of the total shear. second vibration modes. Core wall resists 77.36% ofof the total shear. 120 120120
Displacement(mm) Displacement(mm) Displacement(mm)
80 80 80 40 40 40 0 0 0
-40 -40-40 -80 -80-80
-120 -120 0 2 4 6 8 10 12 14 16 -120 0 0 2 2 4 4 6 6 Time(s) 8 8 10 10 12 12 14 14 16 16 Time(s) Time(s)
Figure Figure 14. 14. Displacement–time Displacement–time history history curves. curves. Figure Displacement–time history curves. Figure 14.14. Displacement–time history curves.
Appl. Sci. 2017, 7, 314 Appl.Sci. Sci.2017, 2017,7,7,314 314 Appl.
12 of 18
12ofof18 18 12
66 Appl. Sci. 2017, 7, 314
12 of 18
Acceleration(g)
Acceleration(g) Acceleration(g)
44 22
6
00
4
-2-2
2
-4-40 -6-6 -2 -400
22
44
66
10 88 10 Time(s) Time(s)
12 12
14 14
16 16
-6
Figure 15. Acceleration–time history curves. Figure 15. Acceleration–time history 0 15. 2 Acceleration–time 4 6 8 10 12 curves. 14 16 Figure history curves. Time(s)
Base shear(kN)
Base shear(kN) Base shear(kN)
Figure 15. Acceleration–time history curves. Column 200 Column 200 Corewall wall Core 100 100
Column Core wall
200
00
100
-100 -100
0
-200 -200 -100 00
22
44
66
0
2
4
6
-200
10 88 10 Time(s) Time(s) 8
10
12 12 12
14 14 14
16 16 16
Figure 16. Shear columns and corewall wallatat atthe thebottom. bottom. Figure 16. Sheardistribution distributionof ofcolumns columns andcore wall the bottom. Figure 16. Shear distribution Time(s)and Figure 16. Assessment Shear distribution of columns and core wall at the bottom. 4.2. Criterion ofSeismic Seismic Damage Assessment Criterion Damage Assessment 4.2.4.2. Criterion of ofSeismic Damage
According to Standard forSeismic SeismicAppraisel Appraiselof ofBuilding Building(GB50023-2009) (GB50023-2009) of of China, structural According Standard for Seismic Appraisel structural According Standard for of Building (GB50023-2009) ofChina, China, structural 4.2. Criterionto ofto Seismic Damage Assessment damage is classified into five levels, as shown in Table 5 and Figure 17. D is the index for assessing damage is classifiedinto intofive fivelevels, levels, as as shown shown in Table 55and Figure 17. DDisisthe index forfor assessing damage isAccording classified in Table and Figure 17. the index assessing to Standard for Seismic Appraisel of Building (GB50023-2009) of China, structural damageof ofstructure. structure. damage damage of structure. damage is classified into five levels, as shown in Table 5 and Figure 17. D is the index for assessing damage of structure.
IntactState State Intact D ≤ 0.08 Intact State
Intact D State ≤ 0.08 D ≤ 0.08
D ≤ 0.08
Table5.5.Damage Damageindex index(D) (D)related relatedtotodamage damage level Table Table 5. Damage index (D) related to damagelevel level. Table 5. Damage index (D)Damage related to damage level Minor Damage Medium Damage Serious Damage Collapse Collapse Minor Damage Medium Serious Damage Minor Damage Medium Damage Serious Damage Collapse 0.08 0.16 Medium 0.16
