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Figure from:VULNERABILITY OF CODE-COMPLIANT RC BUILDINGS UNDER MULTI-AXIAL EARTHQUAKE LOADING

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Table 1. Characteristics of the investigated structural systems

Table 1 Characteristics of the investigated structural systems

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Figure 1. Description of the investigated buildings and sample reinforcement details of IF-M-030 Tu: Elastic period in horizontal direction. Ty: Elastic period in vertical direction. | H: Design ductility high; M: Medium; L: Low.
Figure 1. Description of the investigated buildings and sample reinforcement details of IF-M-030 Tu: Elastic period in horizontal direction. Ty: Elastic period in vertical direction. | H: Design ductility high; M: Medium; L: Low.
Inelastic response history analysis is performed using the above-mentioned natural horizontal ground motions applied with and without VGM. The acceleration response spectra of the natural records used in analysis are compared with the design spectrum in Fig. 2. The spectra are scaled to a PGA of 0.30g. The inelastic fundamental periods of vibration of the twelve buildings investigated herein are also depicted in Fig. 2. These were identified by Mwafy and Elnashai (2001) for eight seismic excitations and at different input ground motion levels. The average inelastic periods for the three groups of structures are 1.40, 1.75 and 0.9 sec, respectively. It is worth noting that a refined normalization approach is adopted in the current study, whereby all records are scaled to possess equal velocity spectrum intensity in the period range of the buildings. One of the advantages of this scaling approach is the reduction in response variability under different excitations, thus allowing the use of fewer input ground motions. It is observed that the spectral acceleration of the longitudinal component of Loma Prieta (SAR) at the period range 0.1-0.5 sec is significantly higher than Kobe (KBU). Amplifications of higher mode effects are therefore anticipated under the Loma Prieta horizontal component. It is also noteworthy that the spectra of the vertical components of Kobe (KBU) and Lome Prieta (SAR) were comparable before normalization. Employing the HGM scale factors to normalize VGM causes an observable reduction in the vertical component spectrum of Kobe (KBU) compared with Loma Prieta (SAR), as shown from Fig. 2. This approach was adopted to avoid changes in the V/H ratio of the records (1.09 and 1.56 for Loma Prieta and Kobe, respectively). The effect of the vertical component of Lome Prieta (SAR) is therefore expected to be more pronounced compared with Kobe (KBU). This is despite the fact that the PGA of the vertical component of Kobe (KBU) is higher than Loma Prieta (SAR).
Inelastic response history analysis is performed using the above-mentioned natural horizontal ground motions applied with and without VGM. The acceleration response spectra of the natural records used in analysis are compared with the design spectrum in Fig. 2. The spectra are scaled to a PGA of 0.30g. The inelastic fundamental periods of vibration of the twelve buildings investigated herein are also depicted in Fig. 2. These were identified by Mwafy and Elnashai (2001) for eight seismic excitations and at different input ground motion levels. The average inelastic periods for the three groups of structures are 1.40, 1.75 and 0.9 sec, respectively. It is worth noting that a refined normalization approach is adopted in the current study, whereby all records are scaled to possess equal velocity spectrum intensity in the period range of the buildings. One of the advantages of this scaling approach is the reduction in response variability under different excitations, thus allowing the use of fewer input ground motions. It is observed that the spectral acceleration of the longitudinal component of Loma Prieta (SAR) at the period range 0.1-0.5 sec is significantly higher than Kobe (KBU). Amplifications of higher mode effects are therefore anticipated under the Loma Prieta horizontal component. It is also noteworthy that the spectra of the vertical components of Kobe (KBU) and Lome Prieta (SAR) were comparable before normalization. Employing the HGM scale factors to normalize VGM causes an observable reduction in the vertical component spectrum of Kobe (KBU) compared with Loma Prieta (SAR), as shown from Fig. 2. This approach was adopted to avoid changes in the V/H ratio of the records (1.09 and 1.56 for Loma Prieta and Kobe, respectively). The effect of the vertical component of Lome Prieta (SAR) is therefore expected to be more pronounced compared with Kobe (KBU). This is despite the fact that the PGA of the vertical component of Kobe (KBU) is higher than Loma Prieta (SAR).
Figure 4. Tracing the effect of VGM on the global response of the FW-M-030 building using incremental dynamic analysis: (a) top displacement; (b) interstory drift; (c) base shear Figure 3. Tracing the effect of VGM on the global response of the RF-M-030 building using incremental dynamic analysis: (a) top displacement; (b) interstory drift; (c) base shear
Figure 4. Tracing the effect of VGM on the global response of the FW-M-030 building using incremental dynamic analysis: (a) top displacement; (b) interstory drift; (c) base shear Figure 3. Tracing the effect of VGM on the global response of the RF-M-030 building using incremental dynamic analysis: (a) top displacement; (b) interstory drift; (c) base shear
with perimeter columns. The effect of VGM is higher for the buildings designed to a PGA of 0.30g, particularly on the top displacement and interstory drift, which increase by 20% at a PGA of 0.80g.
with perimeter columns. The effect of VGM is higher for the buildings designed to a PGA of 0.30g, particularly on the top displacement and interstory drift, which increase by 20% at a PGA of 0.80g.
Figure 5. Effect of VGM on the axial force variation of a planted column at twice the design PGA adversely affected if high compressive forces are developed or if axial forces changed to tension. In the presence of high vertical forces, the ductility demand also increases due to second order moments. Additionally, the ductility supply is significantly reduced by the presence of high compressive axial forces; hence extensive damage may result due to increased demand and reduced supply. The shear supply may be significantly affected by the variation in column axial forces, which may cause loss or reduction of the axial load contribution to shear strength. Sample results of the effect of VGM on a planted column are shown in Fig. 5. It is observed that maximum axial compressive forces increase by 35% at twice the design intensity. The deterioration in the response of this column under cyclic loading is clear from the axial force response history. It is confirmed from previous studies on the investigated set of buildings (Mwafy and Elnashai, 2001 and 2002; Mwafy, 2001) that the planted columns of irregular buildings exhibit very high curvature ductility demands, reflecting the high energy dissipated in these structural members. Although VGM slightly increases the variation in shear supply, it does not significantly influence the shear demand-supply response for these columns.
Figure 5. Effect of VGM on the axial force variation of a planted column at twice the design PGA adversely affected if high compressive forces are developed or if axial forces changed to tension. In the presence of high vertical forces, the ductility demand also increases due to second order moments. Additionally, the ductility supply is significantly reduced by the presence of high compressive axial forces; hence extensive damage may result due to increased demand and reduced supply. The shear supply may be significantly affected by the variation in column axial forces, which may cause loss or reduction of the axial load contribution to shear strength. Sample results of the effect of VGM on a planted column are shown in Fig. 5. It is observed that maximum axial compressive forces increase by 35% at twice the design intensity. The deterioration in the response of this column under cyclic loading is clear from the axial force response history. It is confirmed from previous studies on the investigated set of buildings (Mwafy and Elnashai, 2001 and 2002; Mwafy, 2001) that the planted columns of irregular buildings exhibit very high curvature ductility demands, reflecting the high energy dissipated in these structural members. Although VGM slightly increases the variation in shear supply, it does not significantly influence the shear demand-supply response for these columns.
Figure 7. Effect of VGM on shear response of a ground story internal column
Figure 7. Effect of VGM on shear response of a ground story internal column
Figure 6. Effect of VGM on shear response of a second story internal column
Figure 6. Effect of VGM on shear response of a second story internal column
R= Agiat collapse)/Ag(at yiela)-S24 (Mwafy and Enashai, 2002) H+V: Horizontal plus vertical ground motions are used G: Global criteria are used As shown from the results presented above, yield and collapse may occur under lower PGA when the structure is subjected to HGM and VGM. Based on the definition of the response modification factor (R) proposed by Mwafy and Elnashai (2002) and Mwafy (2001), this may reduce the R factor, leading to higher seismic design forces. The mean values of the response modification factor ‘supply’ for the twelve buildings investigated in the present study are calculated and presented in Table 2. It is clear that the mean R factors are reduced by up to 18% under the effect of VGM. The most observable case is the R factor of IF-M-015, which is reduced by 21% when subjected to Kobe (KBU). The results confirm the inadequacy of the response modification factor calculations in the absence of VGM, especially for reinforced concrete structures.
R= Agiat collapse)/Ag(at yiela)-S24 (Mwafy and Enashai, 2002) H+V: Horizontal plus vertical ground motions are used G: Global criteria are used As shown from the results presented above, yield and collapse may occur under lower PGA when the structure is subjected to HGM and VGM. Based on the definition of the response modification factor (R) proposed by Mwafy and Elnashai (2002) and Mwafy (2001), this may reduce the R factor, leading to higher seismic design forces. The mean values of the response modification factor ‘supply’ for the twelve buildings investigated in the present study are calculated and presented in Table 2. It is clear that the mean R factors are reduced by up to 18% under the effect of VGM. The most observable case is the R factor of IF-M-015, which is reduced by 21% when subjected to Kobe (KBU). The results confirm the inadequacy of the response modification factor calculations in the absence of VGM, especially for reinforced concrete structures.