176 Figure 9.1 a) Pushover curve (Uniform distribution of lateral loads along the +X axis) b) ATC-40 Capacity Spectrum-ADRS (Uniform distribution of lateral loads along the +X axis). 182 Figure 9.16 Deformed shape of the structure at performance point-step 84 (modal distribution of lateral loads along the -Y axis).
- Motivation
- Research Objective
- Research Approach
- Report Outline
In the ninth chapter, the non-linear static analysis of the retrofitted structure is explained and its results are discussed. In the tenth chapter, the non-linear dynamic time-history analysis of the retrofitted structure is explained and its results are discussed.
Required Information for the Assessment of the Structure
- General Information and History of the Building
- Required Input Data
- Materials
- Knowledge Level
- Confidence Factors
Information on the mechanical properties and condition of the constituent materials, such as the overall dimensions and cross-sectional properties of the building elements, should be collected. Data on the current condition of the concrete and reinforcing steel should be collected.
Seismic Action for the Assessment of the Structure
- Seismic Action
- Combination of the Effects of the Components of the Seismic Action 11
- Modal Response Spectrum Analysis
- Nonlinear Static (Pushover) Analysis
- Nonlinear Time-History Dynamic Analysis
EEdx are the action effects due to the implementation of seismic action along the chosen horizontal axis of the structure. The sum of the effective modal masses (for all modes and a given direction) is equal to the mass of the structure (CSi, 1995).
Performance Based Design
- Rehabilitation Objectives
- Structural Performance Levels
- Capacity Curve
- Primary and Secondary Elements and Components
- Component Behaviour F-δ Curve
- Performance Levels of the Elements
- Performance Levels of the Structure
- Target Displacement Check
- Performance Point Estimation
- ATC-40 Methodology
The limit states of the performance levels are defined on the capacity curve of each element according to the corresponding deformations δd. The definition of the first performance point is followed by a bilinear representation of the capacity spectrum.
- Introduction
- Technical Strategies
- Local Modification of Components
- Removal or Lessening of Existing Irregularities
- Global Structural Strengthening and Stiffening
- Reducing Earthquake Demands (mass reduction, seismic isolation,
- Management Strategies
- Retrofit System Selection
- Traditional Methods for the Retrofitting of Buildings
- Addition of shear walls
- Addition of braces in Frames
- Extension of Existing Columns with additional Shear Walls
- Columns Retrofitting-The Application of Jackets to Columns
The result is that the demand for the existing elements in the structure is greatly reduced. Once the goal is to increase the stiffness and strength of the structure, the most effective method of retrofitting is the addition of shear walls. It is followed by adding braced frames, widening the existing columns with additional shear walls and using FRPs.
It is considered the most effective method for increasing the strength and rigidity of the structure.
SAP2000 Overview
Forces such as seismic, wind, vehicle, wave and thermal forces can be automatically generated and assigned according to a set of code-based guidelines. Plastic hinges can be specified in flexural elements according to code-based standards or empirical data (CSi Knowledge Base, 2013). The plastic hinge behavior of slender elements, sliding walls and steel plates can be determined.
Demand capacity spectrum formulation and performance point calculations can be performed (CSi Knowledge Base, 2013).
History and Description of the Structure
The hotel reception is in the northern part of the ground floor, and there are shops in the southern part of the ground floor. It is therefore a frame system (in the X and Y axes), which according to EN is a structural system in which both vertical and lateral loads are carried mainly by spatial frames, whose total shear resistance at the base of the building exceeds 65% of the total shear resistance of the entire structure. However, the design configuration is not compact as the area between the floor outline and the convex polygonal line wrapping the floor exceeds 5%.
Therefore, the criteria of floor plan regularity are not met and a spatial model is required for the analysis of the building.
Modelling of the Structure in SAP2000
- Material Properties
- Frame Sections
- Stiffness- Property Modifiers
- Loading
- Diaphragms
The columns in the ground level of the building are connected to each other through connecting beams. The stiffness of the elements must be changed due to cracks in the concrete sections. 97 Before applying the loads to the model, the load patterns should be defined.
Dead load: it is the dead weight of the elements calculated automatically by SAP2000.
Modal Analysis
Response Spectrum Analysis
Where G+0.3Q is the combination of vertical structural loads considered for dynamic analyzes according to EN.
Modal Response Spectrum Analysis Results
For both main directions of the earthquake, the maximum forces act at the ground floor level. Furthermore, it is observed that the same frames experience the highest forces regardless of the main direction of the earthquake. The total displacements between the two tables are due to the SRSS combination of seismic forces.
114 The larger displacement of the structure is observed at the approachable roof level (25.03 m) along the U2 direction.
Limitations on Use of the Nonlinear Static Analysis-Higher Mode
117 It is concluded that the effects of the higher mode are not significant, as the shear at any story derived from the analysis of the modal response spectrum, considering the modes required to obtain 90% mass participation, does not exceed 130% of the corresponding story shear, considering only the response basic mode in both directions.
Secant Stiffness
The values of the bilinear diagram refer to Mp and Phi-efficiency (idealized) in the cross-section planner, so these are used to calculate the secant stiffness. Thus, a linear response spectrum analysis is performed under the seismic load combination (G+0.3Q) to provide the column axial loads used to calculate the section yielding moment. The percentage of the section that is effective and can carry loads is represented by the eff ratio.
K where Keff is the secant stiffness and Kel is the elastic stiffness of the cross-section Kel E I.
Plastic Hinges
122 Next, FEMA 356 Tables are shown which specify the spine curve of hinges for concrete beams and concrete columns.
Nonlinear Static (Pushover) Analysis
The control node is the link 130 of the structure, as it is closer to the center of mass of the accessible roof (25.03m). The displacement control option is set when the desired displacement of the control node is known, but how much load is required is not known. Displacement monitoring is simply used to measure the displacement at a single point resulting from applied loads and to adjust the magnitude of the load to achieve a specified measured displacement value.
The overall displaced shape of the structure will be different for different load patterns, even if the same displacement is controlled (CSi, 1995).
Results of Nonlinear Static (Pushover) Analysis
133 Figure 6.15 Deformed shape of the structure at the performance point-Step 82 (Uniform distribution of lateral loads along the +Y axis). 135 Figure 6.17 Deformed shape of the structure at the performance point-Step 84 (Uniform distribution of lateral loads along the -Y axis). 137 Figure 6.19 Deformed Shape of the Structure at the Performance Point-Step 89 (Modal Distribution of Lateral Loads along the +X Axis).
140 Figure 6.23 Deformed shape of the structure at performance point step 66 (modal distribution of lateral loads along the +Y axis).
Discussions on the Pushover Analysis Results
The uniform distribution of lateral loads causes higher absolute displacements than the modal distribution, for both X,Y axes. Interstory drift ratios are greater for uniform distribution of lateral loads than for modal distribution, for both X and Y axes. Uniform distribution of lateral loads causes higher interstory drift ratios along the Y axis (2%) than along X axis (1.7%).
However, the modal distribution of lateral loads causes higher interstory drift ratios along the X-axis (1.65%) than along the Y-axis (1.35%).
Nonlinear Characteristics of the structure elements
Earthquake Ground Motion Time-Histories
The user can specify the design ground motions in terms of a target response spectrum and the desired characteristics of the earthquake ground motions in terms of earthquake magnitude, source-to-site distance and other characteristics (Pacific Earthquake Engineering Research Center (PEER), 2010). The values of the acceleration time histories are scaled to the value of ag.S, where for seismic zone II and soil type B is 0.24g1.20.288g. According to EN, the zero-period response spectrum acceleration values must not be lower than the value of ag.S for the site in question.
Figures 7.1 through 7.18 show the scaled and unscaled acceleration time histories and their corresponding response spectra.
Time-History Function Definition in SAP 2000
Load Case Definition in SAP 2000
The values of the time history functions are multiplied by 9.81 m/s2 because the imported values in g. Direct integration is applied to the equations of motion without the use of modal superposition. In direct integration time-history analysis, the damping in the structure is modeled using the full damping matrix, which allows the coupling between modes to be taken into account (CSi, 1995).
For each direct integration time history load case, proportional damping coefficients can be specified that apply to the structure as a whole.
Results of Nonlinear Time-History Analyses
However, all load combinations of the L'Aquila earthquake cause hinges in columns to exceed limit state E). However, all Corinth earthquake load combinations cause column hinges to exceed the life safety limit state. 163 Figure 7.29 Displacement time history of the center of mass (link 130) of the approximate roof due to the Kalamata earthquake.
166 The following figures show the time histories of bending moments and shear forces along the X-axis (M3, V2) and along the Y-axis (M2,V3) of column C20 for each story for the L'Aquila earthquake. are displayed.
Discussions on Nonlinear Time History Analyses Results
Maximum V3-3 is observed in the mezzanine floor level, while the maximum of the others is observed in the A floor level. It is shown from the spine curve of the hinge that before the 18th sec. the element is highly rotated, thus in the 18th sec. the strength of the element is lost. M2-2 (along the Y-axis) is higher than M3-3 (along the X-axis), even though the principal axis of the imposed seismic accelerogram is the X-axis.
This is because C20 is at the edge of the building and there is no other element beyond (to the west) of C20 on the Y-axis to contribute to resisting seismic motion.
Conclusions on the Assessment of the Bearing Capacity of the Structure
171 The most serious damage is observed in floor plans A and B and in the tops of the columns, in the west, south-west and south sides of the building. The maximum drift ratios between floors from all the analyzes are approx. 2% along the Y axis due to pushover analysis with uniform distribution of lateral loads. The Corinth earthquake causes the highest interstory drift ratios (1.7% along the X-axis in floor levels A-B) of the three earthquake events.
The maximum displacement of the center of mass of the accessible roof is 0.26m, due to the earthquake in Corinth, which is too high.
Modal Analysis Results
In addition, a modal analysis of the retrofitted structure is performed when the stiffness represented by table 4.1 of KANEPE is performed. It would be interesting to compare the periods and the participating mass ratios when using the stiffness suggested by table 4.1 and the secant stiffness. 178 Table 8.2 Modal Participating mass ratios of the converted structure using the stiffness suggested by table 4.1 of KANEPE.
Wall System Check
Discussions on Pushover Analyses Results
Discussions on Nonlinear Time-History Analyses Results of the
Conclusions on the Assessment of the Bearing Capacity of the Retrofitted
Check of Shear Resistance of Shear Walls
Check of Shear Resistance of Existing Members
Modal Analyses Comparison
Pushover Analyses
- Comparison of the Capacity Curves of the Non-Retrofitted and the
- Hinges Limit States Results
- Maximum Absolute Displacements Comparison
- Inter-Storey Drift Ratios Comparison
Nonlinear Time-History Dynamic Analyses
- Hinges Limit States
- Comparison of the Maximum Absolute Displacements of the Non-
- Comparison of the Inter-storey Drift Ratios of the of the Non-
- Comparison of the Maximum Forces along the Column C20 of the
Summary
Conclusions