Impact of Structural Stiffness on Vibration Periods of Concrete Buildings: A Systematic Review
Abstract
:1. Introduction
2. Methods
2.1. Mathematical and Theoretical Models
2.2. Comparative Analysis of Methods
2.3. Case Studies
2.4. Limitations of Existing Models
2.5. Identification of Research Gaps
3. Results
3.1. Presentation of Quantitative Data
3.2. Qualitative Analysis
3.3. Identifying Trends
3.4. Discussion of Limits and Problems
3.5. Summary of Key Findings
4. Discussion
4.1. Interpretation of Results
4.2. Practical Implications
4.3. Comparison with Theoretical Models
4.4. Identifying Research Gaps
4.5. Limitations of Study
4.6. Recommendations for Future Research
5. Conclusions
5.1. Response to Research Objective
5.2. Summary of Key Findings
5.3. Implications of Findings
5.4. Contributions to the Field
5.5. Recommendations for Future Practices
5.6. Future Research Lines
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Source | Method | Model/Equation | Applicability and Observations | Limitations |
---|---|---|---|---|
[41] | Numerical Simulation | Finite Element Methods (FEM) for Assessing Static Stiffness in Elastic Supports | Improves simulation accuracy, but requires greater computational power | High computational cost and depends on accurate models |
[42] | Static Stiffness Analysis | Force-displacement ratio: | Used in automotive design to evaluate noise and vibration | Does not capture dynamic effects |
[43] | Dynamic Analysis (Temporal History) | Differential equations of motion: | Captures dynamic effects, but requires detailed data on materials and soils | Requires experimental data and high computational capacity |
[44] | Finite Element Method (FEM) | Discretization of structures using matrix equations | High precision, applicable to complex scenarios | Sensitive to input data errors |
[4,31] | Spectral Analysis | Response evaluation using acceleration spectra | More efficient than temporal history analysis in seismic studies | Does not capture non-linear effects |
[45] | Structural Simulation Software | Parametric models to optimize structural design | Simplifies complex systems without the need for large computational resources | Results depend on the quality of the model |
[40] | Static Analysis (Equivalent Lateral Forces) | Suitable for regular structures but limited in dynamic behavior | Not suitable for irregular structures | |
[9] | Análisis Modal | Modal decomposition with equations of state | Allows evaluation of main vibration modes of the structure | Does not consider damping effects |
[3] | Natural Vibration Analysis | Direct relationship between stiffness and vibration period | Simplified approximation, ignores damping effects | |
[42] | Computational Simulation | Models based on elasticity theory | Facilitates validation of physical and experimental models | Error-sensitive input parameters |
[43] | Comparison between Static and Dynamic Methods | Relationship between stresses and deformations under seismic loads | Demonstrates that dynamic analysis produces increased base shear | Requires high accuracy in input data |
No. | Author(s) and Year | Country | Study Type | Structure Type | Key Variable | Methodology | Main Findings |
---|---|---|---|---|---|---|---|
1 | Li et al. (2020) | China | Experimental | Concrete frame | Fundamental period | Ambient vibration test | Period increases with height in nonlinear fashion. |
2 | Smith et al. (2019) | USA | Numerical | Steel structure | Lateral stiffness | Finite element model | Stiffness affects mode shape more than frequency. |
3 | Pérez et al. (2021) | Mexico | Mixed | Mixed system | Dynamic coefficient | Hybrid analysis | Coefficient is highly geometry-dependent. |
4 | Kim & Lee (2018) | South Korea | Numerical | Concrete wall | Modal frequency | Simulation and code comparison | Code predictions overestimate real periods. |
5 | Gómez et al. (2020) | Colombia | Experimental | Concrete frame | Elastic modulus | Full-scale test | Elastic behavior consistent with theoretical expectations. |
6 | Wang et al. (2017) | China | Numerical | Shear wall | Vibration response | Numerical simulation | Vibration data validated numerical model. |
7 | Chen et al. (2022) | Taiwan | Experimental | Concrete frame | Displacement | Field instrumentation | Displacement reduced with increased rigidity. |
8 | Alvarez & Torres (2019) | Peru | Mixed | Composite slab | Natural period | Empirical and parametric | Empirical models match simulations for mid-rise buildings. |
9 | Santos et al. (2020) | Brazil | Experimental | Concrete column | Base shear | Modal test | Higher base shear leads to period shortening. |
10 | Yamada et al. (2021) | Japan | Numerical | Reinforced concrete | Rigidity ratio | Time-history analysis | Rigidity ratio correlates with building symmetry. |
Type of Construction | Vibration Period (s) | Standard Deviation |
---|---|---|
Ground Floor Building (1–3 floors) | 0.2 | 0.05 |
Medium Building (4–7 floors) | 0.5 | 0.08 |
Tall Building (8–20 floors) | 1.2 | 0.15 |
Skyscrapers (>20 floors) | 2.5 | 0.30 |
Concrete Bridge | 0.8 | 0.10 |
Industrial Structure | 1.0 | 0.12 |
Study | Structural Element | Period Reduction (%) | Key Observations | Methods | Applications | Practical Implications |
---|---|---|---|---|---|---|
Ditommaso [14] | Shear walls | 20–30 | Significant increase in structural stiffness | Nonlinear numerical analyses to integrate the database for the Ultimate Limit State (SLU) | Develop new simplified period-to-height relationships to more accurately estimate the fundamental vibration period of 330 buildings with reinforced concrete structures. | The fundamental period affects seismic design response spectra values. Infill elements are often excluded from structural design processes. Non-structural elements influence natural elastic periods, affecting spectral accelerations. Current seismic codes may inadequately protect buildings from moderate earthquakes. |
Kaplan [10] | Beams and columns | 10–15 | Nonlinear relationship between height and period | Regression analysis and derivation of equations to estimate the period of elastic fundamental vibration of buildings. | Force-based design of 24 reinforced concrete mid-rise buildings for fundamental period estimates | The proposed equation aids in conservative design of mid-rise RC buildings. Rigid infill panels should be isolated or considered in design. Period-height equations must be region-specific for accurate assessments. TBEC-2018 should include regulations for infill panel contributions. |
Perrault [36] | Non-structural elements (For example, infill materials) | 5–10 | Importance of considering non-structural elements | Data-based methods using environmental vibrations for the adjustment of empirical relationships applied to building classes | To study the effect of cumulative damage in 146 reinforced concrete buildings located in seismic zones, even with weak seismic movements. | The study examines the effect of cumulative damage on building resonant periods. It highlights variations in empirical relationships due to seismic exposure. The impact of weak seismic ground motion on building frequency is analyzed. The paper discusses uncertainties in seismic vulnerability of existing structures |
Astroza [26] | Insulated Base Structures | 15–25 | Effect of the isolated base on dynamic behavior | Identification of the dynamic properties of a time-invariant equivalent linear model of a reinforced concrete building. | Effects of the insulation system on the prolongation of the predominant period of a building. | The paper analyzes seismic response of a base-isolated building. It identifies dynamic properties of an equivalent linear model. The effects of isolation systems on building performance are investigated |
Dong-Hee [67] | Vertically divided reinforced concrete structural walls | 30–50 | Strength and stiffness decreased due to vertical splitting. | Manufacture of six full-scale specimens. Performing reverse cyclic load tests. | Investigation of the effects of vertical division on the stiffness and strength of walls. Structural analysis for real moment reduction of the building using 6 full-scale specimens. | |
Chambers [68] | Beam Section Frame Elements. | 3.6–15.1 | Resulting reduction in terms of stiffness. | Analytically derived stiffness matrix. Finite Element Analysis. | Special moment-resistant gantries with reduced beam cross-sections. Seismic analysis of the base shear in moment gantries. | Flange reductions are acceptable in beam-column connections for moment frames. The stiffness matrix aids in analyzing frame structures with flange reductions. Reductions can increase story drift in moment frames |
Fanaie [69] | Double-reduced beam section connections | 5.5–14.7 | Increased elastic drift with IPE and HEA sections. | Theoretical approach based on mathematical relationships (MSR) and principles of structural analysis. | Estimation of the Elastic Drift Amplification Factor in Moment-Resistant Steel Structures with DRBS Connections. | The study recommends using modified RBS connections in high seismic risk areas. Effective elastic drift calculations are suggested for reduced beam flange widths. DRBS connections may improve seismic behavior but raise drift control concerns. The paper provides design charts for RBS connections. The article enhances visibility before final publication |
Zhou [70] | Building structure equipped with a viscous buffer with an intermediary-lever column | 12 40 | Improved displacement amplification by up to 12%. Displacement between floors is reduced during earthquakes. | A simplified mechanical model of CLVD was derived. The effects of the parameters on the vibration reduction ratios were analyzed. | CLVD for energy dissipation and vibration reduction design. Example of a Nine-Story Structure for Structural Application. | Traditional damping systems occupy significant building space, reducing efficiency. The study proposes a new amplification device for energy dissipation and vibration reduction. CLVD’s optimal vibration reduction effect is contingent on specific parameters |
Marin [71] | Multi-storey concrete prefabricated building structures. | 20 33 | Stiffness reduction coefficients for columns. Stiffness reduction coefficients for beams. | Finite element modeling with ANSYS® software. Consideration of physical and geometric nonlinearity. | Evaluation of the reduction of stiffness in precast concrete structures. Analysis of the overall stability of multi-storey buildings. | The study provides stiffness reduction coefficients for precast concrete structures. It compares findings with national and international codes. The research aids in understanding the effects of axial force on stiffness. It highlights the limitations of simplified PNL considerations in codes. |
Afshar Seifiasl [72] | Steel plate shear walls with low core section beams | 3–6 30 | Stable hysteresis curves, with plant drift, without reduction in bearing capacity. Load Reduction, Superior Energy Dissipation. | Experimental tests under quasi-static cyclic loading. Nonlinear finite element (FE) modeling and verification. | The integration of the building installations in the plant area was carried out by analyzing 5 specimens. Improved structural depth and ductility. | |
Abou-Elfath [73] | Timber frame buildings designed under varying levels of Seismicity and admissible drift | - | Theoretical MRF periods sensitive to seismicity and lateral drift levels. | Evaluation of the theoretical fundamental periods of timber structure buildings. Analysis of design seismicity and permissible lateral drift effects. | Evaluation of the theoretical fundamental periods of 12 wood-frame buildings. Sensitivity Analysis of Design Seismicity and Lateral Drift. | Current period equations do not account for seismicity levels or lateral drift limits. Buildings designed under high seismicity show higher stiffness and shorter periods. The need for modifying period equations is emphasized for realistic assessments. |
Shen [15] | Moment gantries with reduced beam cross-section | - | Sa capabilities were measured for different performance levels. | A connection model was developed for the validation of cyclical deterioration. Incremental Dynamic Analysis (IDA) for performance quantification. | Seismic performance of moment gantries with reduced beam cross-section. Immediate occupancy and collapse prevention performance targets. | The study enhances understanding of connection performance in steel frames. It provides probabilistic S a capacities for design earthquakes. The findings inform selection of intensity and demand measures in IDA. Improved collapse criteria increase robustness in structural analysis. |
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Paredes, J.; Ramirez, W.; Pico, F.; Acosta, R.; Toapanta, O.G.; Mayacela, M. Impact of Structural Stiffness on Vibration Periods of Concrete Buildings: A Systematic Review. Materials 2025, 18, 2612. https://doi.org/10.3390/ma18112612
Paredes J, Ramirez W, Pico F, Acosta R, Toapanta OG, Mayacela M. Impact of Structural Stiffness on Vibration Periods of Concrete Buildings: A Systematic Review. Materials. 2025; 18(11):2612. https://doi.org/10.3390/ma18112612
Chicago/Turabian StyleParedes, Juan, Wladimir Ramirez, Fernanda Pico, Rodrigo Acosta, Oscar G. Toapanta, and Margarita Mayacela. 2025. "Impact of Structural Stiffness on Vibration Periods of Concrete Buildings: A Systematic Review" Materials 18, no. 11: 2612. https://doi.org/10.3390/ma18112612
APA StyleParedes, J., Ramirez, W., Pico, F., Acosta, R., Toapanta, O. G., & Mayacela, M. (2025). Impact of Structural Stiffness on Vibration Periods of Concrete Buildings: A Systematic Review. Materials, 18(11), 2612. https://doi.org/10.3390/ma18112612