Detailed explanation of stiffness ratio, displacement ratio, period ratio, and shear load ratio

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Cycle ratio – Regulatory requirement: Clause 4.3.5 of the new regulations stipulates that for high-rise buildings of Class A, the ratio of the first cycle Tt, which is dominated by structural torsion, to the first cycle T1, which is dominated by translational motion, should not be greater than 0.9； For Class B high-rise buildings, high-rise buildings with mixed structures, and complex high-rise buildings, it should not be greater than 0.85. For a typical regular single-tower structure, the cycle ratio for verification is as follows: 1) Determine whether each mode is a torsional mode or a translational mode by checking whether the translational coefficient of each mode is greater than 0.5 or the torsional coefficient is greater than 0.5. 2) Generally, the torsional mode with the longest period corresponds to the first torsional period Tt, while the translational mode with the longest period corresponds to the first translational period T1. 3) Refer to the “schematic diagram of the overall spatial vibration of the structure” to determine whether the first torsional/translational period causes overall vibration; if only local vibration occurs, it is not the first torsional/translational period. Let’s consider the next sub-longer period. 4) Check whether the base shear ratio for the first translational period is the maximum. 5) Calculate Tt/T1 to see if it exceeds 0.9 (0.85). What does the period ratio control? Similar to the control of the displacement ratio, the period ratio focuses on controlling the relative relationship between lateral stiffness and torsional stiffness, rather than their absolute values. Its purpose is to make the planar arrangement of the lateral resistance members more effective and rational, thereby preventing the structure from experiencing excessive torsional effects relative to lateral displacement. In short, cycle ratio control does not require the structure to be sufficiently strong; rather, it demands that the layout of the structure’s loads is reasonable. If the cycle ratio does not meet the requirements, how should it be adjusted? Once the cycle ratio fails to meet the requirements, it is generally only possible to improve this situation by adjusting the layout; such changes are usually comprehensive, as minor local adjustments tend to yield little effect. If the period ratio does not meet the requirements, it indicates that the torsional stiffness of the structure is lower compared to its lateral displacement stiffness. The general principle for adjustment is to enhance the stiffness of the outer layer of the structure and reduce the stiffness of its inner cylinder. The purpose of the F-check period ratio is mainly to control the torsional effect of the structure under extreme seismic events. F Multi-tower structure period ratio: For multi-tower structures, the above method cannot be used for verification directly. If there is no connection at the upper part, each tower should be calculated and checked separately; if there is a connection at the upper part, the method of verification is not clear. For F-type sports venues, open structures, and special industrial buildings, there is generally no need to control the cycle ratio unless there are specific requirements. When it is complex to create openings in the floors of high-rise buildings, or when the structure has a stepped layout, local vibrations may occur in the structure; in such cases, the \"forced rigid floor assumption\" should be used to calculate the structural period ratio. To filter out the cycles generated by local vibrations. 　 Displacement ratio: According to clause 4.3.5 of the new code, the maximum horizontal displacement of vertical structural elements in a floor and the inter-story displacement angle should not exceed 1.2 times the average value for that floor in high-rise buildings of categories A and B ； Furthermore, the height of high-rise buildings of Class A should not exceed 1.5 times the average height of that floor, while for high-rise buildings of Class B, high-rise buildings with mixed structures, and complex high-rise buildings, the height should not exceed 1.4 times the average height of that floor. Program processing: For this item, the program calculates and displays for each layer the maximum horizontal displacement, maximum inter-layer displacement angle, average horizontal displacement, average inter-layer displacement angle, as well as the corresponding ratios. This allows users to easily determine whether the requirements of the standards are met. The limit for the displacement ratio is determined under the assumption of a rigid floor, and the method for calculating the average displacement is also based on this assumption of a rigid floor. The calculation model for the F-control displacement ratio: According to the definitions specified in the codes, the displacement ratio is expressed as “maximum displacement/average displacement”, with the average displacement being calculated as “(maximum displacement + minimum displacement)/2”. The key factor here is the “minimum displacement”; when there is a node with a displacement of 0 in a floor, the minimum displacement will definitely be 0, which results in the average displacement being half of the maximum displacement, giving a displacement ratio of 2. Otherwise, the displacement ratio loses its significance as a reference parameter for this structural characteristic; therefore, when calculating the displacement ratio, if \"elastic nodes\" appear in the floors, the \"forced rigid floor assumption\" should be adopted. Code requirement: According to Article 4.3.5 of the High-rise Code, the floor displacement ratio of the structure should be examined under the condition of accidental mass eccentricity. Inter-story displacement angle: The program uses the “maximum inter-column (wall) displacement angle” as the inter-story displacement angle for each floor, allowing for calculation under the condition that “accidental eccentricity is not considered”. In complex structures such as pitched-roof buildings, stadiums, stands, and industrial buildings, the columns and walls are not at the same elevation, or there is no floor slab in certain floors. In such cases, if a \"forced rigid floor assumption\" is used, the structural analysis becomes severely distorted, and displacement ratios lose their meaning. Therefore, for such structures, the torsional effect can be examined through the “detailed output” of displacements or by observing the deformation diagrams of the structure. For staggered or mezzanined structures, which always feature a large number of inter-story columns, when the \"forced rigid floor assumption\" is selected, these inter-story columns are constrained by the floors above and below; if there are many such columns, the calculations become distorted. In summary, the validity of the calculation models for structural displacement characteristics should be determined based on the actual conditions of the structure; for complex structures, various methods should be employed