Simplified Seismic Design for Mid-Rise Buildings with Vertical Combination of Framing Systems
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The mid-rise building with vertical combination of framing systems consists of a structural system in which the seismic-force-resisting-system (SFRS) of the upper structure is commonly a lightweight structural system such as cold-formed steel (CFS) frame or wood frame, while the SFRS associated with the lower one adopts a traditional structural system, such as reinforced concrete (RC) or structural steel frame. In current practice, the presence of: (a) vertical irregularities on mass and stiffness, and (b) damping difference between lower and upper structures creates challenges for the seismic design of such buildings. Presented in this thesis is research with aiming to solve the challenges arising from the foregoing two aspects in relatively simple and practical ways. Because of the mass irregularity in the vertical direction, the stiffness arrangement for the lower and upper structures in the combined framing system is quite different from that of the “regular” building. A simplified approach is proposed for the determination of storey-stiffness arrangements of such buildings based on the pre-determined mass distribution and specified storey drift limit. In addition, by considering both the mass and stiffness irregularities, two manually-based simplified methods, i.e., modified equivalent lateral force procedure (ELF) and two-stage analysis procedures, are proposed to evaluate seismic loads of the combined framing systems. The simplified approaches to determine the required storey-stiffness arrangements and compute seismic loads are developed based on the USA standard American Society of Civil Engineers 7 (ASCE 7) (ASCE, 2010) at first. Then, by considering the difference in seismic design provisions between ASCE 7 and the Canadian code National Building Code of Canada 2010 (NBCC 2010) (NBCC, 2010), several modifications are made on the simplified approaches based on ASCE 7 for their Canadian application. In the proposed approach to evaluate the storey-stiffness arrangements, the effects of the interaction between the lower and upper structures in terms of mass and stiffness on the seismic load are investigated. The feasible stiffness arrangements can be obtained based on the required relationship between the stiffness of the lower structure and that of the upper one determined by the proposed approach. Two examples are presented to demonstrate the efficiency of the proposed approach. The result obtained from the proposed approach is justified by the code-specified modal response spectrum analysis. The two examples demonstrate that the relative seismic weight between the lower and upper structures has a significant influence on the required stiffnesses of the lower and upper structures. In general, when the number of the storey and total seismic weight associated with the lower structure are much greater than those of the upper one, the required stiffness of the upper structure will be greatly affected by the interaction between lower and upper structures in terms of mass and stiffness. On the other hand, if the number of the storey and total seismic weight associated with the lower structure are much smaller than those of the upper one, such interaction has less effect on the required stiffness of the upper structure. In such case, the required stiffness of the upper structure is based primarily on the characteristics of the upper structure. The modified ELF procedure is applied to the combined framing systems in which there is only one-storey upper structure. Both the applicable requirements and seismic load distributions associated with the modified ELF procedure are proposed. If the storey-stiffness ratio between lower and upper structures is less than a specific value designated as rkb1, the lower structure is dominated primarily by the first mode and the traditional ELF procedure can be used to approximate the seismic load of the lower structure. However, the seismic load of the one-storey upper structure may still be underestimated as the behaviour of the upper structure may be dominated by higher vibration modes of the entire structure. Consequently, the shear force of the one-storey upper structure cannot be estimated based on the traditional ELF procedure. Equations for evaluating the shear force of the one-storey upper structure are presented in the modified ELF procedure. The two-stage analysis procedure prescribed in ASCE 7 (ASCE, 2006; 2010) ignores the interaction between lower and upper structures in terms of mass and stiffness and permits the lower and upper structure to be analyzed by the conventional ELF procedure, separately. New applicable requirements and seismic load distributions associated with the two-stage analysis procedures are proposed. The proposed procedure is compared with that prescribed in ASCE 7. It is found the stiffness requirement of ASCE 7 two-stage analysis procedure may be inappropriate, which may result in the underestimation of the base shear force of the upper structure in certain cases. Furthermore, the shear force for the top storey of the upper structure may also be considerably underestimated by the ASCE 7 two-stage analysis procedure. Therefore, an additional top shear force is to be applied to the top of upper structure. Equations to compute the additional top shear force are also provided. The accuracy of the proposed two-stage analysis procedure, either the one based on both ASCE 7 or the one based on NBCC 2010, is greatly improved compared to that prescribed in ASCE 7 (ASCE, 2006; 2010). Finally, damping difference between lower and upper structures in the combined framing system is investigated. By assuming the combined framing systems are classically damped, i.e., the damping matrix of the combined framing systems is orthogonal to the un-damped mode shape, an analytical method to approximate the equivalent modal damping ratio for the case where lower and upper structures have different damping ratios is proposed. However, as the combined framing system in fact is non-classically damped, if the lower and upper structures have different damping ratios, the proposed approximation of the equivalent modal damping ratio may lead to significant errors on seismic load in certain cases. Therefore, errors on seismic loads resulted from the classical damping approximation, which determine whether the proposed equivalent modal damping ratio is acceptable or not, are investigated. It is found large errors of seismic response associated with the proposed equivalent modal damping ratio usually occur when the dominating modes of the structures have closely spaced natural frequencies. However, for most combined framing systems in practice, the dominating modes have well separated natural frequencies and the proposed equivalent modal damping ratio is applicable to evaluate the seismic response of the combined framing systems. In addition, a new index of damping non-proportionality is suggested in this study to quantify the extent of non-proportional damping.