This section presents information about the lateral performance of the considered modular structures through a series of nonlinear static analyses conducted on assumed structures with inter-connections having various behaviours, as detailed in Table 2. The specified target drift is assumed to be 8% of the total height of the structure. The objective is to examine the impact of inter-connections' stiffness properties on the lateral behaviour of the structures. Figure 7 (a) to (c) visually depict the pushover curves of the three considered structures, each characterized by different inter-connection behaviours.
The graphs indicate that the linear behaviour of the analysed structures is influenced by the stiffness of the inter-connections. The period of a structure provides a suitable representation of its linear characteristics. Table 3 provides information on the first mode of structures and the fundamental period of structures, as determined from ASCE/SEI 7–16 for regular braced frame structures.
Table 3
Results of eigen analysis of each structure (in seconds).
Connection’s name | Eigen analysis | ASCE/SEI 7–16 (= 0.0724 hn0.8) |
4-storey | 8-storey | 12-storey | 4-storey | 8-storey | 12-storey |
IC1 | 0.784 | 1.371 | 2.086 | 0.571 | 1.011 | 1.402 |
IC2 | 0.806 | 1.447 | 2.312 |
IC3 | 0.812 | 1.465 | 2.346 |
IC4 | 0.832 | 1.514 | 2.424 |
The eigen analyses implies that a decrease in the stiffness of inter-connections results in an increase in the period of the structures. This period alteration in the 4-storey structure due to change of inter-connection behaviour compared to rigid behaviour is 2.2%, 2.8%, and 4.8% for IC2, IC3 and IC4, respectively. For the 8-storey modular building, transitioning from rigid behaviour (IC1) to the most flexible inter-connection (IC4) results in an increase of almost 14.31%. A similar trend is observed in the 12-storey building, where the fundamental period of considered structure increases by 33.8% from 2.086 seconds for rigid inter-connections (IC1) to 2.424 seconds with the use of IC4 inter-connection, implying that the change in the inter-connection behaviour have a substantial effect on the fundamental period of these structure.
It's worth noting that, based on eigen analysis, the fundamental periods of CSMSBs are underestimated compared to those derived from ASCE/SEI 7–16. Lacey et al. (2020) and Sanches et al. (2021) also reported that the underestimation of code-determined fundamental period compared to eigen analysis results, which highlights a potential limitation in standard codes for conventional structures.
In Fig. 7 (a), the pushover curve of the 4-storey structure with IC1 inter-connections exhibits elastic behaviour up to a roof drift level of 1.57%, followed by a reduction in stiffness up to the peak lateral capacity of 1883.97 kN. The lateral capacity of the structure remains nearly constant up to a roof drift of 8.0%. For the 4-storey structure with IC2 inter-connections, the structure shows linear behavior up to a 1.61% roof drift level. After a reduction in lateral stiffness, the peak lateral capacity of 1878.84 kN occurs at a 7.35% roof drift, and remain almost constant up to a roof drift level of 8.0%. Utilising the most flexible inter-connection (IC4) results in a similar trend in the pushover curve. The structure behaves linearly up to 1.01%, followed by a gradual stiffness reduction. The lateral capacity reaches its maximum at 1867.09 kN, indicating a 0.89% decrease compared to IC1 and a 0.27% decrease compared to IC2. This indicates that the lateral capacity of the structure is not substantially affected by the stiffness properties of the inter-connections.
Referring to Fig. 7 (b), the structure exhibits linear behaviour up to 1.42%, 1.34%, 1.32%, and 1.27% roof drift levels for IC1, IC2, IC3, and IC4, respectively. The lateral capacity increases to its maximum in all cases at roof drift levels of 8% for all inter-connections, in which the maximum base shear of the structure is 2697.28 kN, 2666.39 kN, 2648.99 kN, and 2537.23 kN, corresponding to IC1, IC2, IC3, and IC4, respectively. This indicates that the utilisation of different inter-connection behaviours has an effect of almost 6% on the maximum lateral capacity of this structure. However, the results show that there is a substantial decrease in the lateral capacity of the structure around the 2.71% roof drift, where a 20.21% reduction in the maximum base shear can be observed. The graph indicates that the maximum base shear decreases 2347.85 kN to 1873.35 kN corresponding to IC1 and IC4, respectively. This reduction for IC2 and IC3 compared to IC1 is 10.08% and 12.73%, respectively.
The pushover curve of the 12-storey structure with rigid behaviour indicates a linear response up to a 1.01% roof drift level, reaching a base shear of 114.2 kN. The pushover curve of the structure with IC4 shows linear behaviour up to a 0.92% roof drift level, with the base shear reaching 91.92 kN. The lateral capacity of the structure with rigid inter-connections increases to 2936.85 kN. With the IC4 inter-connection, the base shear reduces to 2188.62 kN, reflecting a 25.47% decrease in the maximum base shear. The observed lateral performance observed in the considered structures highlights the substantial impact of inter-connection behaviour on their response in both elastic and inelastic ranges. Similar to the 8-storey building, the obtained responses indicate a substantial difference between the lateral capacity of the 12-storey building having IC4 compared to IC1 around 4% roof drift, where employing IC1 results a base shear of 2730.29 kN. On the other hand, the base shear of the structure is 1830.08 kN, when the IC4 is employed, indicating almost 32.97% reduction in the base shear.
Figure 8 (a) to (c) illustrate the inter-storey drift of the 4-storey modular building corresponding to the IO, LS, and CP performance levels. The figures show that the maximum inter-storey drift occurs at second storey for all inter-connections. It is seen that the maximum reduction percentage between the inter-storey drift of IC1 and IC4 is 33.8%, 32.86%, and 73.42% corresponding to IO, LS, and CP performance levels, which occurs at fourth storey. This implies that the stiffness of inter-connections plays a crucial role in lateral performance of these building, resulting in influencing their inter-storey drift. Figure 9 (a) to (c) display the inter-storey drift of the 8-storey designed building corresponding to the IO, LS, and CP performance levels. The responses obtained from nonlinear static analysis indicate that for the case of employing IC1 the maximum drift occurs in the fourth storey. However, the drift distribution changes by using other types of inter-connections (i.e. IC2, IC3 and IC4). The graphs illustrate that in the case of employing IC2, IC3 or IC4, the maximum storey drift occurs in the third level. The results reveal the maximum percentage reduction in the inter-storey drift of the building between the stiffest and most flexible inter-connections. (i.e., IC1 and IC4) is 53.37%, 54.99%, and 233.65%, respectively, indicating that the mechanical properties of inter-connections significantly impact the lateral performance of the 8-storey structure.
Figure 10 (a) to (c) depicts the inter-storey drift of the 12-storey building at IO, LS, and CP performance levels, respectively. It demonstrates a similar trend compare to the 4- and 8-storey structures, illustrating that the alteration of the inter-connections has a notable impact on the lateral performance of the analysed structures. The maximum reduction percentage between the inter-storey drift, when IC1 and IC4 are employed, is 66.32%, 67.61%, and 76.11%, corresponding to IO, LS, and CP performance levels. Hence, it is evident that the stiffness properties of inter-connections in modular structures have a significant influence on their lateral performance, which should be considered during the analysis and design processes of such structures.
Figure 11 (a) to (c) demonstrates how the inter-connection properties influence the storey shear distribution of the 4-storey building at IO, LS, and CP performance levels. The figure indicates that the storey shear distribution is impacted by the stiffness of the inter-connections. Specifically, at the IO performance level, the use of IC4 inter-connection decreases the maximum storey shear by almost 16.2% compared to the use of IC1 inter-connection. Furthermore, compare to IC1 inter-connection, the storey shear decreases by 12.6% and 7.8% at LS and CP performance levels when the IC4 inter-connection is being used in the 4-storey modular building.
Figure 12 (a) to (c) show the storey shear of the 8-storey modular building. The results demonstrate that incorporating IC4 inter-connections leads to a change in storey shear at each level when compared to the use of IC1 inter-connections. The maximum difference between the maximum storey shear at each level corresponding to IO, LS, and CP performance levels is 23.61%, 24.41%, and 24.95%, respectively. This demonstrates that the mechanical properties of the considered inter-connections have a considerable impact on the storey shear of the 8-storey building.
Finally, a comparison was carried out for the storey shear of the 12-storey building, considering various stiffness values for the inter-connections at IO, LS, and CP performance levels. The results obtained, depicted in Fig. 13 (a) to (c), indicate that the behaviour of the inter-connections significantly influences the shear distribution of the building. Employing IC4 results in a reduction of the storey shear by approximately 26.72%, 29.58%, and 36.82% in comparison to IC1 inter-connection at IO, LS, and CP performance levels. These results indicate that the lateral performance of corner-supported moment-frame modular buildings is notably influenced by the mechanical properties of inter-connections.