Seismic and economic performance of a mid-rise cassette structure

Abstract

In this article, a new structure called cassette structure is presented. A comparative analysis of seismic and economic performance of a cassette structure and a frame structure is conducted. An existing frame office building is selected and redesigned as a cassette structure to compare the performance of the two kinds of structures. Three-dimensional finite element models are built for the two prototype structures, where fiber elements are used to simulate plastic behavior. To assess the advantages fully, seismic analysis and economic analysis are performed. Eighteen Federal Emergency Management Agency recommended seismic records are used, and the roof displacement, story drift ratio, plastic hinges development, and Park–Ang damage index are compared. Furthermore, the material, template, transportation, and assembling costs are calculated based on Chinese quotas, and the overall economic impact is evaluated. In this case, all indexes show that the cassette structure has an obvious advantage over conventional frame structure.

Keywords

cassette structure economic analysis frame structure mid-rise building seismic analysis

Introduction

The cassette structure, which is named as such because of its cassette-like appearance, is a new structure system (Ma et al., 2006). Unlike the widely used frame structure, a cassette structure consists of open-web sandwich slab (OWSS) and grid frame wall (GFW) (shown in Figure 1(a)). The OWSS is the floor system of cassette structure and bears gravity load. Another structural component of the cassette structure is called GFW, which bears lateral load and gravity load. The GFW, which has high stiffness and small element size, is consisted by dense columns and interlayer beams. The advantage of a cassette structure is that it has a good span capacity, high stiffness, and good seismic performance (Chen et al., 2018). The cassette structure has been applied in large-span buildings spanning more than one million square meters in China. For instance, the Sports Hall of Shandong Weifang Sports School, which is a three-floor large-span public construction, is built as a cassette structure. The plane size of the sports hall is 64 × 56 m², and the thickness of the OWSS is 1250 mm, which is only 1/25 of the total span (32 m). The concrete and steel usages of the structure are 0.55 t/m² and 82 kg/m², respectively. Using the cassette structure, the entire construction saves more than 1200 m³ concrete and 600 t steel compared to conventional prestressed frame structure or traditional frame structure.

Figure 1.

Components of cassette structure. (a) Construction of cassette structure, (b) cassette structure, (c) construction of OWSS, and (d) OWSS.

Currently, mid-rise buildings (height between 24 and 100 m in Chinese Code JGJ 3-2010) are widely seen in large cities, especially for use as apartments, hotels, and offices (Jiang et al., 2014b; Ali and Moon, 2007). Frame structure is widely used among mid-rise buildings (Faramarz and Mehdi, 2011), but the large element cross section and fixed space division limit the architectural design and functional usage of it (Carpinteri et al., 2014). Furthermore, since frames did not demonstrate the expected performance during the 1994 Northridge and 1995 Kobe earthquakes, new solutions have been sought. One widely known way is using buckling restrained braces (BRBs) (Avci-Karatas, 2019). According to previous studies and tests, BRBs can achieve a good energy dissipation performance and can be used to increase the lateral stiffness and strength of frame structures (Avci-Karatas et al., 2019; Jeffrey et al., 2011). However, adding BRBs needs extra causes, affect the function of the structures, and cannot improve the span of frame structures. To address these concerns, the cassette structure is applied in mid-rise buildings, combining the advantages of BRBs and traditional frame structures. According to this study, a cassette structure can reduce the cost of the entire construction by approximately 25% and allow users to design the inner space freely (Ma et al., 2000).

Based on the statements above, a comparative study is conducted. An existing 47-m frame office building is selected and redesigned as a cassette structure. The configuration, seismic performance, and economic performance of the frame structure and the redesigned cassette structure are compared. Finite element models are built and dynamic time-history analysis and economic analysis are conducted to clarify the advantages of the cassette structure from numerous aspects.

Cassette structure overview

Components of cassette structure

The configuration of cassette structure is shown in Figure 1(a) and (b), which is mainly consisted by OWSS and GFW.

The construction of an OWSS is shown in Figure 1(c) and (d). It has a similar configuration to rib floor system, but the entire beam web is hollowed. Its mechanical property is a sandwich slab considering shear deformation. There are three main components of the slab: top rib, bottom rib, and shear key. The two ribs can be regarded as the upper and bottom fibers of a solid beam. To make them work together, shear keys are added. A shear key is a block element whose height-to-width ratio should be less than one. The bending and shear stiffness of shear keys are much larger than that of the two ribs, and both ribs can be connected rigidly by the shear keys (Zhang et al., 2006). When bearing loads, through the connection of shear keys, the two ribs can work together like the upper and bottom fiber of a solid beam. A pair of tension and pressure force is produced in the two ribs and can resist bending force, and both ribs can resist shear force together. To maintain the stiffness and overall performance of the slab, the distance between two shear keys (i.e. the grid size of the OWSS) should be below 4 m, and the range from 1.5 to 3 m is recommended. According to the current research, experiments, and application, a properly designed OWSS can reduce 50% self-weight of the floor system without noticeably affecting structural performance (Ma et al., 2009). In large-span structures, 50% or more vertical load comes from self-weight of beams and large beam cross section restrain the structural span ability. However, as the beam web of OWSS is hollowed, it can largely decrease the load of the total floor system and span up to 40 m with a comparatively small height (usually 1/25 to 1/30 of the total span). Furthermore, as the entire beam web is hollowed, all the pipelines and equipment can be placed in it, and this can increase the net height and structural function of the story.

The GFW, which is shown in Figure 1(a), is a dense frame with interlayer beams. Compared with traditional frame structure, the column space of GFW is 4 m or less, and one or two interlayer beams are added (shown in Figure 1(b)). As extra columns and interlayer beams are used, the structure stiffness increases rapidly (seen in next section). Another character of GFW is that all the columns are placed around the structure and no column is placed inside the structure. By combining OWSS and GFW together rigidly, cassette structure has the characteristic of high stiffness and large-span capacity.

Mechanical characteristics of cassette structure

Unlike in traditional constructions, in which the shear stiffness of beam is negligible, the shear displacement in an OWSS cannot be ignored. Shear key guarantees the performance of the entire slab, and the stiffness of it cannot be assumed as infinite. As a result, the mechanical model of the slab is considered as a sandwich slab with shear displacement. The differential equation of the slab is proposed by Ma et al. (2006) and practical computing methods are studied.

The mechanical characteristics of GFW are described in Figure 2(a) and equation (1), where E_cI_c is the flexural rigidity of the column, m is the total number of columns, and n is the total number of beams. When a bent structure is used, lateral force F will cause a drift Δ1. When changing to frame structure (as shown in Figure 2(b)), the drift Δ2 will decrease to 0.25Δ1, because of the restraint of the beam and the increase in structure stiffness. To increase the structural stiffness further, two ways are considered. One is adding columns inside and another is adding interlayer beams. When using m columns in the single-story frame (shown in Figure 2(c), in which m− 2 columns are added), the drift of this structure Δ3 will drop to $(1 / 2 m) Δ 1$ (shown in equation (2)). Similarly, when n beams are used in a single-story frame (shown in Figure 2(d), in which n− 1 beams are added), the drift of it will drop to $(1 / 4 n^{2}) Δ 1$ . As per the discussion above, adding extra beams and columns can considerably increase the structure stiffness and then decrease lateral drift. When changing large beams and columns in frame structure to comparatively small inside columns and interlayer beams, the stiffness of the entire structure can largely increase without using extra material. However, considering the short column effect, architectural requirement, and column-to-beam stiffness ratio, one or two interlayer beams and a 4 m or less column space are used. It should be noticed that all the discussion above is under the assumption that the flexural rigidity of the beams are much larger than columns and the axial deformation of beam is ignored. Moreover, the connections between beams and columns are rigid and there is no rotation between them. This assumption can be achieved when the rigidity of beams is three times larger than that of the columns (Xu et al., 2014)

{\begin{matrix} Δ 1 = \frac{F / 2}{3 E_{c} I_{c} / h^{3}} = \frac{1}{3 E_{c} I_{c}} \cdot (\frac{F}{2}) \cdot h^{3} \\ Δ 2 = \frac{F / 2}{12 E_{c} I_{c} / h^{3}} = 2 \cdot {\frac{1}{3 E_{c} I}}_{c} \cdot \frac{F}{2} \cdot {(\frac{h}{2})}^{3} = \frac{1}{4} Δ 1 \end{matrix}

(1)

{\begin{matrix} Δ 3 = \frac{F / m}{12 E_{c} I_{c} / h^{3}} = 2 \cdot \frac{1}{3 E_{c} I_{c}} \cdot (\frac{F}{m}) \cdot {(\frac{h}{2})}^{3} = \frac{1}{2 m} Δ 1 \\ Δ 4 = n \cdot \frac{F / 2}{12 E_{c} I_{c} / {(h / n)}^{3}} = 2 \cdot \frac{1}{3 E_{c} I_{c}} \cdot \frac{F}{2} \cdot {(\frac{h}{2 n})}^{3} = \frac{1}{4 n^{2}} Δ 1 \end{matrix}

(2)

Figure 2.

Mechanical characteristics of cassette structure. (a) Bent structure, (b) frame structure, (c) adding inner columns in one floor, and (d) adding interlayer beams in one floor.

Design of prototype structures

To analyze the advantages of a cassette structure, an existing frame structure is redesigned as a cassette structure using the same amount of materials. In addition, the seismic and economic performance of cassette structure and frame structure are compared. The existing building is a 47-m frame office building in Jiangsu, China. The basic design wind pressure of the building is 0.45 kN/m², and the seismic intensity zone is 7°, class II, and the first group, which means the equivalent shear-wave velocity of 30 m soil (V_s30) is between 250 and 500 m/s in the area. Furthermore, the peak ground acceleration (PGA) of fortification level earthquake (i.e. 10% probability of exceedance in 50 years) is 100 cm/s², and the characteristic period is 0.35 s (Li et al., 2016).

Design of the frame and cassette structure

The 47-m frame building is used as an office building and the typical floor plan is shown in Figure 3(a). The entire building plane is 58.8 × 22 m², and the column grid is generally 8400 mm along the x-axis and 7400 or 7300 mm along the y-axis. The dead load, which includes self-weight of the slab, waterproof layer, and other coating, is 5 kN/m², while the live load is 2 kN/m². Considering the partition walls, windows, and the self-weight of beams, for the first three floors, a 12.5 kN/m linear load is added on the inner beams and a 22 kN/m load is added on the surrounding beams. For other floors, a 9 and 15 kN/m liner loads are used for inner beams and surrounding beams, respectively. The dimensions of the frame structure are shown in Table 1.

Figure 3.

Type floor plan of (a) the frame structure and (b) the cassette structure.

Table 1.

Dimensions of element of the frame structure (unit: mm).

Structure type	Floor	Floor height	Column	Surrounded beam	Main beam/OWSS	Secondary beam/interlayer beam
Frame	1–3	5400	1000 × 800	950 × 300	900 × 300	650 × 300
	4	3800	800 × 800	950 × 300	650 × 350	550 × 250
	5–6	3800	700 × 700	950 × 300	650 × 350	550 × 250
	7–11	3800	600 × 600	950 × 300	650 × 350	550 × 250
Cassette	1–3	5400	800 × 700	–	900	300 × 200
	4–6	3800	700 × 500	–	900	300 × 200
	7–11	3800	650 × 450	–	900	300 × 200

OWSS: open-web sandwich slab.

The plan of the redesigned cassette structure is shown in Figure 3(b) and there are several major differences between the cassette structure and the older one. First, all the columns are placed at the edges of the cassette structure and there is no column inside it, which means the total span of the structure reaches 22 m. Second, the partition wall can be placed unconstrained, which means the interior space need not be previously designed and can be arranged as per user’s wishes.

The column grid of the cassette structure is 3700 mm in x-ray and 3667 mm in y-ray, and a 300×200 mm² interlayer beam is used. The top and bottom ribs of the OWSS used in the first three stories are 250×300 mm². The dimension of the shear key is 450 × 450 mm² and the height-to-width ratio is larger than 1. Though the height of the OWSS is 900 mm, the element section is small and most portions of slab are empty. Furthermore, considering the 400-mm fire sprinkler and 450-mm equipment pipeline can be placed in the open-web of the slab, the net height of the cassette structure and the frame structure is same. For other floors, the top and bottom ribs are both 250 × 300 mm² and 200 × 300 mm², respectively, and the shear key is 450 × 450 mm² with a height of 450 mm. The entire OWSS is 900 mm in height, which presents 200 mm more net height than the original frame structure. As with the load cases, the dead load of the cassette structure is 5 kN/m², and a 3.8 kN/m liner load considering the self-weight is added. The live load is 3.6 kN/m², which includes the free placed partition wall. Other information of the cassette structure is listed in Table 1.

Developed numerical model

To analyze the two abovementioned prototype models, finite models are established in finite software Perform-3D. As shown in Figure 4(a), the Menegotto–Pinto constitutive relationship for reinforcement is used, and piecewise linear lines are used for simplification (Menegotto, 1973). For concrete, the modified Kent–Park constitutive relationship is used to simplify the complicated constitutive relationships (Scott et al., 1982). As shown in Figure 4(b) to (d), due to the limit of finite software, piecewise lines are used to simplify both the confined and unconfined concrete, and a smooth segment is added in unconfined concrete based on Chinese code GB50010-2010. Considering the tension stress is much smaller than the compression stress (only 6% of the compression stress in Chinese code GB50010-2010) and concrete will soon crack and lose strength in nonlinear plastic analysis, the tension stress is ignored in this simulation to promote computational efficiency. This is feasible and secure based on Chinese code and design criteria. In this simulation, considering the stress condition, unconfined concrete is used to simulate the surface concrete, and confined concrete is used in core concrete. (Jiang et al., 2014a) In this procedure, the conservation of energy principle is used to acquire the parameters of corresponding key points (Feng et al., 2018).

Figure 4.

Stress–strain relationship and the elements used in simulation. Stress–strain relationship of (a) steel, (b) unconfined concrete, (c) confined concrete, and (d) C50 concrete.

For element simulation, fiber elements are used for all columns and beams. Taking the cassette structure as an example (Figure 5), since flexural deformation is the main controlling factor for elements that have a large-span depth ratio, nonlinear behavior of bending is considered, while the shearing deformation is regarded as elastic (Baloevic et al., 2013). Furthermore, plastic hinges are used to balance the accuracy and the enormous calculation. M interaction is considered in beams and P–M–M interaction is considered for columns (Radnic et al., 2013). At the cross-sectional level, based on the constitutive law mentioned above, the force–deformation relationship is calculated automatically by the program (Feng et al., 2015).

Figure 5.

The elements used in the finite element models.

For dynamic analysis, Newmark-beta integration method is used and the modal damping ratio is set as 0.05 for all structures.

Seismic analysis

Time-history record

To compare the structural performance underground motions, 18 records suggested by Federal Emergency Management Agency (FEMA) are selected as seismic excitation (Cao et al., 2019). Since the stiffness of two buildings are relatively high and are not sensitive to far ground motions, all the records selected are near ground motion and the elastic acceleration spectra are shown in Figure 6.

Figure 6.

Comparison of spectrum acceleration.

In accordance with the Chinese code, all the time-history records are scaled into three levels (Jiang et al., 2014a). These three levels in Chinese code respond to levels of immediate occupancy (IO), life safety (LS), and collapse prevention (CP), respectively. Because these two buildings are designed on 7° seismic intensity zone as mentioned above, the scaled PGA limits are 35,100 and 220 cm/s², which represent a probability of exceedance in 50 years of 63%, 10% and 2%, respectively. When scaling, the seismic response of LS and CP level is relatively small, so the seismic records are rescaled to the limit of each phase (100 and 220 cm/s² PGA). In addition to these three levels, a 0.4 g PGA analysis is added to study the structural performance during heavy earthquake (Lu et al., 2015).

Dynamic characteristics of the analyzed structures

The mode shape and period of the two structures are shown in Table 2, and a 5% damping ratio are used for both structures. The modes of both structures are similar and match the theoretical calculation well. Meanwhile, the mode periods of the frame structure is much larger than the cassette structure, which represents the stiffness of the frame structure is smaller than the cassette structure while using the same amount of concrete and reinforcement.

Table 2.

The dynamic characteristics of the structures.

Mode number	Cassette structure		Frame structure
Mode number	Mode period (s)	Mode shape	Mode period (s)	Mode shape
1	1.49	Translation in Y direction	2.05	Translation in Y direction
2	1.30	Translation in X direction	2.01	Translation in X direction
3	1.00	Rotation	1.77	Rotation
4	0.51	Translation in Y direction	0.71	Translation in Y direction
5	0.46	Translation in X direction	0.69	Translation in X direction
6	0.35	Rotation	0.61	Rotation

Seismic analysis results

The seismic analysis results of the two structures are shown in Figure 7. Comparing these results, the advantage of the cassette structure is obvious. The average maximum drift of the cassette structure in IO level is 0.0012 (Figure 7(a)), which is only 70% of that in the frame structure. This advantage is observed in LS and CP levels. In 0.4 g PGA level, which is a high intensity level and both the structures are in completely plastic stage, the drift of the cassette structure is 0.034 while that of the frame structure is 0.051. Caused by numerous nodes in cassette structure, the advantage of cassette structure is even larger in plastic stage. Numerous nodes and elements can dissipate vast energy and make cassette structure stable during earthquake. The drift limit of IO, LS, and CP level is 1/550, 0.02, and 0.04, respectively. Response of cassette structure and frame structure both satisfy the drift limit but the drift of cassette structure is much smaller compared to frame structure. In addition, even in 0.4 g PGA level, while the drift of frame structure largely exceeds the drift limit, the cassette structure is still stable and the drift of it still satisfies the limit. Moreover, the roof displacement of the two structures show the same tendency (Figure 8), where the displacement of the frame structure is much larger than the cassette structure.

Figure 7.

Average drift ratio of the two structures. Average drift ratio in (a) IO level, (b) LS level, (c) CP level, and (d) 0.4 g PGA.

Figure 8.

The roof displacement of the two structures. Roof displacement for (a) IO and LS stage and (b) CP and 0.4 g stage.

Development of plastic hinges

The development of plastic hinges of the two structures in three different levels is shown in Figure 9. To make the figures look clear, two interlayer beams in cassette structure are combined and drawn as one fine line due to their similar performance, and the OWSS and beams are drawn as thick lines. In these figures, large circles mean that the elements are totally plastic and dangerous; while the small circles represent that the elements reach 60% of their plastic limit. It is obvious that plastic hinges develop more seriously in frame structure. In LS phase, only a small part of elements in cassette structure reach 60% of their plastic limit, while in frame structure, more than 50% floors have elements in plastic phase, and some of beams in bottom floors even reach their plastic limit. As load increases, plastic hinges develop rapidly in frame structure, but in the cassette structure, only some elements in bottom floors reach plastic limit, while others either only reach 60% of their plastic limit or just stay elastic. Furthermore, while the entire frame structure is nearly plastic and failed at the 0.4 g PGA phase, the plastic hinges in cassette structure only develop in bottom floors and the entire structure’s function is maintained. These can also be seen in Figure 9(g) and (h), which shows the detail of plastic development in CP phase. In Figure 9(g), only interlayer beams and some fringe open-web sandwich elements reaches plastic limit (in red), and other elements either only reach 60% of their plastic limit (in blue) or remain elasticity (in white). In Figure 9(h), however, half of main beams and all corner columns in frame structure are totally plastic, and the rest elements reach 60% of the plastic limit. This shows a better seismic performance of cassette structure, which fits the conclusion mentioned above.

Figure 9.

Overall plastic hinges in two structures. Plastic hinges of (a) cassette structure at LS phase, (b) frame structure at LS phase, (c) cassette structure at CP phase, (d) frame structure at CP phase, (e) cassette structure at 0.4 g PGA phase, (f) frame structure at 0.4 g PGA phase, (g) cassette structure at first floor, and (h) frame structure at first floor.

Park–Ang damage index for the two structures

Introduction of Park–Ang damage index

Park–Ang damage index was proposed by Park and Ang in 1985 and has been widely accepted in seismic studies. The index is shown as

D = \frac{X_{m}}{X_{u}} + β \frac{ε}{F_{y} X_{u}}

(3)

where X_m is the maximum displacement of an element during earthquake, X_u is the maximum displacement of an element under monotonic load, β is an index, which is 0.15 for frame structure, ε is the energy dissipation, and F_y is the yield shear force of element.

Damage index for the entire structure

Once the damage index of elements is known, the damage index for the whole structure can be calculated as follows

D = \sum_{i = 1}^{n} γ_{i} D_{i}

(4)

where D is the damage index for the whole structure, n is the number of elements, $γ_{i}$ is the weighting index, and D_i is the damage index of an element. $γ_{i}$ can be calculated as

γ_{i} = \frac{N + 1 - i}{\sum_{i = 1}^{N} (N + 1 - i) D_{i}} D_{i}

(5)

where N is the number of stories and D_i is the damage index of the ith story.

Damage index analysis

To obtain the parameters for damage index calculation, a pushover analysis is needed. The maximum drift of all columns presented by pushover analysis is listed in Table 3, and the final Park–Ang damage indexes are shown in Figure 10(a). The damage indexes have the same tendency as the drift ratio, and the advantage of the cassette structure is obvious. When in IO level, both indexes are under 0.1, which means structures only have minor damage. With the increase in PGA, a much larger damage is observed in the frame structure. When in LS and CP level, the indexes of the frame structure are 0.18 and 0.5, respectively, which are much larger than 0.1 and 0.36 in the cassette structure. Furthermore, the index of the frame structure is approximately 1 in 0.4 PGA level, which means the entire structure is in failure stage and unstable. However, the index of the cassette structure is below 0.9 in this stage, which indicates that the structure is largely damaged, but the main element is still stable and there is no risk of collapse. The Park–Ang damage index time-history records are shown in Figure 10(b). All the curves show that the development of damage is much faster and larger in the frame structure, especially in 0.4 g PGA level. In all, based on both the final damage index and the time-history development, cassette structure presents a much better performance in the control of seismic damage.

Table 3.

Maximum drift of elements.

Structure	Element (unit: mm)	Maximum drift (unit: mm)
Frame structure	1000 × 800	53
	800 × 800	41
	700 × 700	60
	600 × 600	75
Cassette structure	800 × 700	19.3
	700 × 500	49
	650 × 450	38

Figure 10.

Park-Ang damage analysis for the two structures. (a) Park–Ang damage indexes for the two structures and (b) Park–Ang damage indexes development for the two structures.

Economic analysis

Overall introduction

In previous discussion, the advantage of the cassette structure in structural performances are obvious. However, these performances are not the only factors that are considered in the practical application. In addition to structural performance, economic performance is another important factor that should be considered. Therefore, economic analysis is conducted. The material usage and construction cost are based on Chinese code and quota, and the factor of building industrialization is considered.

Chinese quota

The Chinese quota used in this study is listed in Table 4. This quota specifies the essential cost of labor force, material usage, and other necessary processes. As building industrialization is the priority in China, all elements are manufactured in factories, and further transportation and assembling are needed. These extra costs are also included.

Table 4.

Chinese quota for beam and column.

Element	Name of cost	Unit	Cost per unit (CNY)
Beam	Concrete	m³	497
Beam	Template	m²	10,354
Column	Concrete	m³	508
Column	Template	m²	10,314

CNY: cost per unit.

Economic analysis

The consumption of concrete and steel of both two structures is nearly the same. The concrete usage of the cassette structure and the frame structure are 2472.4 and 2422.9 m³, respectively, and the steel usages are 276.8 and 282.1 t, respectively. Thus, the material cost for both structures are almost the same.

As these structure elements are made in specialized factories, careful element division is needed. The frame structure is dissembled into various single beams and columns, but the cassette structure is dissembled into four units shown in Figure 11. Unlike the frame structure, elements in the cassette structure are quite similar, only a few kinds of templates are needed. The number of elements used in a typical floor for both structures is shown in Table 5 and Figure 11. Considering the construction speed, three sets of templates are needed for the A unit, two sets for the D unit and all columns, and one set for all other elements in both structures. After counting seam and fabrication loss, the templates needed for one typical floor of the cassette structure are 110.75 and 152.6 m² for the frame structure. As two different types of typical floors are designed for both structures, the usage of templates is doubled. The entire template cost for the frame structure is 1.58 million CNY, while for the cassette structure, it is 1.147 million CNY, saving approximately 37% of the cost.

Figure 11.

Separated elements in the cassette structure.

Table 5.

Template usage of the two structures (unit: mm).

	Cross section/unit	Maximum length	Amount of element	Area of template
Frame structure	950 × 300	8700	20	1.97 × 10⁷
	650 × 300	8700	28	1.43 × 10⁷
	750 × 350	8700	15	1.66 × 10⁷
	900 × 300	7400	18	1.61 × 10⁷
	400 × 200	9075	7	9.23 × 10⁷
	550 × 250	9200	3	127 × 10⁷
	1000 × 800	5400	32	1.67 × 10⁷
Cassette structure	A		75	1.22 × 10⁷
	B		21	6.1 × 10⁶
	C		4	4.25 × 10⁶
	D		40	5 × 10⁶
	800 × 700 column		44	1.56 × 10⁷

After cast and maintenance, individual transportation is needed for the beams and columns of the frame structure, as the weight may exceed the limit of trucks. For the cassette structure, as the elements are comparatively small, two elements can be transported together. Therefore, the entire transportation cost is similar, but the costs for the frame structure will be slightly higher.

When considering the assembly of these two structures, the numerous nodes in the cassette structure is challenging. Take the first floor of cassette structure as an example; there are 121 nodes in the frame structure, while there are 436 nodes in the cassette structure, nearly four times of those in the frame structure. However, the size of the node in the cassette structure is only 1/3 of that in frame structure is, and all of them are in the middle of beams (shown in Figure 11). Therefore, only 1/5 of time cost is needed when assembling a node of cassette structure in practice.

Through current quota, assembling one frame node costs one worker a day, while the same worker can assemble five nodes of the cassette structure. Considering the entire structure, approximately 22 workdays can be saved in the construction of the 47-m height building.

The entire costs of these two structures are shown in Figure 12. It is obvious that compared with cassette structure, the template cost is much larger in the frame structure, while the other costs are nearly the same. Considering all the procedures, approximately 0.43 million CNY (approximately 7% of the total cost) and approximately 22 workdays can be saved when the frame structure is redesigned to a cassette structure. In addition, the structure can achieve much better performance under seismic and other loads. Therefore, it is a good option to replace the frame structure with the cassette structure when designing some mid-rise buildings.

Figure 12.

Entire cost of the two structures (unit: million CNY). (a) Entire cost of the frame structure, (b) entire cost of the cassette structure, and (c) cost comparison between the two structures.

Conclusion

Based on the previous discussion, the following general conclusions may be drawn:

The cassette structure is a novel, large-span structure system that can be used in mid-rise structures. Compared with frame structure, cassette structure can overcome the drawbacks of traditional frame structure like large element size and fixed space separation.

Based on dynamic time-history analysis, a redesigned cassette structure has much better performance than the frame structure. With the introduction of 18 time-history records recommended by FEMA as seismic excitation, the drifts of the cassette structure in four PGA levels are only approximately 70% of those of the frame structure.

Based on the Park–Ang damage index and plastic hinge analysis, the advantages of the cassette structure are obvious. The damage index and plastic hinge analysis can indicate the superiority of the cassette structure. At the 0.4 g PGA level, when the frame structure has failed and become unstable, the cassette structure can still maintain its structural integrity.

Furthermore, the cassette structure can achieve a better performance at a lower price. After analyzing material usage, template usage, transportation, and assembly, approximately 0.43 million CNY and 22 workdays can be saved when redesigning the frame structure as a cassette structure. Therefore, replacing a frame structure with a cassette structure can be a good option for mid-rise buildings.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors greatly appreciate the financial supports from the National Natural Science Foundation of China (Grant Nos. 51838004, 51525801, and 51708106).

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