Research on the flexural behavior of a novel inter-module connection with a bolt and shear key fitting for modular steel buildings

Abstract

Modular steel buildings (MSBs) can meet the needs of building industrialization and have been developed in many countries. The inter-module connection is crucial to the overall performance of MSBs. An inter-module connection with bolt and shear key fitting was proposed in this paper, which is convenient for the on-site erection of the steel modules. The flexural performance of the connection was studied. Static tests were carried out to study the contribution of the key load-bearing components to the flexural performance of the novel connection. A finite element model was then proposed and verified, by which a parametric analysis to study the effects of the key components was conducted. It is found that the parameters significantly affecting the flexural performance of the connection include the diameter of the bolt and the thickness of the bottom plate. The results also showed that the contribution of the shear key to the flexural performance of the connection could be ignored. The flexural performance of multi-module connection was studied, and the results revealed that the multi-module connection can be designed as multiple two-module connections. Formulas for calculating the flexural capacity and rotational stiffness of the connection were finally proposed and verified.

Keywords

modular steel buildings inter-module connection flexural performance static test finite element theoretical formula

Introduction

The modular steel building (MSB), built by stacking modules on-site, is one of the most integrated prefabricated buildings. It can achieve the goal of better quality control, less construction time and being more environmentally friendly by recycling modules (Luo et al., 2019). The disadvantage of MSBs is mainly the limited structural span caused by the module’s size (Lacey et al., 2018). Due to the characteristics of fast construction speed and mass production of modules, various MSBs have been used in diverse applications such as hotels, schools and military facilities (Sanches et al., 2018). However, with the rapid development, the lack of design guidance and specification of MSB remains one main concern.

The steel modules used in the MSB are manufactured off-site, transported and assembled on-site. According to the force-transferring path, steel modules can be divided into corner-supported modules and continuously supported modules (Lacey et al., 2018). The corner-supported steel modules have a better vertical capacity and are more applicable in high-rise buildings (Chen et al., 2017b). The steel modules are divided into MSB modules and light steel frame modules according to the section of beams and columns (Lacey et al., 2018). For light steel frame modules, the section of beams and columns is wide section. So the light steel frame modules are light in weight and suited to low-rise buildings. While the MSB modules have high strength and suitable for high-rise buildings, for the section of beams and columns is hollow section. In addition, the hollow section has a closed internal space, which is convenient for welding with the corner of module and fit for more types of inter-module connections. Therefore, in most of the research on the inter-module connections, the section of beams and columns is hollow section.

Due to the importance of inter-module connection in erection efficiency and load transfer for MSBs, various inter-module connections have been proposed and studied. Chen et al. (2017b) proposed a new type of design with beam-to-beam connections and studied its flexural performance and seismic behavior. Results revealed that beams and connections had independent and individual bending behaviors. Annan et al. (2009a, 2009b) evaluated the hysteretic characteristics of MSB, using welding as the vertical connections and field-bolting of clip angles as horizontal connections between modules. By comparing the performance between a regular braced frame and a modular braced frame, they concluded that the detailing requirements of the system need to be incorporated in the design of the modular braced frame. Chen et al. (2017a) investigated the seismic performance of a modular frame with pretension inter-module connections, in which the columns are vertically connected by pre-stressed strands. It was found that the pretension assembled framed modular system had different internal stress distribution from the traditional one. Chen et al. (2020) also studied the tensile and shear performance of a rotary inter-module connection. The performance of the critical components was investigated under tensile and shear loads, and simplified calculations were developed. Lee et al. (2017) proposed a new inter-module connection to form a rigidly connected modular system and verified the seismic performance of the proposed system. The results showed that the maximum resisting force of the proposed connection exceeded the theoretical parameters. A splice connection (Li et al., 2019; Lyu et al., 2021) was studied in full-scale corner-supported modular building. The proposed connection was sufficient to transfer the vertical load and had an acceptable tolerance for initial imperfections. Choi et al. (2016) adopted a bolted connection with an access hole opening at the end of the column in nonlinear static analyses of modular structures. It was found that the modeling of overlapped elements and the rotational behavior of connections can influence the structure’s lateral stiffness. Sendanayake et al. (2021) proposed a novel steel inter-modular connection and studied the performance of the connection under monotonic and cyclic lateral loads. The results revealed that the connection can display superior dynamic behaviour. Dhanapal et al. (2020) introduced a unique cast-steel connector, which was studied through full-scale tests. The study concluded that the connection can safely carry the design loads. These connections mentioned above include the following types: bolted, welded, pretensioned, and concreted. Welded and concreted connections (Annan et al., 2009a, 2009b) have better stiffness but cannot take advantage of the detachability of MSBs. Although there are already several connection types and relevant research for bolted connections (Chen et al., 2020; Choi et al., 2016; Lee et al., 2017; Li et al., 2019; Sanches et al., 2018), the problems of weakening members' sections and sensitivity to installation errors are still unsettled. Pretensioned connections (Chen et al., 2017a) possess excellent stiffness and strength but have high requirements for on-site construction and are prone to slip. Therefore, more reasonable connections, which have sufficient capacity and on-site construction convenience, need to be proposed (Dai et al., 2019).

This paper proposed an innovative inter-module connection with a bolt and shear key fitting to solve the existing problems mentioned above. The proposed connection can transfer the vertical loads and horizontal actions separately with independent components, which is easy for analysis and design. In addition, the inter-module connections at different locations can be installed inside the module and have a high tolerance to manufacturing and hoisting errors of the modules. The flexural performance of the novel connection was studied in this paper. The flexural performance is one of the properties of the inter-module connection, which is of great significance to the structural safety of MSBs during normal operation and integrity in emergency occasions (Lawson and Richards, 2010; Lawson et al., 2008).

The static monotonic tests were conducted to study the flexural performance of the proposed connection, and the stress distribution of the key components was obtained. A finite element model was then presented to conduct the parametric study, by which main parameters affecting the connection’s flexural performance and different failure modes were obtained. Multi-module connections were studied by the verified finite element model. The formulas for calculating the flexural capacity and rotational stiffness of the connection were proposed, which were validated against the experimental results and can be used as a design guide.

Configuration of the proposed inter-module connection

The details of the proposed connection at the corner are shown in Figure 1(a). The connection is composed of three components: connecting plate (green part), bolt (red part), and steel castings (blue and yellow part). The beams and columns are welded to the steel castings. The connecting plate is located between the steel castings. Two shear keys are welded on both sides of the connecting plate. The shear keys will be embedded in the shear keyhole without any connection, indicating that the shear key can only transfer the horizontal load. The bearing-type bolt connects the adjacent modules through the slotted hole.

Figure 1.

Details of the proposed connection. (a) Inter-module connection with bolt and shear key fitting, (b) Ceiling steel casting.

The detail of the ceiling steel casting is shown in Figure 1(b). The ceiling steel casting is composed of an L-shaped hollow box (blue part) and a triangular plate (yellow part). The slotted hole is opened on the triangular plate, and the shear keyhole is opened on the bottom plate of the L-shaped box. The thickness of the triangular plate is the same as that of the bottom plate. The plates of the L-shaped except for the bottom plate are called side plates. The structure of the floor steel casting is similar to that of the ceiling steel casting.

The proposed connection has the following advantages in mechanical performance and on-site erection. Firstly, the connection separates the vertical load-bearing components from the horizontal ones. There is no connector between the shear key and the steel castings, so the shear key cannot transfer tension and bending moment. Since the shape of the bolt hole is semi-slotted, it is hard to form the shear plane between the bolt and plates. Therefore, under the action of horizontal force, it is difficult for the bolt to transfer the horizontal force before the shear key is broken. Secondly, the bolt holes are opened on the triangular plate instead of the beam and column, ensuring the integrity of the members in the steel module. And thirdly, the bolts are located inside the module so that the insufficient construction space problems can be settled. Therefore, the connection can be completed conveniently inside the module through the reserved opening at various positions.

Experimental study

Materials and specimen

Steel Q345B and high-strength bolts M24 with grade 10.9 satisfying Standard for design of steel structures (GB 50017-2017, 2017) were used in the experiment. According to Metallic Materials-Tensile-Part 1: Method of test at room temperature (GB/T 228.1-2010, 2010), tensile tests were carried out to obtain the material properties, as shown in Table 1. A total of six round bar coupons were tested. Three were cut from the steel plate used to process the connection, and the other three were obtained from the remaining bolts of the same batch.

Table 1.

Material properties.

Material	Elastic modulus (MPa)	Yield strength (MPa)	Ultimate strength (MPa)	Ultimate strain	Elongation (%)
Bolt	209766.70	1019.80	1163.67	0.04	11.30
Steel	206333.33	328.33	627.25	0.23	30.73

The flexural specimen is shown in Figure 2. The bottom column, top column and fixed beam were welded to the connection. The loading beam was welded to the top column through stiffeners. Dimensions of the steel castings and connecting plate are shown in Figure 3, and the dimensions were determined by preliminary theoretical and numerical analysis before the experiment. The thickness of the bottom plate of steel castings $t_{b}$ is 25 mm, and the thickness of the side plates $t_{s}$ is 18 mm. The height of the shear key is the same as the thickness of the bottom plate, and the diameter of the shear key $d_{k}$ is 49 mm. The diameter of the shear keyhole is 4 mm larger than that of the shear key to avoid installation problems caused by processing and hoisting errors. As shown in Figure 3(a) and (b), the ceiling steel casting and floor steel casting differ only in height, for reasons that the floor beam is higher than the ceiling beam in steel modules. The steel castings in the test are produced by welding. The diameter of the bolt $d_{b}$ is 24 mm.

Figure 2.

Specimen. (a) Ceiling steel casting (b) Floor steel casting (c) Connecting plate.

Figure 3.

Dimensions of connection’s components (unit in mm).

Test setup

The test setup is shown in Figure 4(a), which includes the specimen, 2000 kN horizontal actuator, cantilever support and reaction frame. The specimen is fixed on the reaction frame. The top view of the test setup is shown in Figure 4(b), the out-of-plane displacement of the specimen is restricted by the cantilever support, and the specimen can only move within the red frame. As shown in Figure 4(e), the cantilever support consists of an end plate, stiffener, pedestal and two cantilever beams. The loading head of the actuator is close to the end of the loading beam without any connector. As shown in Figure 4(c) and (d), 2 mm plates made of PTFE (poly tetra fluoroethylene) are set in the gap between the actuator and the loading beam, as well as between the cantilever support and the top column. Two specimens were tested: one specimen was loaded along $x_{+}$ direction and the other specimen was loaded along $x_{-}$ direction, as shown in Figure 4(a). During the loading process, the actuator remains horizontal and the loading head of the actuator can rotate. The tests would be terminated when the specimen is damaged.

Figure 4.

Test setup. (a) Test setup, (b) Top view of the test setup, (c) Photograph of the test setup, (d) PTFE plates between the cantilever support and specimen, (e) Cantilever support.

The measurement arrangement of the experiment is shown in Figure 5. Displacement meters BD1∼BD3, BD4∼BD5 and BD6∼BD7 are used to measure the horizontal displacement of the loading beam, floor steel casting and ceiling steel casting, respectively. Strain gauges BS1∼BS2 and BS7∼BS8 are mounted vertically at the side plates close to the triangular plates, and strain gauges BS3∼BS6 are located at the triangular plates. Strain gauge BS9 is intended to measure the tensile strain of the bolt.

Figure 5.

Measurement arrangement.

Experiment results and discussion

Test loaded along $x_{+}$ direction

The deformation state and failure behaviors of specimens loaded along

x_{+}

are shown in Table 2 and Figure 6. As the load increased, the actuator moved horizontally, and the specimen rotated under the restraint of the cantilever support. When the load reached the maximum value of 82.34 kNm, obvious gaps appeared between the steel casting and the connecting plate. At this time, the axis of rotation of the specimen may be assumed to be at point C+ in Figure 6(b) and was perpendicular to the loading direction. After the load reached the maximum value, the specimen continued to rotate until the bolt broken. The moment was 80.37 kNm when the bolt broken, and other parts of the specimen did not deform significantly.

Table 2.

Phenomena in the test loaded along $x_{+}$ .

Moment (kN·m)	Rotation(rad)	Phenomena	Figure
67.72	2.34 × 10⁻²	The end of the loading beam and the loading head rotated together.	Figure 6(a)
82.34	3.72 × 10⁻²	There were gaps between the connecting plate and the steel castings.	Figure 6(b)
82.34	3.72 × 10⁻²		Figure 6(c)
80.37	4.51 × 10⁻²	The bolt was broken, resulting in the failure of the specimen.	Figure 6(d)
80.37	4.51 × 10⁻²		Figure 6(e)

Figure 6.

Deformation state and failure behaviors in the test loaded along $x_{+}$ . (a) Initial deformation state, (b) Axis of rotation, (c) Gaps in the test, (d) Final deforming state, (e) Broken bolt.

The load-strain curves are shown in Figure 7. According to the data measured by the strain gauges on the side plates, as shown in Figure 7(a), the side plates were in the elastic stage during the whole loading process. As shown in Figure 7(b), when the load reached 68.3 kN, the triangular plate of floor steel casting began to yield. And the strain close to the gap of the same triangular plate developed faster. The strain of bolt kept increasing until the bolt failed, as shown in Figure 7(c). When the bolt failed, the tensile stress at the strain gauge BS9 was 920.67 MPa. Calculated according to the pitch diameter of the thread, the tensile stress at the thread was 1090.56 MPa, which had exceeded the yield strength of the bolt.

Figure 7.

The load-strain curves measured by strain gauges. (a) Strain of the side plates, (b) Strain of the triangular plates, (c) Strain of the bolt.

The moment-rotation curve of the specimen loaded along $x_{+}$ is shown in Figure 10. The moment and rotation are calculated by the formula (1) and (2). The initial rotational stiffness is 3901.46 kN∙m/rad, and the flexural capacity is 84.05 kN∙m.

M_{x +} = F_{x +} \cdot h

(1)

θ_{x +} = \frac{1}{h} \cdot (\frac{∆_{b d 1} + ∆_{b d 2} + ∆_{b d 3}}{3} - \frac{∆_{b d 6} + ∆_{b d 7}}{2})

(2)

where,

M_{x +}

is the moment on the connection;

F_{x +}

is the load of the actuator;

h

is the height from the loading point to the rotation axis;

θ_{x +}

is the rotation of the connection;

∆_{b d i}

is the horizontal displacement measured by displacement meter SDi.

Test loaded along $x_{-}$ direction

The phenomena of specimens loaded along

x_{-}

is shown in Table 3 and Figure 8. As the actuator moved horizontally, the loading head of the actuator rotated with the specimen. When the load reached 11.8 kNm, large gaps appeared between the steel castings and the connecting plate, which indicated that the rotational stiffness of the specimen in this direction was relatively small. The axis of rotation was approximately at point C- in the Figure 8(a) and was perpendicular to the loading direction. When the load increased to 40.36 kNm, the shear key came out of the hole. When the load increased to 42.34 kNm, the rotation of the specimen was large and the load increased slowly, so the loading was stopped. After loading, the bolt did not break but had obvious bending deformation.

Table 3.

Phenomena in the test loaded along $x_{-}$ .

Moment (kN·m)	Rotation(rad)	Phenomena	Figure
11.80	1.96 × 10⁻²	The gap appeared between the connecting plate and the ceiling steel casting.	Figure 8(a)
40.36	7.91 × 10⁻²	The shear key came out of the shear key hole.	Figure 8(b)
42.34	11.62 × 10⁻²	The specimen was deformed greatly, but the bolt was still not broken.	Figure 8(c)
42.34	11.62 × 10⁻²		Figure 8(d)

Figure 8.

Deformation state and failure behaviors in the test loaded along $x_{-}$ . (a) Gaps in the test, (b) Pulled out shear key, (c) Final deforming state, (d) Deformed bolt.

The load-strain curves measured by strain gauges are shown in Figure 9. The strain of the side plates increased linearly except for the BS2. When the load was less than 30 kN, the side plate at BS2 was under compression; when the load was greater than 30 kN, the side plate at BS2 was under tension. This showed that in the early stage of loading, the axis of rotation was not at the point C-. When the load increased to about 30 kN, the axis of rotation moved to point C-. Similar to the test loaded along $x_{+}$ , the strain near the axis of rotation developed more slowly. As shown in Figure 9(c), the strain of the bolt at BS9 was also affected by the movement of the rotation axis. At the beginning of loading, the rotating axis passed through the bolt, so the side of the bolt close to the axis C- will be compressed. When the load exceeded 25.7 kN, the rotation axis was gradually transferred to the axis C-, and the stress in bolt measured by strain gauge BS9 changed from compressive stress to tensile stress. Finally, the tensile stress at the position of strain gauge BS9 was 588.61 MPa, and the tensile stress at the thread was 697.23 MPa.

Figure 9.

The load-strain curves measured by strain gauges. (a) Strain of the side plates, (b) Strain of the triangular plates, (c) Strain of the bolt.

The moment-rotation curve of the specimen loaded along $x_{-}$ is shown in Figure 10. Before the curve enters plasticity, there are two stiffness $K_{1}$ and $K_{2}$ in the curve. In section $K_{1}$ , the initial gap between the components of the specimen leads to the lower stiffness. In section $K_{2}$ , the initial gap and the gap generated by the pull-out of the shear key in section $K_{1}$ were closed, so the stiffness is large. Due to the initial gap and the gap generated by the pull-out of the shear key during rotation, neither $K_{1}$ or $K_{2}$ are the true initial rotational stiffness. Therefore, the weighted average method is used to calculate the initial rotational stiffness, as shown in formula (3). The initial rotational stiffness is 841.48 kN∙m/rad, and the flexural capacity is 42.34 kN∙m. Compared with loaded along $x_{+}$ , specimen loaded along $x_{-}$ has smaller capacity and stiffness, but has better ductility. When loaded in different directions, the working mechanisms of the connection are similar, but the rotation axis changes. When loaded along the $x_{-}$ direction, the bolt is closer to the rotation axis, so the connection is more likely to rotate.

K_{x -} = \frac{K_{1} \cdot M_{1} + K_{2} \cdot ∆ M_{2}}{∆ M_{1} + ∆ M_{2}}

(3)

Figure 10.

Moment-rotation curve of the specimen.

In this part, the flexural performance of the connection was studied through monotonic experiments. Flexural capacity, initial rotational stiffness and key components were obtained. The arm of force at the shear key is small, and the pull-out of the shear key did not lead to a significant drop in flexural capacity. It can be found that the shear key is not the main moment-bearing component. And the expected failure mode of the connection is the yield of the bolt, which is convenient to replace.

Numerical study

Finite element model

A finite element model was proposed to study further the flexural performance of the proposed connection by finite element software ABAQUS. The meshing result and boundary conditions are shown in Figure 11. The properties of the material and the dimensions of the parts in the FE model were the same as those in the tests. For the material model, the trilinear elastic model was adopted. All elements of the model used the eight-node linear hexahedral reduction element C3D8R. The welding connection was simulated by “tie”. The displacement load was applied to the end of the loading beam.

Figure 11.

Finite element model.

In order to verify the rationality of the model, the load-displacement curve and failure mode of the numerical study were compared with those in the test. The load-displacement curve of the finite element model is shown in Figure 12. At the initial stage of loading along $x_{-}$ direction, the experimental stiffness is less than the numerical stiffness due to the presence of initial gap between the components in the experiment. After the initial gap was closed, the stiffness of the test increases and exceeds the numerical stiffness. Other than that, it can be found that the model can properly simulate the flexural performance of specimens. As shown in Table 4, the flexural capacity and rotation stiffness in the numerical study are similar to those in the test. When the finite element model is loaded to 82.34 kNm along $x_{+}$ direction, the stress contour of the connection is shown in Figure 13(a). In both the test and finite element model, there were gaps between the connecting plate and the steel castings. As shown in Figure 13(b), the finite element model can simulate the pull-out of the shear key in the test loaded along $x_{-}$ direction. When the shear key is pulled out in the finite element model, the load (41.17 kNm) is similar to that in the test (40.36kNm). These results proved the reliability of the numerical model for further research.

Figure 12.

Load-displacement curve of the finite element model. (a) Test loaded along $x_{+}$ direction, (b) Test loaded along $x_{-}$ direction.

Table 4.

Comparison of numerical and analytical results with experimental results.

Item	Rotational stiffness (kN·m/rad)	Abs (error) (%)	Flexural capacity (kN·m)	Abs (error) (%)
Experimental ( $x_{+}$ )	3901.46		84.05
Numerical ( $x_{+}$ )	3556.18	8.85	84.02	0.04
Analytical ( $x_{+}$ )	3276.30	16.02	74.14	11.79
Experimental ( $x_{-}$ )	841.48		42.34
Numerical ( $x_{-}$ )	857.78	1.94	42.64	0.71
Analytical ( $x_{-}$ )	819.07	2.66	37.29	11.93

Figure 13.

Stress contours of connection. (a) Model loaded along $x_{+}$ direction, (b) Model loaded along $x_{-}$ direction.

Parametric study

In order to study the effect of the dimensions of different components on the flexural performance of the connection, parametric analysis was performed using the validated finite element model. The working mechanism of the connection loaded along the two directions is consistent. The finite element model loaded along

x_{-}

direction was selected for parametric study. As shown in Figure 3, the parameters affecting the flexural performance of connection are determined as: the diameter of the bolt

d_{b}

, the thickness of the side plates

t_{s}

, the thickness of the bottom plate

t_{b}

and the side length of the shear key

d_{s k}

. These parameters are the key parameters for designing the connection. The value of each parameter is shown in Table 5. Only one parameter was changed in each analysis to study the influence of this parameter on the flexural performance of the connection.

Table 5.

The value of parameters.

Constant1 (mm)	Constant2 (mm)	Constant3 (mm)	Variable (mm)
$t_{s} = 18$	$t_{b} = 25$	$d_{s k} = 43$	d_b is 22, 24, 27, 30, 36.
$d_{b} = 24$	$t_{b} = 25$	$d_{s k} = 43$	t_s is 8, 10, 14, 18, 22, 26.
$d_{b} = 24$	$t_{s} = 18$	$d_{s k} = 43$	t_b is 20, 22, 24, 25, 30.
$d_{b} = 24$	$t_{s} = 18$	$t_{b} = 25$	d_sk is 39, 44, 49, 54, 59.

Moment-rotation and capacity curves of different parameter values are shown in Figure 14. For $d_{b}$ : With the increase of $d_{b}$ , the flexural capacity and rotational stiffness of the connection will rise. For t_s: When $t_{s} > 10 m m$ , the curves change little with the increase of $t_{s}$ ; when $t_{s} < 10 m m$ , the flexural capacity and rotational stiffness will obviously rise with the increase of t_s. For t_b: When $t_{b} > 24 m m$ , there is no obvious change in flexural performance; when $t_{b} < 24 m m$ , the rotational stiffness and capacity of the connection are significantly reduced. For $d_{s k}$ : The change of $d_{s k}$ has little influence on the curves. It can be concluded that $d_{b}$ and $t_{b}$ have great impact on the flexural performance, while the influence of $t_{s}$ is smaller. The side length of the shear key $d_{s k}$ has almost no influence on the flexural performance.

Figure 14.

Moment-rotation and capacity curves of different parameter values. (a) The diameter of the bolt $d_{b}$ , (b) The thickness of the side plates $t_{s}$ , (c) The thickness of the bottom plate $t_{b}$ , (d) The side length of the shear key $d_{s k}$ , (e) The thickness of the side plates $t_{s}$ , (f) The thickness of the bottom plate $t_{b}$ .

As shown in Figure 14(e), when $t_{s} =$ 8 mm, the side plates yield in a large area while the connection is destroyed. When $t_{s} > 10 m m$ , the side plates are thick enough to take full advantage of the bolt. As shown in Figure 14(f), when $t_{b} = 20 m m$ , the triangular plate is so thin that it undergoes a large out-of-plane deformation before the bolt yields. When $t_{b} > 24 m m$ , the capacity changes little, and the triangular plate has no obvious plastic deformation. The results show that when $d_{b} = 24 m m$ , $t_{s} > 10 m m$ and $t_{b} > 24 m m$ , the failure mode can be guaranteed to be the yield of bolt and other components of the connection do not yield.

Connection between multiple modules

The previous tests and analyses are all for two-module connections. For multi-module connections, the connections connect adjacent modules by sharing the same connecting plate. In order to study the influence of sharing the same connecting plate on the performance of multi-module connections, a four-module connection is analyzed by numerical method. As shown in Figure 15(a), four modules A, B, C and D are connected by connection A and B. The verified finite element model is used to study the flexural performance of the four-module connection in the direction shown in Figure 15(b). The comparison of moment-rotation curves between the four-module connection and the two-module connection is shown in Figure 15(c) and (d). The results reveal that the flexural performance of each connection in the four-module connection is basically the same as that of the two-module connection. And the difference is smaller when loaded along the Y direction. It can be concluded that each connection in the multi-module connection can be analyzed and designed as a two-module connection.

Figure 15.

Connection between multiple modules. (a) Four-module connection, (b) Direction of loading, (c) Loaded along X, (d) Loaded along Y.

In this section, a finite element model was proposed to simulate the flexural performance of the connection. By comparing with the results in the test, the finite element model was verified. The proposed model was used for parametric analysis to obtain the parameter affecting the flexural capacity and rotational stiffness of the connection. The diameter of the bolt $d_{b}$ and the thickness of the bottom plate $t_{b}$ have a greater impact on the flexural performance, while the thickness of the side plates $t_{s}$ has a smaller impact on the flexural performance. The side length of the shear key $d_{s k}$ has little effect on the flexural performance of the connection, indicating that the connection can separate the horizontal load bearing components from the vertical load bearing ones. When $d_{b} = 24 m m$ , $t_{s} > 10 m m$ and $t_{b} > 24 m m$ , other components will not have significant plastic deformation before the bolt yields. The flexural performance of multi-module connection was studied, and the results revealed that the multi-module connection can be designed as multiple two-module connection.

Analytical study

Based on the results of the experiment and numerical study, the main parameters affecting the flexural performance of connection and different failure modes were obtained. These parameters are used to calculate the flexural capacity and rotational stiffness of the connection in the experiment. Conservative assumptions were proposed as follows

a. For the side plates of the steel casting, only the side plates close to the triangular plate is considered to transfer the moment.

b. According to the stress distribution in the numerical results, it is assumed that the distribution of yield lines in the triangular plate is shown in Figure 16.

c. Ignore the compression and tensile deformation of the side plates in the experiment.

Figure 16.

Schematic diagram of calculation of flexural capacity.

Flexural capacity

The formulas of flexural capacity for different failure modes are analytically derived and given below.

1. Failure mode 1: Yield of the bolt

When the connection is damaged due to the yield of the bolt, the formula for calculating the flexural capacity of the connection is given by

M_{1} = F_{y b} l_{b r} = A_{b} f_{y b} l_{b r}

(4)

where,

f_{y b}

is the yield strength of the bolt;

A_{b}

is the cross-sectional area of the bolt;

l_{b r}

is the distance from the bolt to the rotation axis.

2. Failure mode 2: Yield of side plates

As shown in Figure 16, according to the stress contours of the finite element model, it’s assumed that when the L-shaped box is subjected to moment, only the side plates close to the triangular plate (the yellow area) transfer the load. The formula for calculating the flexural capacity $M_{2}$ is given by

M_{2} = f_{y s} W_{s p}

(5)

where,

f_{y s}

is the yield strength of the steel casting;

W_{s p}

is the flexural section coefficient of the side plates close to the triangular plate.

3. Failure mode 3: Yield of triangular plate

The yield line theory is used to calculate the tension of the bolt when the triangular plate yields. According to the results of the parametric analysis, the stress distribution of the triangular plate at yield is shown in Figure 17. The yield area of the triangular plate is roughly shown by the blue line. According to the blue line in Figure 17, three assumed yield lines are shown in Figure 16. Based on the principle of virtual work, the tension of the bolt when the triangular plate yields is given by

W_{p l} = \sum W_{i} = W_{b} = F_{b v} ∆_{v}

(6)

W_{1} = W_{3} = m_{p} l_{1} φ_{1} = \frac{f_{y s} t_{b t}^{2} \sqrt{2} l_{t} ∆_{v} l_{t} 2 \sqrt{2}}{422 d_{d} l_{t}} = \frac{∆_{v} l_{t} f_{y s} t_{b t}^{2}}{4 d_{d}}

(7)

W_{2} = m_{p} l_{2} φ_{2} = \frac{f_{y s} t_{b t}^{2} 2 \sqrt{2} ∆_{v} l_{t}}{4 l_{t} 2 d_{d}} (\sqrt{2} d_{d} - 0.5 d_{b}) = \frac{{∆_{v} f}_{y s} t_{b t}^{2}}{4 d_{d}} (2 d_{d} - \frac{\sqrt{2} d_{b}}{2})

(8)

F_{b v} = \frac{\sum W_{i}}{∆_{v}} = \frac{f_{y s} t_{b t}^{2}}{2} (\frac{l_{t}}{d_{d}} + 1 - \frac{\sqrt{2} d_{b}}{4 d_{d}})

(9)

where,

W_{p l}

is the internal virtual work;

W_{b}

is the external virtual work done by the bolt;

W_{i}

is the internal virtual work done by the ith yield line;

l_{i}

is the length of the ith yield line;

φ_{i}

is the angle of the ith yield line;

l_{t}

is the side length of the triangular plate;

d_{d}

is the distance from the bolt to the side plates;

F_{b v}

is the tension of the bolt when the triangular plate yields;

∆_{v}

is the virtual displacement at the bolt.

Figure 17.

stress distribution of the triangular plate at yield.

And the flexural capacity controlled by the triangular plate is given by

M_{3} = F_{b v} l_{b r}

(10)

By summarizing the above three failure modes, the tensile capacity of the connection $M_{c}$ is given by

M_{c} = \min (M_{1}, M_{2}, M_{3}) = \min (A_{b} f_{y b} l_{b r}, f_{y s} W_{s p}, F_{b v} l_{b r})

(11)

Rotational stiffness

According to Eurocode 3: Design of steel structures-Part1-8: Design of joints (BS EN 1993-1-8:2005, 2005), the rotational stiffness of the connection in the test is calculated by the component method. As shown in Figure 18, according to the component method, the connection can be divided into tension area (red line) and compression area (green line). The components of the tension area include the bolt, triangular plates and side plates away from the rotation axis (Side Plates 1). The components of the compression area include the connecting plate and side plates close to the rotation axis (Side Plates 2). Since the tensile and compressive stiffness of the side plates and connecting plate are much greater than the tensile stiffness of the bolt and the flexural stiffness of the triangular plate, the tensile and compressive stiffness of the side plates and connecting plate are ignored. According to Eurocode 3: Design of steel structures-Part1-8: Design of joints (BS EN 1993-1-8:2005, 2005), the rotational stiffness of the connection is given by

S_{c} = E l_{b r}^{2} {(\frac{1}{k_{b}} + \frac{2}{k_{t p}})}^{- 1}

(12)

where, E is the elastic modulus;

S_{c}

is the rotational stiffness of the connection;

k_{b}

is the stiffness coefficient of the bolt;

k_{t p}

is the stiffness coefficient of the triangular plate.

Figure 18.

Schematic diagram of component method.

The triangular plate can be regarded as a stiffened column flange. The bolt is adjacent to the stiffener, and the bolt hole is semicircular. According to Eurocode 3: Design of steel structures-Part1-8: Design of joints (BS EN 1993-1-8:2005, 2005), the stiffness coefficients are given by

k_{b} = \frac{1.6 A_{b}}{l_{b}}

(13)

k_{t p} = \frac{0.9 l_{e f f} t_{b}^{3}}{m^{3}}

(14)

where,

l_{b}

is the bolt length;

l_{e f f}

is the effective length;

m

is the distance from the bolt to the welding root of the triangular plate.

Validation

In the process of proposing the theoretical formulas, many conservative assumptions were made. The results obtained by the theoretical study are compared with the results in the test, as shown in Table 4. Since the theoretical calculation method is conservative, the flexural capacity and rotational stiffness obtained in experiment are larger.

In addition, the results of theoretical formulas are compared with the results of parametric analysis. As shown in Figure 19, the theoretical formula can safely calculate the capacity of the connection. For the diameter of the bolt, when $d_{b} > 24 m m$ , the numerical results are significantly larger than the theory. However, at this time, the steel castings have undergone large plastic deformation, and the capacity should not be determined by the breaking of bolt. For the thickness of the side plates, when $t_{s} > 10 m m$ , the capacity of the connection is basically unchanged, which is consistent with the parametric analysis. For the thickness of the bottom plate, when $t_{b} > 25 m m$ , similar to the numerical results, the growth of capacity slows down. It can be concluded that the theoretical formulation can safely guide the design and can be used to guarantee the expected failure mode.

Figure 19.

Comparison of theoretical results and parametric analysis. (a) The diameter of the bolt $d_{b}$ , (b) The thickness of the side plates $t_{s}$ , (c) The thickness of the bottom plate $t_{b}$ .

Combining the conclusions of the experimental and numerical study, formulas for calculating the flexural capacity and rotational stiffness were proposed. The proposed formulas were validated by comparison with results in the test and parametric analysis. And it is proven that the formulas can be used to design the connection and obtain the desired failure mode.

Conclusions

This article proposed an inter-module connection with a bolt and shear key fitting and investigated the flexural performance of the connection. The main conclusions are summarized as follows:

(1) The proposed inter-module connection separates the vertical load-bearing components and the horizontal load-bearing components with the bolt resisting the tension and moment and the shear key resisting the shear force, which simplify the configuration of the connection and ease the erection of steel modules. The connection can be installed in various locations through the reserved opening and has a high tolerance to installation errors.

(2) By experimental research, the stress development of key components and failure mode of the specimen were obtained. It is found that the shear key contributed little to the flexural performance of the specimen, for the pull-out of the shear key did not lead to a significant drop in flexural capacity.

(3) A finite element model was built and validated to simulate the flexural performance of the connection. The parametric study was conducted by the proposed model, and the parameters affecting the flexural performance and different failure modes were obtained. The diameter of the bolt $d_{b}$ and the thickness of the bottom plate $t_{b}$ have a significant impact on the flexural performance of the connection. The change of the diameter of the shear key $d_{s k}$ has little effect on the flexural performance, which indicates that the shear key is not the main moment-bearing component. When $d_{b} = 24 m m$ , $t_{s} > 10 m m$ and $t_{b} > 24 m m$ , other components will not have significant plastic deformation before the bolt yields. The flexural performance of multi-module connection was studied, and the results revealed that the multi-module connection can be designed as multiple two-module connection.

(4) Based on the experimental and numerical study, analytical formulas for calculating the flexural capacity and rotational stiffness were proposed. The results obtained by the formulas were compared with experiment and parametric analysis. It can be concluded that the formulas can be used to guide the flexural design of the proposed connection safely and guarantee the expected failure mode.

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 research work presented hereinabove was supported by the National Key Research and Development Program of China (Project No.2017YFC0703803-04) and the National Science Foundation for Young Scientists of China (Grant No.51808068).

ORCID iD

Guo-Qiang Li

References

Annan

Youssef

El Naggar

(2009a) Experimental evaluation of the seismic performance of modular steel-braced frames. Engineering Structures 31: 1435–1446.

Annan

Youssef

El Naggar

(2009b) Seismic overstrength in braced frames of modular steel buildings. Journal of Earthquake Engineering 13: 1–21.

BS EN 1993-1-8:2005 (2005) Eurocode 3: Design of Steel Structures-Part1-8: Design of Joints.

Chen

, et al. (2017a) Research on pretensioned modular frame test and simulations. Engineering Structures 151: 774–787.

Chen

Liu

(2017b) Experimental study on interior connections in modular steel buildings. Engineering Structures 147: 625–638.

Chen

Wang

Liu

, et al. (2020) Tensile and shear performance of rotary inter-module connection for modular steel buildings. Journal of Constructional Steel Research 175: 15.

Choi

Lee

Kim

(2016) Influence of analytical models on the seismic response of modular structures. Journal of The Korea Institute for Structural Maintenance and Inspection 20: 74–85.

Dai

X-M

Zong

Ding

, et al. (2019) Experimental study on seismic behavior of a novel plug-in self-lock joint for modular steel construction. Engineering Structures 181: 143–164.

Dhanapal

Ghaednia

Das

, et al. (2020) Behavior of thin-walled beam-column modular connection subject to bending load. Thin-Walled Structures, 149: 106536.

10.

GB 50017-2017 (2017) Standard for Design of Steel Structures. (in Chinese).

11.

GB/T 228.1-2010 (2010) Metallic Materials-Tensile-Part 1: Method of Test at Room Temperature. (in Chinese).

12.

Lacey

Chen

Hao

, et al. (2018) Structural response of modular buildings - an overview. Journal of Building Engineering 16: 45–56.

13.

Lawson

Byfield

Popo-Ola

, et al. (2008) Robustness of light steel frames and modular construction. Structures & Buildings 161: 3–16.

14.

Lawson

Richards

(2010) Modular design for high-rise buildings. Proceedings of the Institution of Civil Engineers-Structures and Buildings 163: 151–164.

15.

Lee

Park

Kwak

, et al. (2017) Verification of the seismic performance of a rigidly connected modular system depending on the shape and size of the ceiling bracket. Materials 10: 263.

16.

G-Q

Cao

(2019) Column effective lengths in sway-permitted modular steel-frame buildings. Proceedings of the Institution of Civil Engineers-Structures and Buildings 172: 30–41.

17.

Luo

Ding

Styles

, et al. (2019) End plate-stiffener connection for SHS column and RHS beam in steel-framed building modules. International Journal of Steel Structures 19: 1353–1365.

18.

Lyu

Y-F

G-Q

Cao

, et al. (2021) Behavior of splice connection during transfer of vertical load in full-scale corner-supported modular building. Engineering Structures 230: 111698.

19.

Sanches

Mercan

Roberts

(2018) Experimental investigations of vertical post-tensioned connection for modular steel structures. Engineering Structures 175: 776–789.

20.

Sendanayake

Thambiratnam

Perera

, et al. (2021) Enhancing the lateral performance of modular buildings through innovative inter-modular connections. Structures 29: 167–184.

Research on the flexural behavior of a novel inter-module connection with a bolt and shear key fitting for modular steel buildings

Abstract

Keywords

Introduction

Configuration of the proposed inter-module connection

Experimental study

Materials and specimen

Test setup

Experiment results and discussion

Test loaded along x + direction

Test loaded along x − direction

Numerical study

Finite element model

Parametric study

Connection between multiple modules

Analytical study

Flexural capacity

1. Failure mode 1: Yield of the bolt

2. Failure mode 2: Yield of side plates

3. Failure mode 3: Yield of triangular plate

Rotational stiffness

Validation

Conclusions

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References

Test loaded along $x_{+}$ direction

Test loaded along $x_{-}$ direction