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New interlocking inter-module connection for modular steel buildings:
Experimental and numerical studies
Andrew William Lacey, Wensu Chen*, Hong Hao*, and Kaiming Bi
Centre for Infrastructural Monitoring and Protection,
School of Civil and Mechanical Engineering, Curtin University, Australia
*Corresponding authors
Submitted 09 May 2019, Accepted 30 July 2019
https://doi.org/10.1016/j.engstruct.2019.109465
Abstract
To improve the constructability and performance of modular buildings, a number of inter-module connections
have been developed, each with their own associated advantages and disadvantages. Interlocking inter-module
connections have emerged as a promising type of improvement; however, it is not clear how to provide the
required installation tolerance without allowing slip. At the same time, the existing model for the shear force-
slip behaviour is known to be inadequate. This study introduces a novel interlocking inter-module connection
which combines structural bolts with interlocking elements to improve the constructability and shear force-
slip behaviour. An experimental study was conducted to investigate the shear force-slip behaviour of the
proposed connection. The effects of the interlocking elements, bolt preload, hole tolerance, and fabrication and
assembly tolerance on the shear behaviour are evaluated and discussed. Numerical simulations were carried
out to support the experimental program, following which the distinguishing features of the force-slip
behaviour were examined, and an empirical model was proposed.
Keywords: Modular building, Inter-module connection, Bolted connection, Stiffness, Slip resistance
1. Introduction
In a previous study [1], the authors presented an overview of the structural response of modular buildings, for
which the design and construction of reliable inter-module connections was identified as a major challenge.
Further research was recommended to improve understanding of the structural performance of the existing
inter-module connections, and to prevent overly conservative design due to the currently limited understanding
of the structural behaviour. A similar conclusion was reached by Ferdous et al. [2] in their state-of-the-art
review of modular buildings. It was reported that the existing connections were unable to meet the integrity
requirements of modular buildings. Further research of novel interlocking connections was therefore
recommended to develop efficient inter-module connections. Navaratnam et al. [3], in their performance
review for prefabricated buildings, reported that prefabricated structural systems can use non-conventional
connections. They noted an absence of testing standards specific to prefabricated components and
recommended appropriate design standards be developed. They also noted a redundancy in the existing
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
Andrew William Lacey, Wensu Chen*, Hong Hao*, and Kaiming Bi
10.1016/j.engstruct.2019.109465
Page 2 of 27
structural systems of prefabricated buildings. They reasoned, however, that the cause of the redundancy was
the individual assessment of components and indicated a need for whole structure assessment. The literature
clearly indicates that further research on the inter-module connections is required to improve understanding,
and enable development of enhanced connection systems.
The typical inter-module connections include site welded and bolted plate details [1, 4]. For example, several
details are illustrated in Fig. 1. However, these existing inter-module connections suffer from several
disadvantages. The inter-module connection must provide suitable tolerances to allow positioning of the
module on site. However, providing suitable tolerances introduces a potential for tolerance accumulation over
multiple storeys, and a vulnerability to significant slip displacements if the structure is subject to extreme
lateral loading [5]. To prevent this vulnerability to large slip displacement, the typical bolted connections are
limited to small tolerances. In contrast, the site welded detail can provide greater flexibility in positioning of
the modules on site. However, the site welding process introduces another trade to the site work, which is
counterproductive if the goal is to maximise construction speed while improving the quality of the work. Both
the bolted and the welded details require external access to the inter-module connection, which is not possible
at all corners of the modules. Further, the relatively simple details can become complex if connection is
provided between modules in three directions, while maintaining access during the site installation [1]. It is
clear that improved inter-module connections are required.
Fig. 1. Typical inter-module connections for modular steel buildings [1, 6]: (a) Site welded [7, 8], (b) Tie plate [9, 10],
(c) Bolted side plate [11], (d) Bolted end plate [12], and (e) Bolted end plate [11].
In response, a number of improved inter-module connections are proposed in the literature. Chen et al. [13]
proposed a composite concrete/steel connection (Fig. 2a) which offered good strength, no slip, and a compact
size. However, the use of concrete added site work, and resulted in a connection which was not demountable.
Chen et al. [14] proposed an interior connection (Fig. 2b) which was reported to offer easy working access for
assembly. The proposed connection had two components: a cast plug-in device, and beam-to-beam bolts. The
plug-in component, which may be classified as an interlocking element, allowed horizontal connection
between adjacent modules. However, the bolted detail, which allowed vertical connection between stacked
modules, may be considered too complex. Sharafi et al. [15] proposed an interlocking connection (Fig. 2c)
which was reported to be easy to assemble with the potential for automation of assembly. However, the
integrating connection strips require adhesive to provide the resistance to uplift of the module. Further, it is
not clear how to provide the tolerance without allowing slip. In general, the proposed interlocking connections
require modules which are individually unique, because the precise inter-module connection detailing depends
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
Andrew William Lacey, Wensu Chen*, Hong Hao*, and Kaiming Bi
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on the location of the module within the overall structure. The modules must then arrive to site and be installed
in a specific sequence which complicates the construction process. Zheng et al. [16] and Sanches et al. [4]
proposed post-tensioned connections (Fig. 2d,e), which can be described as tubular steel columns with
tensioned tie rods located centrally within the columns. These connections were reported to offer a more rigid
connection and allow for connection where direct access is not possible. However, it may be difficult to access
and tension the tie rod, with a single large tie rod located within the columns. Sultana et al. [17] proposed the
use of shape memory alloy bolts to replace the standard bolts in a typical bolted vertical connection detail (Fig.
2f). This detail offered the potential for a reduction in the maximum residual inter-storey drift, and better
damage distribution, in comparison with the standard structural bolts. However, the proposed connection was
disadvantaged by the relatively high cost of the shape memory alloy bolts, and the possible increase in the
maximum inter-storey drift. Overall, it is apparent that each of the proposed inter-module connections has its
own associated advantages and disadvantages. However, the interlocking inter-module connection emerges as
a promising type of improvement.
Fig. 2. Proposed inter-module connections including (a) Pretension connection [13], (b) Interior connection with plug-in
device [14], (c) Integrating connection strips [15, 18], (d) Tie rod connection [16], (e) Vertical post-tensioned
connection [4], and (f) Shape memory alloy bolts in typical vertical connection [17].
Lacey et al. [6] presented a review of inter-module connections for modular steel buildings. The purpose of
inter-module connections was outlined, including the structural performance and site construction
requirements, and the existing methods for estimating the inter-module connection stiffness were reviewed. In
the existing model for the shear force-slip curve, a linear response is assumed for the initial friction/slip
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
Andrew William Lacey, Wensu Chen*, Hong Hao*, and Kaiming Bi
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behaviour, and the initial stiffness is calculated as the ratio between the slip resistance and the bolt hole
tolerance. Use of the bolt hole tolerance results in a relatively low estimate for the initial stiffness, which
matches the low initial stiffness of the existing inter-module connections in the previous studies [5, 11].
However, the existing model does not reflect the physical friction/slip behaviour, and may underestimate the
initial stiffness of inter-module connections with greater bolt hole tolerance. Given that the vulnerability to
slip under shear loading is indicated as a disadvantage of the existing inter-module connections, it is important
to establish a reliable model for the shear force-slip behaviour. This model can then be applied in the
development of improved inter-module connections. It therefore remains to investigate the shear behaviour of
inter-module connections, and to propose an improved model for the shear force-slip behaviour.
Following the previous works, this study investigates a new interlocking inter-module connection for modular
steel buildings. The proposed inter-module connection combines structural bolts with interlocking elements to
improve the constructability and shear force-slip behaviour. An experimental study was conducted to establish
the shear behaviour. A method and setup were developed, and in-plane displacements were recorded
throughout the experiments using digital image correlation (DIC). The bolt tightening torque was defined to
control the bolt preload with reference to the manufacturer supplied k-factor. Parametric studies were
conducted considering the effects of the interlocking elements, bolt preload, and bolt hole tolerance on the
shear behaviour. Finally, an improved model was proposed for the shear F-d behaviour of the proposed
interlocking inter-module connection.
1. Proposed interlocking connection
An interlocking connection detail is envisaged which combines structural bolts with interlocking elements.
The pre-tensioned bolts provide the initial shear stiffness and the slip resistance can be demonstrated based on
the preload and slip factor. After the initial slip, the connection transitions to a bearing type where the bolts
and the interlocking components contribute to the shear resistance. The interlocking components assist with
correct positioning of the module during site installation and provide safety during construction, prior to
installation and tensioning of the bolts. The tolerance may be adjusted to suit the anticipated accuracy in site
positioning of the modules, and the desired interplay of the connection elements in the shear slip sequence.
More specifically, the interlocking connection proposed in the present paper is shown in Fig. 3. The features
of the proposed connection, which was developed for modular buildings with steel columns, include:
horizontal connection by plate P2, vertical connection by structural bolts (the grey bolts in the figure), and
locating pins for site assembly and improved shear stiffness. The locating pins are inserted through and welded
to the underside of plate P1. The P1/locating pin assemblies are then welded to the top end of the lower columns
during shop fabrication of the lower modules. After placement of the lower modules on site, the plate P2 is
placed on top of the P1 plates, with the locating pins extending through P2. The upper modules are then placed
on top, with the locating pins extending through the P3 plates, which were shop welded to the bottom end of
the upper module columns. Structural bolts are then inserted through the combined thickness of the plates P1,
P2, and P3. The proposed connection offers a simplification of detailing with the ability to provide connection
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
Andrew William Lacey, Wensu Chen*, Hong Hao*, and Kaiming Bi
10.1016/j.engstruct.2019.109465
Page 5 of 27
between up to eight modules, i.e., four lower and four upper modules. The site installation is relatively easy,
as is the end of life deconstruction. Safety during construction is considered and improved by the interlocking
component, i.e., the locating pin. Considering the disadvantages, the detail requires site installation of the P2
plates, and site installation and tensioning of the bolts. The latter may require external access which may
interfere with the building finishes, which is another disadvantage. However, the potential advantages are
expected to compensate for the disadvantages.
Fig. 3. Illustration of the proposed interlocking inter-module connection.
2. Experimental study
2.1. Method and specimens
An experimental study was completed to investigate the shear force-slip (F-d) behaviour of the proposed
connection. Six specimens were fabricated with different bolt preload, bolt hole tolerance, and presence or
absence of locating pins, as shown in Table 1. There were three main specimen types: A, B, and C. The
geometry for the A specimens is shown in Fig. 4 which includes a cut away view showing the otherwise hidden
components. The plates are labelled SP14t, SP14b, SP16, SP15t, and SP15b for convenience in the following
discussions. These labels follow the fabrication drawings where SP referred to single parts, and t and b referred
to the top and bottom of the assembled specimen (Fig. 4). The A specimens had a standard bolt hole tolerance
of 2 mm, i.e., a 14 mm diameter hole, as specified for M12 bolts in the Australian standard AS 4100 [19]. The
12 mm diameter locating pins had a corresponding 16 mm diameter hole. This gave a tolerance of 4 mm for
the locating pins which ensured that the bolts would bear on the plates at the same time as the plates contacted
the locating pins. During assembly the specimens were aligned to allow the maximum slip displacement during
the test, thereby ensuring the initial shear resistance was due to friction between the plates. The B specimens
were fabricated without locating pins but were otherwise the same as the A specimens. The C specimens had
slotted holes with a diameter of 14 mm and a length of 22 mm, as illustrated in Fig. 5. Slotted holes were
included to investigate the effect on the F-d behaviour. The slotted hole was expected to give a reduced slip
resistance and greater slip displacement in comparison with the standard hole tolerance.
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
Andrew William Lacey, Wensu Chen*, Hong Hao*, and Kaiming Bi
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Table 1. Test matrix.
Each specimen consisted of a simplified two-column connection detail which was duplicated to give a balanced
loading arrangement. The loading arrangement is illustrated in Fig. 6 and the actual setup is shown in Fig. 7
The connection was tested in shear using a compression load from a Shimadzu AGS-300kNX universal testing
machine (UTM). Load was applied to the specimen by the top compression plate at a rate of 0.1 kN/s, starting
from zero and increasing to a maximum of 250 kN. The load was transferred from the top compression plate
to the upper hollow section columns by two upper bearings, which provided clearance around the bolts (Fig.
6a). Similarly, at the bottom, the load was transferred from the specimen through the lower bearing to the lower
compression plate. For the upper bearings there was a nominal gap of 7 mm between the bearing and the
adjacent end plate, allowing for the weld between the plate and hollow section (Fig. 6b). The lower bearing
was located approximately centrally, giving a nominal gap of 5mm (Fig. 6c). A chamfer was provided to the
lower bearing edge to ensure adequate clearance between the bearing and the weld (Fig. 6c).
Prior to testing, the specimens were assembled and the bolts were tensioned using a torque wrench. The torque
(Mr) required to give the specified preload (Nt) was calculated based on the general relationship given in
AS/NZS 1252.1 [20] as,
r m t
M k DN
(1)
where D is the nominal bolt diameter (12 mm), and km is a coefficient determined based on bolt assembly tests
as per Appendix D of AS/NZS 1252.1 [20] and EN 14399-2 [21]. From the manufacturer supplied test
certificate, the mean k-factor (km) was 0.119, and the corresponding coefficient of variation was 0.042 based
on five assembly tests. The five tests were performed by the manufacturer in accordance with EN 14399-2
[21].
A summary of the materials used for the specimens is given in Table 2. The faying surfaces of the steel plates
were maintained in the clean mill scale condition. The slip factor was 0.31 as determined by slip factor testing
in accordance with Annex G of EN 1090-2 [22]. Lacey et al. [23] provides details on the slip factor testing and
associated analysis. The M12 bolts were hot dip galvanised, giving a clean mill scale / galvanised interface
between the plates and bolts. The bearings had a smooth machined surface which was in contact with the
factory painted finish of the hollow sections.
Specimen
A1
A2
B1
B2
C1
C2
Bolt preload (kN)
50
35
50
35
50
35
Hole tolerance
Standard
Standard
Standard
Standard
Slotted
Slotted
Locating pin
Y
Y
N
N
Y
Y
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
Andrew William Lacey, Wensu Chen*, Hong Hao*, and Kaiming Bi
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Fig. 4. Illustration of specimen A showing (a) bolt hole, and (b) locating pin details. (All dimensions in mm)
Fig. 5. Illustration of specimen C showing (a) bolt hole, and (b) locating pin details. (All dimensions in mm)
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
Andrew William Lacey, Wensu Chen*, Hong Hao*, and Kaiming Bi
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Fig. 6. (a) Conceptual view of experimental setup showing (b) Upper and (c) Lower bearing details.
Fig. 7. Photo of experimental setup.
Table 2. Summary of material properties.
Description
Part (refer
Fig. 4)
Grade
Cross-
section
dimensions
(mm)
Min. yield
stress
(MPa)
Min. tensile
strength
(MPa)
Min.
elongation
(%)
Hollow section, AS/NZS 1163
SP10, SP12
C350L0
75x75x6
350
430
12
Square bar, AS/NZS 3679.1
Bearings
300
75x75
290
440
22
Round bar
SP11
300
R12
375
530
34
Plate, AS/NZS 3678
SP14, SP15,
SP16
G350
75x8
360
450
20
M12x1.75Px50,8.8, HR Bolts
AS/NZS 1252
B
Class 8.8
-
640
800
12
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
Andrew William Lacey, Wensu Chen*, Hong Hao*, and Kaiming Bi
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2.2. Results and analysis
A speckle pattern was applied to the front surface of each specimen and digital image correlation (DIC) was
undertaken to determine the vertical displacements following the established method [23-26]. For example,
Fig. 8 shows the vertical displacement contour of A1 at two selected time increments. For each time increment
the vertical displacements (mm) were determined at selected points as shown in Fig. 8. Points 1 to 4 were
located along the lower column centreline, and the slip was calculated as the average difference in vertical
displacement between the points 1 and 2, and 3 and 4. That is, the slip at the lower columns (dlower) was
calculated as,
1 2 4 3
0.5
lower
d
,
(2)
where δi is the vertical displacement at point i. Similarly, points 5 to 8 were located along the upper column
centreline, and the slip at the upper columns was calculated as,
5 6 8 7
0.5
upper
d
.
(3)
Fig. 8. Vertical displacement contour (mm) of A1 for an applied force of (a) 46.2 kN and (b) 93.8 kN.
The force obtained from the UTM was then plotted against the slip determined from the DIC. For example,
the resulting F-d curves for A1 are shown in Fig. 9. Although reasonable care was taken in the fabrication and
assembly, variation in the part dimensions and straightness resulted in some gaps between the connection
elements prior to loading. Due to the gap between SP15t and SP15b (Fig. 9a), the initial slip for the lower
column centreline was resisted by friction at the SP15b / SP16 interfaces. Therefore, only the preload of the
two lower bolts contributed to the initial slip resistance resulting in a lower initial slip resistance. The full
connection slip resistance, to which the preload of all four of the bolts contributed, was not reached until after
the initial gaps were closed.
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
Andrew William Lacey, Wensu Chen*, Hong Hao*, and Kaiming Bi
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Fig. 9. Force-slip plot for A1 showing slip at the lower and upper column centrelines.
For the upper column centreline, the F-d curve was affected by the initial gap between SP14t and SP16 (Fig.
9b). The gap (b) was present in the specimens due to the fabrication process, during which the plate SP14 was
welded to column SP10. The plate was welded on three sides and the heat from the process resulted in a small
curvature in plate SP14. As a result, when the specimen was assembled, there was a gap between SP14t and
SP16. This initial gap (b) allowed the SP14t / SP10t assembly to rotate as the load was applied. The rotation
increased the vertical displacement at points 5 and 8 (Fig. 8), and therefore increased the slip (mm), which was
calculated following Eq. 3, prior to the initial slip resistance (kN). The slip at the lower column centreline was
less affected by the plate curvature. Therefore, to reduce the effect of the SP14 plate curvature, the slip for the
remaining specimens was calculated from the lower column centreline only. The resulting F-d curves are
shown in Fig. 10.
Each of the specimens had initial gaps between the connection elements, although the size of the gaps varied.
As a result, the F-d curves in Fig. 10 generally exhibit a lower initial slip resistance for which only two of the
four preloaded interfaces were effective. The position of the initial slip points were determined as the first
significant change in slope of the F-d curve. Once the initial gaps were closed, the full connection slip
resistance was reached as all four of the preloaded interfaces contributed to the friction resistance. The position
of the full connection slip points were similarly determined by examining the slope of the F-d curve. For A2,
the initial gaps were small and the lower initial slip resistance was not apparent by visual inspection of the F-
d curve (Fig. 10b). Therefore, only the full connection slip resistance was determined for A2. The slip
resistances are summarised in Table 3.
Table 3. Summary of experimental slip resistance.
Specimen
A1
A2
B1
B2
C1
C2
a. Full connection slip resistance (kN)
93.8
68.6
97.8
70.2
105
60.2
b. Initial slip resistance (kN)
46.2
-
48.2
31.8
51.3
30.2
b / a
0.49
-
0.49
0.45
0.49
0.50
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
Andrew William Lacey, Wensu Chen*, Hong Hao*, and Kaiming Bi
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Page 11 of 27
Fig. 10. Experimental force-slip plots for (a) A1, (b) A2, (c) B1, (d) B2, (e) C1, and (f) C2.
For A2 and B2 the point at which the bolts started to slide was clearly identifiable as a small increase in the
slip resistance at approximately 2 mm slip, as shown in Fig. 10(b) and Fig. 10(d), respectively. To explain how
the bolts could slide, Fig. 11 illustrates a possible slip sequence focussing on one of the top bolts as shown in
Fig. 11(a). In the illustrated sequence, the connection slips at the SP15t/SP16 and SP16/SP14t interfaces until
SP14t comes into contact with the bolt shank, as shown in Fig. 11(b). SP16, SP14t and the bolt then slide
together until the bolt shank comes into contact with SP15t, as shown in Fig. 11(c).
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
Andrew William Lacey, Wensu Chen*, Hong Hao*, and Kaiming Bi
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Fig. 11. Illustration of possible slip sequence in the experiments.
Once the tests were completed the specimens were disassembled to examine the faying surfaces and
performance of the locating pins. Plastic deformation of the locating pins was observed for the A and C
specimens, as shown in Fig. 12 for C2. In all the specimens, wear of the plate was observed around the bolt
hole and at the upper SHS flange as shown in Fig. 12(a). The wear of the plates at the upper SHS flange
location was caused by the rotation of the outer hollow sections, i.e., SP10t, due to the bending induced by the
offset loading. Damage of the mill scale layer around the bolt holes was observed for some specimens as shown
in Fig. 13 for C2 and Fig. 14 for B2. This explains the increasing slip resistance observed for some specimens,
for example B2 (Fig. 10d). As the surfaces slid over one another, the mill scale layer was damaged exposing
the underlying steel surface and so increasing the friction resistance.
Fig. 12. Post-test faying surfaces of C2 for (a) SP16 and (b) SP15b.
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
Andrew William Lacey, Wensu Chen*, Hong Hao*, and Kaiming Bi
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Fig. 13. Post-test faying surfaces of C2-SP14t and SP14b showing wear around slotted holes.
Fig. 14. Post-test faying surface of B2-SP15t showing wear around standard round holes.
3. Discussion and evaluation of experimental results
3.1. Accuracy of the slip load
Slip factor testing was completed to establish the slip factor for the G350 steel plate interfaces. The mean slip
factor for the clean mill scale surface was 0.3146, and the standard deviation was 0.02365, based on nine
measurements of the slip load [23]. The 95% confidence interval for the mean slip factor can be given as [27],
1.96 1.96
mm
ss
nn
,
(4)
where µm is the mean slip factor from the nine samples, s is the sample standard deviation, and n is the number
of samples. Following Eq. 4 the mean slip factor can be given as, 0.31 ± 0.015, or 0.31 ± 4.9% expressed as a
percentage of the mean.
The variation of the slip factor was due mainly to variation of the bolt preload and the surface profile. For
further analysis it is desirable to estimate the proportion of the slip factor variation which was due only to the
surface profile. This requires an estimate of the variation of the bolt preload. The bolt preload for the slip factor
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
Andrew William Lacey, Wensu Chen*, Hong Hao*, and Kaiming Bi
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tests was torque controlled based on a manufacturer supplied k-factor (Eq. 1). The mean k-factor for the M16
bolts used for the slip factor tests [23] was 0.136, and the coefficient of variation was 0.044, based on five
assembly tests completed by the manufacturer in accordance with EN 14399-2 [21]. The standard deviation
was therefore 0.0060, and the 95% confidence interval was ± 3.9% of the mean. This gives an indication of
the uncertainty of the preload in the slip factor tests. Given that the slip factor was calculated as a ratio between
the slip load and preload [23], the variation due to the surface profile can be estimated using the confidence
intervals as [28],
22
0.049 0.039 3.0%
(5)
where 0.049 represents the confidence interval for the slip factor, and 0.039 represents the confidence interval
for the preload.
For the M12 bolts used in the present inter-module connection tests, the mean k-factor was 0.119, and the
coefficient of variation was 0.042, based on five assembly tests completed by the manufacturer in accordance
with EN 14399-2 [21]. The 95% confidence interval for the preload in the connection tests is therefore ± 3.7%
of the mean. Combining the variation of the preload with that of the surface profile, the uncertainty of the inter-
module connection slip load is estimated as,
22
0.037 0.030 4.8%
(6)
where 0.037 represents the confidence interval for the preload, and 0.030 represents the confidence interval
for the slip factor.
3.2. Behaviour of locating pins and bolts
The locating pins had little influence on the F-d behaviour in the initial friction/slip stage (Fig. 10a). This was
because the locating pins were not engaged until after the initial slip which allowed the plates to slide into
contact with the locating pins. As a result, the slip resistance for the type A and B specimens is expected to be
the same, except for variation in the surface profile and bolt preload. Therefore, the slip resistance for A1 and
B1, and A2 and B2 may be averaged, giving 95.8 kN and 69.4 kN for the 50 kN and 35 kN preload,
respectively.
The locating pins reduced the slip displacement in the bearing stage. The presence of the locating pins in
combination with the bolts increased the shear resistance. Therefore, while the B specimens showed an increase
in slip approaching shear yield of the bolts, this was not observed for the A specimens. For example, the force-
slip stiffness for B2 (Fig. 10d) starts to reduce once the load approaches approximately 218 kN. This
corresponds well with the estimated shear yield capacity of the four M12 bolts with threads excluded from the
shear plane (224 kN) as per AS4100 [19]. For B1 (Fig. 10c) the reduction in stiffness is not shown as clearly.
This is because the DIC process resulted in less accurate measurements of the slip due to a relatively poorer
quality of the speckle pattern on this specimen. Several inaccurate data points were excluded from Fig. 10(c).
In contrast, the A specimens did not show a significant reduction in stiffness before the maximum force of 250
kN was reached, as shown in Fig. 10(a, b), because the shear resistance was increased by the locating pins.
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
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Fig. 15 shows a bolt from B1 after testing. The bolts had one interface with threads excluded, i.e., SP15/SP16,
and one interface with threads included, i.e., SP16/SP14. Deformation of the bolt is visible at the SP15/SP16
interface and at the SP16/SP14 interface. B1 slipped at the SP16/SP14 interface first causing SP14 to contact
the bolt shank before SP16. This resulted in a bending action in the bolt as the shear load was applied by SP14
and resisted SP15 which was offset by the thickness of SP16 (8 mm). The photo (Fig. 15) shows that the bolt
was approaching, but had not yet exceeded, the shear yield capacity. This confirms that the bolts in the B
specimens were carrying most of the applied shear force. That is, after slip, the applied shear force was resisted
by the bolts, rather than friction between the plates.
Fig. 15. Photo of post-test bolt from B1.
In comparison there was less visible deformation of the bolts in the A specimens after testing due to the
presence of the locating pins. Deformation of the locating pins was observed as shown in Fig. 16 for A2. Local
bearing of the locating pin can be seen due to contact from SP14. Bending of the locating pin was caused by
the bending action generated due to the load applied by SP14 being offset from SP15 by the thickness of SP16
(8 mm). The yielding of the locating pins occurred because the locating pins were engaged before the bolts, as
shown in Fig. 10(a, b). After the locating pins were deformed the bolts were engaged and the applied shear
force was shared between the bolts and locating pins. A similar behaviour was observed for the C specimens,
except that a larger deformation of the locating pins occurred as a result of the increased hole tolerance, as
shown in Fig. 12 for C2. The slip sequence for the C specimens is discussed further in Section 4.3.
Fig. 16. Photo of post-test locating pin from A2.
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
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The slip at the transition into the bearing stage differed between the A and B specimens. For the A specimens
(Fig. 10a, b), the plates came into contact with the locating pins at an average slip of 3.48 mm. Then, at an
average slip of 4.12 mm, the bolt was also in bearing. For the B specimens (Fig. 10c, d) the bearing stage
started when the plates came into contact with the bolts at an average slip of 4.23 mm. Thus, for the A and B
specimens, the bolts were in bearing at an average slip of 4.17 mm and the locating pins were in bearing at a
slip of 3.48 mm. The difference may be explained by the bolts having on average a slightly smaller diameter
than the locating pins. In addition, local deformation of the thread on the bolt shank may have contributed to
the larger slip for the bolts.
3.3. Effect of bolt preload
The bolt preload influenced the F-d behaviour in the friction/slip stage (Fig. 10a), with the slip resistance being
greater for the higher preload. Average slip resistances of 95.8 kN and 69.4 kN were recorded for preloads of
50 kN and 35 kN, respectively. The slip resistance was approximately proportional to the preload, i.e.,
95.8 1.92
50 kN
kN
and
69.4 1.98
35 kN
kN
. The ratio of the slip resistance to the bolt preload was slightly higher for
the smaller preload of 35 kN, suggesting the slip factor was slightly greater. Although increasing the preload
increased the slip resistance, the slip factor decreased slightly due to the increased preload. The decrease in the
slip factor can be explained by a relatively greater flattening of the surface asperities in response to the
increased contact pressure. If, for example, 0.31 is accepted as the slip factor for the 50 kN preload, then a slip
factor of 0.32 may apply for the 35 kN preload. However, the difference in the slip factor was small and may
equally be explained by variation in the surface profile or bolt preload. Therefore, the effect of the preload on
the slip factor was neglected and the slip factor was taken to be a constant value of 0.31 based on the slip factor
testing.
3.4. Hole tolerance
Comparing Fig. 10(a, b) with Fig. 10(e, f), it can be seen that the slotted holes for the C specimens increased
the slip displacement which occurred after the slip resistance was exceeded. Considering the effect on the slip
resistance, the use of slotted holes was expected to increase the contact pressure which would have the effect
of flattening the surface asperities and so reduce the slip resistance [29, 30]. This was observed for the 35 kN
preload for which the slip load reduced from 69.4 kN to 60.2 kN, i.e., 13%. Conversely, for the 50 kN preload
the slip load increased from 95.8 kN to 105 kN, i.e., 9.6%. This difference in behaviour may be explained by
the surface mill scale layer. For example, for the smaller preload of 35 kN the increase in the contact pressure
due to the slotted holes may flatten the surface asperities leading to a reduced slip resistance. However, the
larger preload starts with higher contact pressure, and the additional contact pressure due to the slotted hole
may be enough to damage the mill scale layer exposing the underlying steel thereby increasing the slip
resistance. This explanation is supported by the photos of the post-test faying surfaces which show the
specimens with slotted holes (Fig. 13) had more severe damage to the mill scale layer than the specimens with
standard hole tolerance (Fig. 14).
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3.5. Fabrication and assembly tolerance
The initial slip resistance of the specimens was reduced due to initial gaps between the connection elements.
For engineering design purposes, the reduction in performance which may be expected due to typical
fabrication and assembly tolerances should be considered. Table 3 shows the initial slip resistance (b), the full
connection slip resistance (a), and the ratio between the two (b/a). As a result of the initial gap (Fig. 9a), only
two of the four bolt preloads contributed to the initial slip resistance. Therefore the initial slip resistance was
approximately half that of the full connection slip resistance, to which all four of the bolt preloads contributed.
This sensitivity to the fabrication and assembly tolerance should be considered when designing the inter-
module connections. Although the connection design may not feature a horizontal gap between the columns,
it may be appropriate to consider a small gap to ensure the assumed behaviour is conservative. In the
experiments the largest initial gap was approximately 0.9 mm for the A and B specimens which had standard
round holes (Fig. 10a), and 1.9 mm for the C specimens which had slotted holes (Fig. 10e).
3.6. Comparison with existing connections
To evaluate the shear behaviour of the proposed interlocking connection, a comparison may be made with the
shear behaviour of the existing inter-module connections. Two inter-module connections were selected for
comparison. The first selected connection was studied by Styles et al. [11], who completed numerical
simulations to establish the shear F-d curve. The inter-module connection joined two 300x200x6 RHS columns
vertically by using 370x410x25 mm end plates with two rows of four M24 property class 10.9 bolts. In
comparison, the interlocking inter-module connection specimens joined 75x75x6 SHS columns using 8 mm
thick plate with two tensioned M12 property class 8.8 bolts and two R12 locating pins. The resulting F-d curves
for the previous connection are shown in Fig. 17(a) labelled as SV-FX and SV-FY for loading in the x- and y-
direction, respectively. In this figure, the x-axis shows the slip divided by the hole tolerance. The hole
tolerance is defined as the approximate slip displacement after which the shear force is transferred by bearing
rather than friction. For example, the hole tolerance was 4 mm for the A and B specimens, and 10 mm for the
C specimens. For the connection presented by Styles et al. [11] the hole tolerance was 2 mm. The y-axis shows
the applied force divided by the actual slip resistance of the full connection, i.e., a value of 1 on the y-axis
corresponds to the actual slip resistance.
The second selected connection was studied by Gunawardena [5], who completed experiments and numerical
simulations to establish the shear F-d curve. This existing inter-module connection detail was also a bolted end
plate as shown schematically in Fig. 17(b). It had 150x150x9 SHS columns with 25 mm thick end plates.
Gunawardena [5] considered three variations of the connection. The first, labelled as TG1, had four M12
property class 8.8 bolts with standard 14 mm round bolt holes. The second, TG2, had four M16 bolts with
corresponding 18 mm holes. The third, TG3, also had M16 bolts, but with slotted holes which were 18 mm
wide and 26 mm long. The hole tolerance was 2 mm for TG1 and TG2, and 6 mm for TG3. The main difference
between the second selected connection and the interlocking inter-module connection specimens was the use
of the locating pins for the interlocking connection, and the simplification of the stacked plate arrangement.
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The resulting experimental F-d curves for the previous connection are shown in Fig. 17(b) labelled as TG1,
TG2, and TG3. It can be seen in Fig. 17(a, b) that the proposed interlocking connection specimens gave an
improved initial shear F-d stiffness in comparison with the selected existing inter-module connection details.
Fig. 17. F-d curve for proposed inter-module connection compared with existing inter-module connections studied by
(a) Styles et al. [11] and (b) Gunawardena [5]. (F/Fslip = ratio of applied force to slip resistance, Slip/Tolerance = ratio of
slip to effective bolt hole tolerance)
4. Numerical simulation
Numerical simulations were conducted to support the experimental program and allow further parametric
study. A finite element model of each experimental specimen was developed using ABAQUS version 6.14
[31]. Taking advantage of the symmetry, only one quarter of the specimen was modelled, for example, as
shown in Fig. 18(a) for specimen A. Symmetry boundary conditions were defined in ABAQUS for the x-
direction (XSYMM) and z-direction (ZSYMM), as shown in Fig. 18(b). A multilinear profile was adopted for
the stress strain curve of the steel materials, using the quad linear profile based on regression analysis by Yun
et al. [32]. The elastic modulus was set as 200 GPa and the Poisson’s ratio as 0.25 following AS4100 [19].
The yield and ultimate strengths were determined based on the relevant material specification, as shown in
Table 2.
Fig. 18. (a) ABAQUS numerical model for specimen A, and (b) Typical loading and boundary conditions.
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
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4.1. Interaction and contact property
For the plate interfaces, i.e., SP15/SP16/SP14 an interaction property was defined in ABAQUS using Penalty
friction for the tangential behaviour. Following the slip factor tests the friction coefficient was set as 0.3146
[23], and the elastic slip was set as 0.001 mm [33]. The normal behaviour was defined as Hard Contact with
penalty enforcement. Interaction properties were similarly defined for the other contact areas. The friction
coefficient between the bolt head and plate was taken as 0.05 [34]. The bolt shank to plate contact was taken
to be frictionless [35]. Three steps were defined for the analysis. The contact interactions were established in
the first step. Then, the bolt load was defined in the second step using the applied force method in ABAQUS.
The bolt length was subsequently fixed, and the compression force was applied to the upper bearings in the
third step, as shown in Fig. 18(b). The bottom of the lower bearing was fixed, and the top of the upper bearing
was limited to translation in the y-direction. These boundary conditions reflected the experiments in which
restraint was provided by the universal testing machine compression plates (Fig. 6), with friction developed at
the interface between the compression plates and the bearings.
4.2. Mesh convergence
First order 8-node linear brick, reduced integration elements were used for the mesh. To ensure the mesh
element size was sufficiently small the model was analysed with increasingly smaller mesh size and the
resulting F-d behaviour compared. First, a coarse 4 mm mesh size was used as shown in Fig. 19(a). This was
followed by a general 3 mm mesh with the areas of interest refined to 2 mm (Fig. 19b), and finally with the
area of interest refined to 1 mm (Fig. 19c). The resulting F-d behaviours are shown in Fig. 20. A nominal mesh
size of 2 mm is shown to be fine enough, with little difference in the resulting F-d plot compared with the finer
1 mm mesh. It should be noted that the gap between the locating pin and adjacent plate was set as 3.9 mm in
the numerical simulation. This provided an initial separation of 0.1 mm which was beneficial for the initial
convergence.
Fig. 19. ABAQUS numerical model for specimen A showing nominal mesh sizes (a) 4, (b) 2, and (c) 1 mm.
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
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Fig. 20. Numerical force-slip behaviour of A1 for nominal mesh sizes 4, 2, and 1 mm.
4.3. Numerical calibration
Fig. 21 shows the numerical results as compared with the experimental F-d curves. In the experiments the
effective friction coefficient for the steel plates varied throughout the specimen. The interface with the lower
friction coefficient slipped first, followed by the next lowest in sequence. In comparison, in the numerical
simulations, the same friction coefficient was adopted for all the steel plate interfaces, based on the slip factor
tests. As a result, the slip sequence in the numerical simulations does not necessarily match that from the
experiments.
Fig. 21. Comparison between numerical and experimental F-d curves for the (a) A, (b) B, and (c) C specimens, and (d)
numerical F-d curves for all the specimens.
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
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For example, for B1 the initial slip in the experiment was at the SP14/SP16 interfaces. However, the sliding
interface was constantly changing throughout the slip stage in the experiment. In contrast, in the numerical
simulation the SP14/SP16 interface slipped followed by the SP16/SP15 interface in turn. As a result, the slip
stage for the numerical F-d curve is effectively a horizontal line, with an increase in the force at a slip of 2 mm
as SP14 contacted the bolt shank causing the bolt to start sliding. Other than the different F-d curve in the
friction-slip stage, this difference in slip sequence can change the loading conditions for the bolts in the bearing
stage. For example, with load applied by the SP14 plate and resisted by the SP15 plate there is an 8 mm offset
which results in additional bending in the bolt (Fig. 15). The additional bending deformation is one reason for
the low stiffness in the bearing stage for the experimental result in comparison with the numerical result.
Further, in the experiments, additional deformation was permitted by the deformation of the bolt threads and
the rotation of the bolt shank relative to the nut. The bolt threads were not included in the numerical model,
and the nut was combined with the bolt shank effectively preventing rotation. The numerical stiffness is
therefore greater than the experimental stiffness.
Similarly, for C1 the slip sequence in the numerical simulation differed from the experimental result. In the
experiment the slip occurred at the SP14/SP16 and SP15/SP16 interfaces. With photos at 2 s intervals, and a
loading rate of 0.1 kN/s, it appeared as though the slip occurred at the SP14/SP16 and SP15/SP16 interfaces
simultaneously. This slip continued until SP14 contacted the locating pin. The locating pin then deformed
along with slip between the plates, until SP16 contacted the locating pin, increasing the F-d stiffness. Soon
after, the total slip was enough to engage the bolts in bearing. In the numerical simulation, however, the
SP14/SP16 interface slipped first. After a slip of 7 mm, SP14 and SP16 started to slide along with the bolt.
The slip occurred at the SP16/SP15 interface until SP16 contacted the locating pin. Then, bending of the
locating pins occurred, but the bolts did not come into bearing. These two different slip sequences explain the
difference in the experimental and numerical F-d curves for the C specimens shown in Fig. 21(c).
To match the numerical to the experimental result, the friction coefficient may be varied in the numerical
simulations to ensure the slip sequence is consistent. However, a more meaningful calibration may be achieved
by simply matching the initial stiffness of the force-slip curves. Disregarding the low initial slip resistances
due to gaps, the numerical slip resistance gives a good match to the experimental slip resistance as shown in
Table 4, considering the experimental uncertainty (Section 3.1). For C2 the slip resistance was overestimated
by 16% based on the numerical simulation, compared with the experimental result. This is consistent with the
13% reduction in the slip resistance due to the slotted holes increasing the contact pressure and flattening the
surface asperities (Section 3.4) considering the experimental uncertainty (Section 3.1).
Table 4 Comparison between experimental and numerical slip resistance.
Specimen
A1
A2
B1
B2
C1
C2
Experimental slip resistance, Fslip,exp (kN)
93.8
68.6
97.8
70.2
105.0
60.2
Numerical slip resistance, Fslip,num (kN)
99.9
68.9
102.0
72.2
98.9
70.0
Error
, ,exp ,exp
/
slip num slip slip
F F F
(%)
6.5
0.4
4.3
2.8
-5.8
16.0
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
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5. Proposed F-d model
5.1. OP: Friction/slip
Following the numerical and experimental results, a model is proposed for the shear force-slip behaviour of
the new interlocking inter-module connection as illustrated in Fig. 22. The proposed model differs from the
existing model for inter-module connections [6] in the friction stage OP (Fig. 22). Whereas the existing model
assumes a linear behaviour [6], in the proposed model the initial force-slip behaviour is given by the
exponential function,
( ) 1 exp /F d d
,
(7)
where F is the shear force (kN), d is the slip of the connection (mm) and α and β are parameters which define
the upper limit and initial stiffness, respectively. The exponential function represents the initial stiffness more
accurately than the linear behaviour assumed in the existing model [6]. Eq. 7 was fitted to the calibrated
numerical results for the experimental specimens resulting in a good fit as shown in Fig. 23 for the A (a), B
(b) and C (c) specimens. The exponential model does not capture the increase in the force at a slip of 2 mm as
the bolt starts sliding, resulting in a slightly conservative F-d behaviour which can be seen in Fig. 23(a, b). Fig.
23(d) shows the exponential fit for all the specimens together to allow comparison. As shown, there is little
difference in the slip resistance provided by the specimens A, B, and C, other than due to the differing preload.
It should be noted, however, that the slip factor was not varied for the numerical simulations. For engineering
design, the slip resistance should be reduced where slotted holes are adopted to account for the possible
reduction in the slip factor, as discussed in Section 3.4. A reduction factor of 0.87 is appropriate based on the
present experimental results. This is consistent with the existing design standard AS4100 [19] which specifies
a reduction factor of 0.85 for short slotted holes such as those used in specimen C.
Fig. 22. Proposed force-slip model.
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Fig. 23. Exponential fit to numerical data for (a) A, (b) B, (c) C, and (d) all the specimens.
Following the curve fit for each specimen, the resulting α and β values were examined. The parameter α was
not significantly affected by the presence of the locating pins, or by the bolt hole tolerance. α was affected by
the slip factor and bolt preload, with a larger preload giving a greater value for α, such that α may be estimated
as,
( , ) 6.64
tt
NN
,
(8)
where µ is the slip factor and Nt is the preload (kN). It should be noted that Eq. 8 applies to the full specimen
which incorporated two connections, one on each side. For a single connection with two bolts the value of α
should be halved. Similarly, the parameter β was not significantly affected by the locating pins or the bolt hole
tolerance, but the slip factor and preload did have an effect which may be estimated as,
( , ) 0.149 . 0.0657
473 /
t
tN
N mm mm
kN mm
.
(9)
5.2. PQ: Bearing
The slip displacement at the transition to the bearing stage, i.e., dP in Fig. 22, may be taken as the effective bolt
hole tolerance. As discussed in Section 0, the bearing stage may begin at a slightly smaller or larger slip
displacement depending on the geometry. However, the difference in slip displacement is relatively small, and
the bolt hole tolerance gives a reasonable estimate of the average behaviour. The stiffness in the bearing stage
can be estimated following the method of Konkong et al. [36] as outlined by Lacey et al. [6]. As shown in Fig.
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
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24, the use of three plates can result in an offset bearing arrangement for the bolts, causing a reduction in the
effective stiffness for the bolts, which must be accounted for in design. The effective stiffness for the locating
pins may be estimated by following a similar approach using a cantilever beam model as shown in Fig. 25.
Fig. 24. Illustration of bolt bending due to offset shear loading.
Fig. 25. Illustration of locating pin bending due to offset shear loading.
5.3. QR: Failure
Following the existing model [6] the failure load can be estimated by summing the shear capacities of the bolts
and interlocking elements as appropriate. The slip displacement at the transition to the failure stage can then
be calculated based on the estimated failure load, and the bearing stiffness in the previous stage PQ.
Consideration should be given to the combination of bending and shear, as illustrated in Fig. 24 and Fig. 25.
The combined bending and shear actions may be considered by the equation [37],
**
1
MV
MV
,
(10)
where M* and V* are the applied moment and shear force, and M and V are the plastic moment and shear
yield capacity, respectively.
New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
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6. Conclusions
A new interlocking inter-module connection was proposed for modular steel buildings. The shear force-slip
(F-d) behaviour was investigated by experimental tests and numerical simulations. The main findings are
summarised as follows.
1. The proposed interlocking inter-module connection offers a simplification of detailing with the ability
to connect eight modules. The slip resistance of the inter-module connection depends primarily on the
slip factor and bolt preload, while the locating pins provide additional shear resistance after the initial
slip. The hole tolerance had a small effect on the slip resistance, and the experimental results support
the use of a reduction factor of 0.85 for short slotted holes in comparison with standard round holes.
2. The proposed interlocking inter-module connection offers an improved initial shear F-d stiffness in
comparison with the selected existing inter-module connection details [5, 11].
3. An empirical model was proposed for the shear force-slip behaviour based on the calibrated numerical
results. The model is made up of three stages: friction/slip, bearing, and failure. For the friction/slip
stage, an exponential formula was proposed which accurately represents the initial stiffness. For the
bearing and failure stages, linear functions may be adopted, similar to the existing force-slip model for
inter-module connections [6].
7. Acknowledgements
The authors acknowledge the financial support from the Australian Government through the Australian
Research Council (ARC). The first author acknowledges the support received through the Australian
Government Research Training Program Scholarship. The authors acknowledge the support of Dr. Arne
Bredin, Mr. Rob Walker, and Mr. Mick Elliss in the civil engineering laboratory at Curtin University.
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New interlocking inter-module connection for modular steel buildings: Experimental and numerical studies
Andrew William Lacey, Wensu Chen*, Hong Hao*, and Kaiming Bi
10.1016/j.engstruct.2019.109465
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