Lightweight steel–concrete–steel sandwich composite shell subject to punching shear

Ocean Engineering 102 (2015) 146–161

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Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng

Lightweight steel–concrete–steel sandwich composite shell subject to punching shear Zhen-Yu Huang a, Jun-Yan Wang b,n, J.Y. Richard Liew a, Peter William Marshall a a b

Department of Civil and Environmental Engineering, National University of Singapore, Blk E1A-07-03, 1 Engineering Drive 2, Singapore 117576, Singapore Key Laboratory of Advanced Civil Engineering Materials, Tongji University, Ministry of Education, Shanghai 201804, China

art ic l e i nf o

a b s t r a c t

Article history: Received 10 July 2014 Accepted 24 April 2015 Available online 27 May 2015

The development of Arctic oil and gas fields requires high strength structures that can resist critical loads in extreme environment. A novel conical caisson structure constructed by lightweight steel–concrete– steel (SCS) sandwich shell is proposed for withstanding ice pressure imposed thereon by impinging sheet ice in Arctic region. This paper mainly investigates the ultimate strength behaviour of SCS sandwich shell experimentally and analytically. Two pilot quasi-static tests on the lightweight SCS sandwich composite shells subject to patch loading are carried out. The failure mode of composite shell is punching shear. Tests show that the punching shear resistance depends on the control perimeter of punched concrete frustum and shear connectors. The membrane action of the outer steel plates provides post-hardening strength. On the basis of the experimental failure mechanism, an analytical model is developed to explain the force transfer mechanism and predict the punching shear resistance of SCS sandwich composite shell. The verification of the model shows that the predictions are in good agreement with the test results. It is also shown that the SCS sandwich shell, in accord with the ISO ice load design, is capable of resisting the localised contact and punching loads. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Arctic caisson Ice-resisting wall Punching shear Steel–concrete–steel Sandwich structure Ultra lightweight cement composite

1. Introduction The Arctic continental shelf is believed to be the area with the highest unexplored potential for oil and gas as well as for unconventional hydrocarbon resources such as gas hydrates. World demand for oil is set to increase 37% by 2030, according to the US-based Energy Information Administration’s (EIA) annual report (B.B.C. News, 2006). Moreover, US geological survey showed that 30% of the world’s undiscovered gas and 13% undisclosed oil were found in the Arctic. The growing demand for oil and gas today has reawakened the interest in oil and gas exploration and development in this area. However, one challenge is that waters in this area are covered with vast area of ice. An offshore platform in the Arctic has to be able to withstand the forces imposed by moving ice. The ice will sometimes be broken and sometimes continuous, and may include pressure ridges 30 m or thicker. The forces imposed by that ice will be large, 100 MN or more, and can be greater than those generated by waves on platforms in open water. Therefore, high resistance structure with high ductility is required. Although a great number of Arctic structures have been

n

Corresponding author. Tel.: þ 65 9175 2275; fax: þ65 6779 1635. E-mail address: [email protected] (J.-Y. Wang).

http://dx.doi.org/10.1016/j.oceaneng.2015.04.054 0029-8018/& 2015 Elsevier Ltd. All rights reserved.

proposed and in operation, year-round operations in extremely harsh ice environment still ask for more capable structures. Hence, it suggests new ideas as alternatives for existing design concepts to produce an economical yet feasible solution that allows continual year-round operation in the Arctic region. The great majority of stationary platforms in the south Arctic are fabricated from steel, and held to the seabed by long piles. A few are concrete, often selected for reasons that are partly political, and they are held in position by a combination of weight and some lateral resistance provided by a skirt or by short piles. A very few are steel gravity platforms. Some researchers (McLean, 1987; McLean et al., 1990; Sabnis and Shadid, 1992; Ellis and Macgregor, 1993; Birdy et al., 1985) investigated the punching shear behaviour of RC shell subject to local loads. It offers vast information for early design of concrete shell structures. Thanks to the high performance of steel–concrete composite structures, steel–concrete–steel (SCS) sandwich composite structure that takes advantages of both concrete compression performance and steel tension performance is a good alternative in the civil and offshore domain due to its excellent cost-strength performance (Marshall et al., 2010; Liew and Wang, 2011). The SCS sandwich composite exhibits significant structural and economic advantages over the conventional reinforced concrete structures in terms of higher flexural stiffness and high energy

Z.-Y. Huang et al. / Ocean Engineering 102 (2015) 146–161

Nomenclature AN Ase Av αi Cc ds Es Ec f ut fu Fc Fu Fp Ft

hc hc

projected area of cone surface to the free concrete surface cross-sectional area of shear stud punching shear area of steel plate angle between stud axis and horizontal axis 0.15 for LWC, 0.18 for NWC diameter of shear stud Young’s modulus of steel Young’s modulus of concrete ultimate strength of headed shear stud ultimate strength of steel plate concrete breakout resistance stud tension failure resistance plate punching shear resistance tension resistance of shear stud embedded in concrete which equals to the minimum value among F c , F u and Fp effective height of concrete core height of concrete core

absorption capacity to withstand extreme environmental and accidental loads. The external steel plates may serve as a permanent formwork during concreting, promoting construction efficiency and reducing the site handling costs and time. The waterproof feature inherently provided by external steel plates reduces surface area that needs expensive corrosive protection and makes it easy for inspection and maintenance. As a result, SCS sandwich composite structures can be adopted as heavy duty and protective layers such as ship hulls, ice-resisting walls, tunnels and nuclear power station walls that require resistance against extreme loads. At 1980s, researchers and applications of steel–concrete–steel composite structures were hot topics as the economic growth at that time drove a high demand of new ideas of structural application. Researches on development of composite iceresisting wall structures for Arctic offshore drilling/production structures were examined by scholars at University of Alberta, contributing much fundamental information to design and application (Kennedy Stephen, 1987; O’Flynn, 1987; Zimmerman, 1993). For decades, many researchers have investigated static and dynamic behaviour of steel–composite structure for building and offshore constructions. Solomon et al. (1976) appraised the SCS sandwich structure as a potential structural form to reduce selfweight of the roadway slab on composite bridge. Tomlinson et al. (1990) proposed double skin SCS with shear studs for immersed tube tunnel application under Conwy River. In 1990s, Steel Construction Institute (1994, 1997) issued two design guidelines on the application of SCS sandwich construction. In these applications, the shear transfer between steel skin and concrete relies on the overlapped headed shear studs. Shukry and Goode (1990) carried out the punching tests on circular composite shells for the first time. In order to enhance the composite action of SCS sandwich structure, Liew and Sohel (2009) proposed a novel J-hook shear connector and responsive push-out and pull-out tests showed that the connector possessed high resistance with feasible fabrication comparing to normal headed shear stud connectors (Yan et al., 2014a, 2014b). Later, a couple of novel shear connectors have been proposed by Sohel et al. (2012) for the SCS composite structures to enhance the interfacial bond between the face plate and the internal core. Furthermore, static and impact performances of

hef kf kc n ncp η1 P1 P2 γc s ts τf ;FRC u1 U V vlRd;c vlRd;cs ρ

147

embedded height of shear stud 0:29pisffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi usedffi for synthetic fibres 1 þ 200=hc r 2:0 ratio of Es =Ec amount of the shear studs linking the shear cracks 0:4 þ 0:6ρ=2200 r 1:0 first peak load second peak load partial safety factor for concrete stud spacing thickness of plate 4:23V f ; V f is the percentage of fibre volume faction control perimeter of punching concrete control perimeter of punching plate total punching shear resistance punching shear resistance per unit area of a lightweight concrete slab punching shear resistance per unit area of concrete with shear reinforcement density of concrete (kg/m3)

SCS sandwich beam and plate were evaluated experimentally (Liew et al., 2009; Liew and Sohel, 2010; Sohel and Liew, 2011). Recent tests also showed that the SCS sandwich structure exhibited superior impact performance (Sohel and Liew, 2014). Finite element analysis using ABAQUS has been conducted, with wellagree the experimental results (Huang et al., 2013a, 2013b, 2015). Most of the previous studies focused on the flexural or shear behaviour of flat composite beams and panels. However, very limited works have been done on SCS sandwich shells under larger patch loads and impact loads. SCS sandwich shell is a new form of structure, which may have a single or double curvature. Compared to the flat panel, it has advantages such as longer span between web frames and simpler internal structure. Non-hydrostatic loading creates shell bending and inter-layer shear stresses, which depend on the concrete-to-steel bond. This is a bigger issue than that for flat panel, which must develop shell bending and bond shear for all cases. The researches on ultimate strength behaviour of SCS sandwich shells is scarce. As the force transfer mechanism and failure modes become rather critical in thick SCS sandwich shell members, experimental and analytical researches become essential. This paper first proposes a concept of conical structure with external SCS sandwich shells filled with ultra-lightweight cement composite for Arctic platform structures. Quasi-static tests are then carried out on two SCS sandwich shells under patch loading. On the basic of the experimental results in this paper and those from the published literature, a modified Eurocode 2 model is developed to explain the force transfer mechanism and shear resisting mechanism and to predict the punching shear resistance of SCS sandwich shells.

2. Development of sandwich caisson system for Arctic region 2.1. Structural form For Arctic offshore application, the structures are constantly subject to high pressure loading from huge mass of moving ice driven by wind and sea currents, which may cause catastrophic damage to the structure. The design and feasibility of Arctic offshore structure is often dominated by ice environment.

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Consequently, the structures require high impact resistance, high ductility and extended fatigue lifespan in a mostly below sub-zero temperature environment. With conventional reinforced concrete (RC) structure plus being heavier to transport, it also leads to large amounts of congested reinforcement in order to withstand high magnitude ice pressure. Due to seepage of sea water, corrosion of reinforcement in RC structures would be a dominating factor as that weakens durability of concrete, which may increase the maintenance cost. The optimal form of an Arctic structure is widely debated. A vertical-sided structure has a simple shape. Wind and current drive ice against the structure, and the ice crushes close to the structure. There are significant scale effects (Dempsey et al., 2001; Palmer and Croasdale, 2012). The broken ice fragments move around the structure and are carried by downstream. There are some offshore structures with vertical sides, such as the Nordstromsgrund lighthouse in the Baltic, which was instrumented and has been the object of much research, though it needs to be kept in mind that the northern Baltic is much less saline than the oceans and that its ice has different properties. Another alternative is a structure with sloping sides, either upward-sloping or downwardsloping, typically at 501 to the horizontal. When the slope is upward, advancing ice is lifted and bent, and it breaks in front of the slope or on it. This sloping option has been used in several offshore structures, among them the Confederation Bridge in Canada, platforms in the Bohai Sea, and ice barriers in the northern Caspian Sea (Palmer and Croasdale, 2012). Composite steel– concrete structures use the best qualities of both materials. They have been known and used for a long time, and there have been many books and codes (Johnson, 2004; Johnson and Anderson, 1993; BS EN 1992-1-1, 2004). Most of the applications are to slabs and columns, but they can also be three-dimensional shell structures. One important issue is that if composite action is to be achieved, in conditions other than pure membrane stress, shear must be transmitted across the interface between the steel and the concrete. Much attention has been given to the design of shear connectors (Johnson, 2004; Yan et al., 2014b). Bringing these ideas together suggests one of the possible configurations for the structure illustrated schematically in Fig. 1. A composite cone is made up of an outer steel cone, a concrete infilled, and an inner steel cone, with shear connectors on the inner faces. The concept is to build the steel structure empty of concrete, to launch and tow the structure to site, and then to ballast it to the seabed and fill the shell with concrete. The concept was proposed in an earlier paper (Marshall et al., 2012) shown in Fig. 1(a), which included the results of tests on SCS cylindrical barrel vaults under concentrated loads. The research has now been extended by further tests on segments of cylindrical shells. The scheme will be indicated in the following sections. SCS sandwich shell with a single curvature is adopted as the

slope upward/sideward to break the ice

ice-resisting wall to withstand the ice loading. Because, it is observed that sloping structures would encounter ice impact forces due to that the collided ice sheet would ride up the slope and fail in flexural bending rather than crushing as that occurred to a vertically sided structures. In this way, ice pressure will be alleviated and most parts of the structure are under compression and possess high resistance due to the arch action. The natural geometry also helps to optimize and improve the composite action. On the other hand, for weight sensitive marine and offshore structures, infill core material should be optimized to process both the low density and enough strength. Ultra lightweight cementitious composite (ULCC) has been developed by Wang et al. (2013) for the proposed SCS sandwich shells. SCS sandwich shells are particularly well suited for uniform external pressure loading, e.g. hydrostatic. The external pressure and hoop stress hold the various layers of the sandwich together. Modular construction with rapid installation can be achieved, reducing the fabrication cost compared to reinforced concrete structures. The typical configurations for such SCS sandwich shell has two 30 mm thick steel plates of 355 MPa yield strength and 500 mm thick concrete core of 30–60 MPa compressive strength. The cylindrical shell segment has 5 m span with 10 m length along axis with rise-tospan ratio of 0.21 based on geometric design. (The dimensions are of course exploratory, and this is far from an optimized detailed design). 2.2. Fabrication and installation A steel–concrete–steel platform can be constructed by fabricating two concentric steel shells, cylindrical at the bottom and conical towards the top. A cone has straight generators, and therefore its surface is developable and has zero Gaussian curvature. It can be fabricated from segments formed from a flat plate by inextensional bending. Structurally, it might be preferable to use a surface with positive Gaussian curvature, as is done for domes and parts of the bows of ship, but in this instance it would complicate fabrication. The shells are constructed onshore in the south, where they benefit from lower costs, existing construction yards, and the ability to construct all year round. The platform is buoyant, and can be towed to site. Shear connectors can be welded to each flat plate after roll forming but before it is assembled to make a panel of the cone, which facilitates the use of automatic welding. That applies whether the connectors are simple studs or J-hooks (Liew and Sohel, 2009). Once arrived, it can be ballasted down until it grounds on the seabed, and the space between the two shells is then filled with ultra-lightweight high strength cement composite grout. This will benefit the transportation and installation of pre-filled structures in the Arctic region. These development works are necessary to form a robust and safe structure which is strong enough to resist ice forces in Arctic.

topside platform ice-resisting cone

iceberg bottom caisson

Fig. 1. A possible design of Arctic platform with SCS sandwich shell. (a) Arctic caisson structure (Huang et al., 2013a, 2013b), (b) Arctic platform.

Z.-Y. Huang et al. / Ocean Engineering 102 (2015) 146–161

3. Experimental programme

149

Table 2 Mechanical properties of ULCC.

3.1. Materials

Density (kg/m3)

3.1.2. Steel skins and shear connectors For fabrication of specimens, mild steel plate S275 was used for sandwich face plates. The Young’s modulus Es , poisson ratio νs , yield strength f y and ultimate strength f u were obtained from Table 1 Mix proportion of ULCC (kg/m3). Water

Cement

Silica fume

Cenosphere

SRA

SP

Fiber

245.6

705.2

61.3

318.6

19.1

5.0

6.5

1361 (5) 56.10 (1.47)

Peak strain (10-3)

Elastic modulus (GPa)

Poisson ratio

Splitting tensile strength (MPa)

4.45 (0.22)

14.30 (0.04)

0.247 (0.04)

5.4 (0.58)

(Note: the number in the parentheses means the standard deviation).

70

Axial stress (MPa)

3.1.1. Core material The lightweight SCS sandwich shells apply ULCC as the core material infilled between the inner and outer plates. The ULCC is made of water, cement, silica fume, cenospheres, chemical admixtures and polyvinyl alcohol (PVA) fibers. ASTM Type I Portland cement and silica fume were used. The cenospheres in use had a particle density of 870 kg/m3 and most of the particles had sizes from 10 to 300 μm. A polycarboxylate based superplasticizer was used to obtain comparable flow around 200 mm according to flow table test (BS EN 1015-3-1999). Shrinkage reducing admixture was used to reduce the air void content and shrinkage of ULCC. PVA fibers with length of 6 mm and diameter of 28 mm were added at a dosage of 0.5% by volume to increase the ductility and strength of the ULCC. The mix proportion of ULCC is given in Table 1. The ULCC was mixed by using a concrete pan mixer. The ULCC is a highly workable material similar to the cement grout. It is suitable for pumping and grouting in construction of the SCS sandwich shell, in spite of numerous shear connectors in between of the two steel plates. The workability of fresh ULCC was characterized by the flow value tested according to BS EN 1015-3-1999 and the flow value tested was 200 mm. Besides, the use of ULCC, for example, the type with density of 1400 kg/m3 and strength of 60 MPa, can significantly reduce the self-weight by 40%, compared with normal C50 concrete with density of 2400 kg/m3. Cylinder specimens with diameter of 100 mm and length of 200 mm were prepared to measure the compressive stress–strain curve and splitting strength of ULCC at 28-day according to ASTM C39/ 39M-09 and ASTM C496/C496M-11, respectively. For tests of compressive stress–strain curve, a compressometer, composed of four linear variable displacement transducers (LDVTs) and supporting assembly, were mounted on the lower platen to measure the platen-to-platen displacement of the specimens. Moreover, four TML strain gauges of type PFL-30-11 were attached (two in vertical direction and two in horizontal direction) diametrically opposed onto the sample. The experiment was performed using a displacement control method of 0.5 mm/min velocity. The loading rate was applied continuously without shock loads. Loads and displacements were measured continuously by data collection computer system. Finally, the compressive stress strain curve of ULCC was composed of a prepeak region monitored by the strain gauge to avoid the end effect of the specimen and a post-peak region monitored by the LVDTs when the strain gauges fractured together with the specimen. Detailed mechanical properties of ULCC are listed in Table 2 and compressive stress strain curves of three cylinder specimens are shown in Fig. 2. The ULCC used in this study has a density of 1361 kg/ m3 and 28-day cylinder strength of 56.1 MPa. Optical microscope image of ULCC is shown in Fig. 3. The hollow cenospheres homogeneously distribute in the cement paste matrix, which are the key component of ULCC to achieve the low density and high strength.

Cylinder strength (MPa)

60

Specimen1

50

Specimen2

40

Specimen3

30 20 10 0 0.000

0.004

0.008

0.012

0.016

0.020

-3

Axial strain (10 ) Fig. 2. Compressive stress–strain curves of ULCC.

Fig. 3. Optical microscope image of ULCC.

tensile testing of steel coupon samples. The standard coupon test for the steel follows the procedure outlined in ASTM E8/E8M-13a to determine the uniaxial stress–strain curves, as shown in Fig. 4. Conventional Nelson headed shear studs were used as the shear connector at the steel and concrete interface to achieve the composite action. The tensile properties of the connectors were determined by tensile tests on shear studs which were clamped in the universal material testing servo machine. The detailed mechanical properties of mild steel plate and shear stud are also given in Table 3. 3.2. Test specimens The experimental programme comprises two isolated sandwich shells which are 1/4 scaled models of the arched ice-resisting elements. The clear span (L) of the specimens was 1250 mm. Based on the scaled specimen dimension which is in the range of current proposed design, span-to-depth ratio (L/hc) ratio was selected to be 15.6. Steel plate thickness was ts ¼4 mm and connector spacing

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(s) was 110 mm in the specimen design. Previous parametric study (Huang et al., 2013a, 2013b) showed that rise to span (r/L) ratio of 0.21 was an optimal value which can achieve higher punching shear strength and structural stiffness. For comparison, two r/L ratios 0.1 and 0.21 were considered in this paper. Patch loading simulating the high pressure zone from ice loads (Palmer and Croasdale, 2012) was considered for the tests. Table 4 lists details of the test specimens, in which “SCSS” denotes the steel–concrete– steel sandwich shell. For each specimen, there are two curved steel plates, to which are attached overlapping steel stud shear connects. The space between the plates is filled with concrete. The test shells carried end plates, which rest on foundations that prevent outward movement. Fig. 5 illustrates the typical sandwich shell. For casting, the specimens were set into place and secured against vibration by wooden mould. Silicone sealant was applied at the edges to prevent leakage when casting. All the specimens

Stress σ (MPa)

500 400 300

t=4mm-1 t=4mm-2 t=4mm-3

200

were cast in house. Concrete cylinders were also cast on the day the sandwich shells were made. ULCC was poured sideways and the test samples were naturally cured in the indoor climate of the lab. Fig. 6(a) and (b) stand for the pictures of specimens before and after casting. The sandwich shells were tested at the 28th day after curing.

3.3. Test procedure and instrumentation 3.3.1. Test set-up A maximum capacity of 10 MN actuator was used to conduct the tests. Two special designed triangle supports were installed on the rigid beam base through high strength bolt connection and welding. The specimens were set into the triangle supports through the bolt connection, followed by using the high strength grout to infill the reserved gap. Hence, the boundary conditions were fixed-fixed end supported. The thrust force was balanced by the horizontally restricted beams through high strength bolts. Fig. 7(a) illustrates the specimen, support and test set-up for the test. The specimens were loaded laterally by the actuator in displacement controlled mode. Due to the curvature of the specimens, thin steel loading plates were attached to the arch tip of the specimens to ensure the uniform load distribution. The actuator applied a lateral load with low displacement rate of 0.1 mm/min.

100 0 0

100000

200000

300000

Strain (με) Fig. 4. Stress-strain curve of mild steel plate.

Table 3 Mechanical properties of steel plate and headed shear stud. Item

Es (GPa)

f y (MPa)

f u (MPa)

Poisson ratio νs

Mild steel plate Headed shear stud

200 225

304 524

460 584

0.3

Table 4 Details of test specimens. d  hs @ s (mm)

Specimen ts hc L W L/hc (mm) (mm) (mm) (mm) ratio

r/L

SCSS-1 SCSS-2

0.1 27.5 13  50@110 56.1 0.21 27.5 13  50@110 56.1

4 4

80 80

1250 1250

1250 1250

15.6 15.6

s/ts

fck (MPa)

t

s

3.3.2. Instrumentation and test procedure Linear variable displacement transducer (LVDT) and strain gauges were installed to record the displacement and strain at each time interval during the test. Fig. 7(b) sketches a picture of sandwich shell with LVDTs attached to different locations along the inner and outer plates of the shell to record the global displacement during the test. Eleven LVDTs were placed along the longitudinal centreline and width centreline of inner steel face while seven were placed on the outer steel face, as numbered in Fig. 8. Another two were placed horizontally on the edge of both support ends to capture the movement of the supports. Twenty strain gauges, comprising ten strain-rosettes distributed quarterly along the inner and outer plate, and the other ten post-yield strain gauges attached to the points of the steel face plates, monitored the deformations in each specimen and measured the strain values at each time interval during the test. The data acquisition system recorded signals from the load cell and LVDTs as unit mm and collected the strain data via a strain bridge head as micro strains. The sampling rate in test was 0.1 mm/ min and the experimental data were recorded at a time interval of 2 s, resulting in a detailed deflection of the test process. When all the test set-up was ready, a preload testing loading up to 10% of calculated ultimate load was performed for a few cycles with checking on the instrumentations and the data acquisition system.

Side plate

top plate

d concrete

Side plate r

shear stud hc

bottom plate Side plate

L

FRONT VIEW

3D VIEW

Fig. 5. Typical sandwich shell with overlapped shear studs. (L ¼ 1250 mm, s¼ 110 mm, ts ¼ 4 mm, hc ¼ 80 mm, d¼ 13 mm).

Z.-Y. Huang et al. / Ocean Engineering 102 (2015) 146–161

151

SCSS-1 SCSS-2

SCSS-2 Shear studs Sandwich shell

SCSS-1

Fig. 6. Test specimens before (a) and after casting (b).

10MN actuator

spreader column

loading roller sandwich shell

high strength grout composite triangle support bolt

bolt

bolt

composite triangle support bolt

welding

welding

floor beam

1000-Ton Instron Machine

Transducers SCS shell

Data logger PC monitor

Triangle Support

Floor beams Fig. 7. Specimen, instrumentations and test set-up. (a) Schematic diagram of the test set-up. (b) Picture of specimen in the testing.

4. Experimental results and discussion 4.1. General observations The shells were subject to patch loading until they failed. The inside cracking of concrete core could not be observed during the test due to the presence of outer and inner steel plates. However, some vertical cracks were observed at the two edges of the sandwich shell, shown in Fig. 9. A popping sound was heard when

the maximum load was reached and punching failure occurred in the concrete core. In the post-yield region, a loud noise was also detected due to pull-out failure of shear studs. In general, the behaviour of specimen can be identified from the load–deflection curve. As the mid-span deflection increased, the applied load increased linearly to the first peak load followed by unloading. It is because a local punching-shear failure occurs within the concrete core around the loaded perimeter of the shell, as shown in Fig. 10(a) and (b). After that, the load increased again to the second

152

Z.-Y. Huang et al. / Ocean Engineering 102 (2015) 146–161

2 3 1

Rosette Linear strain gauge

T15

100

100

OUTER

313

300

313

T13 R8

LVDT IDT Infrared Displacement Transducer

75

50

50

L8

OUTER

R10

L9

260

330

313 50

T12 L11

R6

R7

L10

T0

313

T11 T17

T18 313

313

Loading area

T14

R9 313 50

T16

50

50

50

INNER

300

L4

313

65

L7

T6 313

300

313

INNER T4

L6

R5

L5

313

L1

R1-1~3

R2

R3

313

275

L2

IDT

T2

T3

313

313

L3

313

T5

R4 50

300

270

313

T19 60

T7

L

50

L

Fig. 8. Layout of the LVDTs and strain gauges. (a) SCSS-1. (b) SCSS-2.

peak load associated with large deflection. However, the second peak load was not found to excess the first peak load. Finally, the outer plate was punched to fracture failure (Fig. 10(a) and (b)). After failure, an indentation which located on the outer plate was

observed while a larger convex was on the inner steel face plate, as shown in Fig. 10(c) and (d). Plate fracture in inner plate along with two rows of the shear connectors was also observed, as shown in Fig. 10(d). It is due to the excessive downward defection driven by

Z.-Y. Huang et al. / Ocean Engineering 102 (2015) 146–161

153

Fig. 9. Vertical cracking of sandwich shells before the first peak loads. (a) SCSS-1. (b) SCSS-2.

the failure concrete. Overall, the first peak strength of SCS sandwich shell was determined by the punching behaviour of the concrete core while the second peak strength was governed by the fracture strength of either outer plate or inner plate which was smaller. 4.2. Failure mechanism At reaching the first peak load, a punched concrete frustum was formed in the middle arch strip. In that case, the middle arch strip lost the load carrying capacity so that the load dropped. However, benefiting from the tension membrane effect of the outer steel plate, the load may be transferred to the neighbour width strip and arch strip through the outer steel plate. Because the shell was two-edges fixed, the load applied to the structures will be finally transferred to the support through the undamaged arch strip of the composite shell. The load–deflection curve exhibits a strength hardening as highlighted in Fig. 11. In this case, the strength of the shell will be governed by the punching shear strength of the outer steel plate or bending moment capacity of the undamaged arch strip in the shell section. 4.3. Load deflection behaviour and observations The load–deflection curves recorded by transducers of the specimens are plotted in Fig. 11. From the test results, the general load–deflection behaviour of sandwich shells under patch loading is demonstrated in Fig. 12. The two shells followed a similar pattern that the load–defection curves exhibit two peak loads. The curve reached the first peak strength followed by unloading, and then with hardening until ultimate failure. In the first stage before reaching the first peak load, the load increased linearly with some tension cracking in the concrete core which was expected at

stage OA. In the second stage, the load seemed to be rapidly reduced after the first peak load, as shown at stage AB. This reduction indicated a punching failure of the concrete core. A punched concrete frustum of concrete was developed in this stage. It should be noted that because of the large loading area, the concrete punching region may be non-uniform. This non-uniform stress developing around the loaded perimeter of steel face plates tended to delay the punching of concrete core or even led to a presence of oscillation loading, seen at stage AA0 in Fig. 12. After that, the load increased again due to the tension membrane action of the outer steel plates, at stage BC. At a deflection level of around 30–50 mm, punching fracture of steel face plate associated with local buckling of the outer and inner plate or spalling of concrete in the mid-span led to the ultimate failure of the shell, as shown in Fig. 10. Table 5 summarises the two peak loads with corresponding deflection and the failure mode for each sandwich shell. 4.4. Load strain characteristics The strains of the steel face plates were measured at different locations by three-directional strain gauges-rosettes or onedirectional linear strain gauges. The measured locations are shown in Fig. 8 for SCSS-1 and SCSS-2. Tables 6 and 7 list the strain level of representative locations in the sandwich shells when the load climbed up to the first peak value and second peak value, respectively. It was found that, before reaching the first peak load, the strain value at most of the critical locations in the steel face plates did not yield. This unveiled that the steel plates contribute not much to the first peak strength. The concrete would be out of work after it was punched through. The stress was redistributed to develop another critical failure perimeter through membrane effect of outer face plate. The force may be transferred to the outer plates which are subject to

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local convex

local concave

Punching fracture fracture

local concave local convex

Punching fracture fracture

Post buckling

Local convex

SCSS-1

Plate punching fracture Punching belt Local convex

Fig. 10. Failure characteristics of sandwich shells. (a) Failure mode of SCSS-1. (b) Failure mode of SCSS-2. (c) Post buckling of plates. (d) Punching fracture of inner plate.

tension. Fig. 13, Tables 6 and 7 shows the strain development of the selected region of the shell. The strain level of the outer plates was found to be beyond the yield strain as observed at selected location R7-1, R8-3, L9, L10, L11, R9-2 and R10-2 (see Fig. 13(b)) in SCSS-1 and at location L6, R7-1, R8-1, R8-3, R9-2, R9-3, R10-2 and R10-3 in SCSS-2 (see Fig. 13(d)). This indicated the shell could

sustain the load by the tension membrane action of outer plate associated with large deflection. It is also found that the inner plate experiences large strain value at strength hardening stage, see locations L3, R4-2 in SCSS-1 (Fig. 13(a)) and location R5-1 in SCSS-2 (Fig. 13(c)). It is due to the downward deflection driven by the failure concrete.

Z.-Y. Huang et al. / Ocean Engineering 102 (2015) 146–161

reinforcement as

1600 1400

SCSS-1 SCSS-2

concrete punching

1200

Load P (kN)

155

1000

fracture

800

membrane action

600 400 200 0 0

10

20

30

40

50

60

70

80

90

Displacement δ (mm) Fig. 11. Load deflection curves of sandwich shells.

V ¼ vRd;cs u1 d

ð1Þ

d 1 vRd;cs ¼ 0:75vRd;c þ 1:5 Asw f ywd sin a s u1 d

ð2Þ

  vRd;c ¼ C lRd;c kη1 ð100ρ1 f lck Þ1=3 þ k2 σ cp Z vmin þk1 σ cp

ð3Þ

where u1 is the basic control perimeter calculated based on Clause 6.4.1 in Eurocode 2; d is the effective height of concrete; Asw and f ywd are cross sectional area and yield strength of shear reinforcement; C lRd;c ¼ 0:15=γ c for ffi LWC, γ c is partial safety factor for pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi concrete; k ¼ 1 þ 200=hc r 2:0; η1 ¼ 0:4 þ0:6ρ=2200 r 1:0 in which ρ is the density of concrete (kg/m3). To evaluate the feasibility of Eurocode 2 method, this paper collects another 27 SCS sandwich shell tests under punching load. Tables 8 and 9 list the details of test specimens done by Shukry and Goode (1990), Marshall et al. (2012) and Yan (2012). Circular arch sandwich shells with or without shear connector were subject to punching load as similar to that of the test in this paper. As shown in Tables 10 and 11, the calculation and comparison reveals that the formulae suggested by Eurocode 2 for predicting the punching shear resistance of RC slabs was applied to the composite shells. The punching resistance was overpredicted by Eurocode 2 for most composite shells. The mean value of test-to-prediction ratios are 0.69 and 0.64 with standard deviations of 0.14 and 0.20 respectively. Figs. 15 and 16 also show the Eurocode 2 prediction scatters from the test results, by overprediction of about 35%. As a result, a more accurate formulae should be created for prediction of the punching shear resistance of SCS sandwich shells. 5.2. Proposed formulae for punching shear resistance

Fig. 12. Stages of behaviour of SCS shell under patch loading.

5. Analytical prediction Two modes of failure, namely punching shear of concrete core and punching fracture of steel face plates are captured from the tests. Fig. 14 illustrates the two-stage failure mechanism of an SCS sandwich shell. Fig. 14(a) shows the formation of a typical punched frustum in concrete core which is developed at reaching the first load. Fig. 14(b) shows the force transfer mechanism after concrete punched through. The outer steel plate is subject to tension membrane action. Ultimate failure load will be governed by the plate fracture either in outer or inner plate.

5.1. Punching resistance by Eurocode 2 The punching resistance of the concrete core could be calculated in accord with Eurocode 2 approach, on the basis that the headed shear stud connectors act as shear reinforcement while the inner and outer face plates provide resistance to tensile and compressive forces generated by flexural action. The load factors, strength reduction factor, and material factors have been taken as unity. The actual material properties for concrete and steel obtained from the tests are used in the calculation. The punching shear resistance of lightweight concrete slabs or column bases is determined by summing the shear resistance provided by the concrete core and the contribution of the shear

5.2.1. Modification to control perimeter u1 The punching shear resistance of sandwich shell still follows Eq. (1) by summing that the shear resistance was provided by the concrete the shear connectors. It was found that the change of curvature had a significant effect on the punching load (Shukry and Goode, 1990). The shear planes had steeper angles in the circumferential direction than in the longitudinal direction (width direction). The angles were dependent upon the shell curvatures. These conclusions were confirmed by the tests. While calculating the control perimeter u1 in Eq. (1) in Eodecode 2, it ignores the curvature effect and gives a constant control perimeter which is with a distance of 2hc away from loading area. This basic control perimeter induces an over-predicted punching shear resistance. As a result, to express the failure mechanism of punching shear the basic control perimeter u1 in Eq. (1) should be modified. Based on the fact that angles of punching shear planes were dependent upon the shell curvatures, thus it is assumed that the critical perimeter (control perimeter) could be initiated from the reflection point (where the section moment M arc ðxÞ ¼ 0) in the circumferential direction, while in the width direction the angle of punching shear planes followed the minimum value of 26:61 as suggested in Eurocode 2 for checking punching failure at the ultimate limit state. Hence, the basic control perimeter u1 can be expressed by u1 ¼ 2ðLa þ Lb Þ

ð4Þ

where La ¼ 2x which is obtained from making sectional bending moment M arch ðxÞ ¼ 0 while Lb is obtained by Lb ¼ lb þð2hc = tan θwid Þ. 5.2.2. Effect of height of concrete In the SCS sandwich shell, the outer plate participates in transferring the punching load to the concrete. Therefore a modification to

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Z.-Y. Huang et al. / Ocean Engineering 102 (2015) 146–161

Table 5 Failure load and failure mode.

n

Specimen

P 1 (kN)

δ1 (mm)

Failure mode

P 2 (mm)

δ2 (mm)

Failure mode

SCSS-1 SCSS-2

1192.9 1390.9

6.5 4.8

Punching shear of concrete core Punching shear of concrete core

1025.0 1210.0

34.7 50.1

Punching of outer plateþ fracture of inner plate Punching of outer plateþ fracture of inner plate

P 1 ¼ First peak load; P 2 ¼Second peak load.

Table 6 Strain level of critical location in SCSS-1. SCSS-1 Inner plate P1 P2 Outer plate P1 P2

R1-2 653 3121 R6-1  2066  128

R1-3 454 2034 R6-2  1809  1264

R2-1  471  8251 R6-3  1896  799

R3-1  599  3396 R7-1 201 1814

R3-3 962 2052 R8-3  42 1729

R5-1  292  2358 R9-2 815 1746

R5-3  545  1533 L7 120  2754

L3  3386 2012 L10 171 1407

L5  861  2698 L11  32 1681

n

R1-1 represents Rosette-number-X(1), while Y(2) and Z(3).

Table 7 Strain level of critical location in SCSS-2. SCSS-2 Inner plate P1 P2 Outer plate P1 P2

R1-2 844 5791 R6-1  1550  241

R3-1  1503  4754 R6-2  1636  1216

R4-3  409  1941 R7-1 145 2529

R5-1  325 160087 R7-2  244  1694

c

L5  1435 4121 R9-3  162 1234

L9  272  2079 R10-2 340 1139

1600 yield strain

1000

1200

800

1000

600 R1-1 R4-1 R4-2 L1 L3

400 200 0 -3060

-1530

0 Strain (με)

1530

800 L1 L2 L4 R1-1 R4-2 R5-1

600 400 200 0 -2000

3060

d

yield strain

1200

-1000

0 1000 Strain (με)

1600

2000

3000

yield strain

1400

1000

1200

800 600

R8-3 R9-2 R7-1 R10-2 L10 L11

400 200

Load P (kN)

Load P (kN)

L2  533  1565 R9-2 638 2516

1400

Load P (kN)

Load P (kN)

1200

R5-3  191  2225 R8-1  23 2424

1000 800

R7-1 R8-1 R8-3 R9-2 R9-3 R10-2 R10-3

600 400 200

0 0

1500 Strain (με)

3000

4500

0

1500

3000

4500

6000

Strain (με)

Fig. 13. Load–strain curve at different locations in sandwich shells. (a) Inner plate (SCSS-1). (b) Outer plate (SCSS-1). (c) Inner plate (SCSS-2). (d) Outer plate (SCSS-2).

Z.-Y. Huang et al. / Ocean Engineering 102 (2015) 146–161

157

P reflection point

reflection point

Punching truncated rectangular pyramid

la lb

lb

h

la

hc θwid

La Lb

Lb

Circumferential direction

La

Width direction

R

P tension

tension

Shear stud t

Tension membrane

r

lb Lb

la

Fracture

R

Tension membrane

Tension membrane

Steel plate L

Steel plate Punching surface

La Tension membrane

Fig. 14. Two-stage failure mechanism of SCS sandwich shell. (a) Typical punched concrete frustum. (b) Punching fracture of outer plate and inner plate.

Table 8 Details of test specimens by Shukry and Goode (1990). Specimen

ts (mm)

hc (mm)

R/h

Ec (GPa)

fck (MPa)

Es (GPa)

fy (MPa)

c (mm)

P (kN)

Failure mode

Group 3 A1 A2 A3 B1 B2 B3

0.97 0.98 1 2.05 2.03 2.03

17.6 18.1 17.5 17.5 17.3 17.2

10.6 16.5 22 10.2 16.1 21.5

32.2 32.2 32.2 33 33 33

60.5 60.5 60.5 62 62 62

205 190 202 190 195 204

282 275 274 230 231 231

83 83 83 83 83 83

14.4 10.8 8.9 17.1 14.5 12.6

PS PS PS PS PS PS

Group 4 B5 B6 B7 C1 C2 C3 C4 D1 D2 D3 D4

1.97 2 1.97 2 1.95 1.89 1.94 1.95 1.94 1.94 1.93

18 17.3 15.8 25.3 25.1 24.3 26.1 29.7 30.6 28.9 30.8

10.4 15.8 22.8 7.3 10.6 15.9 19.7 7.6 10.4 16 20.1

35.5 35.6 37.1 35.5 35.6 37.1 35.5 35.5 35.5 34.4 34.4

63 66.1 64.6 68 66.1 64.6 63 68 63 66.3 66.3

213 216 213 208 202 206 215 200 206 218 212

249 213 270 255 266 275 271 251 276 265 268

40 40 40 40 40 40 40 40 40 40 40

26.4 24.7 21.5 50.1 40.2 39 32.8 59 49 45.3 43.5

PS PS PS PS PS PS PS PS PS PS PS

Specimens A4, B4 are flat panel which are out of selection in this paper. R¼ radius of shell; P ¼ maximum load from test; c: length of loading area; PS: punching shear failure.

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Z.-Y. Huang et al. / Ocean Engineering 102 (2015) 146–161

Table 9 Details of test specimens by Marshall et al. (2012) and Yan (2012). Specimen ts (mm)

hc (mm)

L (mm)

W (mm)

r/L

Connector s/ts

SA1 SA2 SB1 SB2 SB3 SB4 SB5 SB6 SB7 SCSS-1 SCSS-2

124 124 136 126 121 124 129 132 124 80 80

1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250

1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250

0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.5 0.064 0.1 0.21

Nill J-hook HSS HSS HSS HSS HSS HSS HSS HSS HSS

8.3 8.3 4.8 7.8 11.8 7.8 7.8 7.8 7.8 4 4

– 13.30 22.92 14.10 9.32 26.92 14.10 14.10 14.10 27.5 27.5

d x hs @ s (mm)

fy (MPa)

fu (MPa)

fck (MPa)

Ec (GPa)

Es (GPa)

c (mm)

P1 (kN)

P2 (kN)

Failure mode

Nill 13x100@110 13x100@110 13x100@110 13x100@110 13x100@210 13x100@110 13x100@110 13x100@110 13x75@110 13x75@110

396 396 340 330 340 330 330 330 330 304 304

520 550 495 550 550 495 550 550 495 460 460

29.4 32.6 63.6 63.6 69.8 69.8 186.5 72.4 69.4 56.1 56.1

23.9 24 16.5 16.5 16.5 16.5 45 16.5 16.5 14.3 14.3

208 208 203 202 206 202 202 202 202 200 200

125 125 125 125 125 125 125 125 125 400 400

943.0 1440.0 1083.0 1363.0 1736.9 1154.6 3072.1 1165.8 1209.7 1192.9 1390.9

1218.0 1617.0 725.0 1514.0 2030.0 1183.0 1373.0 1268.0 1108.0 1025.0 1210.0

LB PS PS PS PS PS PS PS PS PS PS

W¼ width of specimen; r ¼rise of arch; P 1 , P 2 ¼first peak load and second peak load from test; HSS ¼headed shear studs; c: length of loading area; LB: local buckling; PS: punching shear.

Table 10 Comparison between predictions and test results by Shukry and Goode (1990). Eurocode 2 Specimen Group 3 A1 A2 A3 B1 B2 B3 Group 4 B5 B6 B7 C1 C2 C3 C4 D1 D2 D3 D4 Mean value Std. dev.

Proposed model

vRd;s ¼

P

P

P EC2 1

P pro 1

(mm) uEC2 1

P EC2 (kN) 1

upro (mm) 1

P pro (kN) 1

553.7 560.0 552.4 552.4 549.9 548.7

16.6 16.8 16.8 26.5 26.4 26.8

582.8 483.3 459.4 582.0 476.9 457.0

12.5 10.4 9.8 15.5 12.7 12.3

0.87 0.64 0.53 0.65 0.55 0.47

1.15 1.04 0.91 1.10 1.14 1.02

637.1 631.0 593.8 752.3 738.6 716.7 765.6 811.0 829.7 819.1 843.1

40.7 41.2 36.4 55.0 51.9 48.1 54.6 61.2 62.1 62.5 65.2

594.2 487.6 449.9 770.0 675.5 664.6 658.3 865.0 759.3 715.7 727.7

28.5 23.9 20.7 42.2 35.6 33.5 35.2 49.0 42.6 41.0 42.2

0.65 0.60 0.59 0.91 0.77 0.81 0.60 0.96 0.79 0.72 0.67 0.69 0.14

0.93 1.03 1.04 1.19 1.13 1.17 0.93 1.20 1.15 1.11 1.03 1.07 0.09

pro EC2 uEC2 1 , u1 ¼ control perimeter predicted by Eurocode 2 and proposed model; P 1 , P pro ¼predicted maximum load by Eurocode 2 and proposed model. 1

concrete height hc may be taken as (Ebead and Marzouk, 2002) h c ¼ nhc

vRd;s which is given by

ð5Þ

in which n ¼ Es =Ec .

5.2.3. Effect of shear connector In view of the shear reinforcement, Eurocode 2 assumes the shear reinforcement yield when reaching the ultimate load. However, for shear studs in the concrete core, there may be several failure modes for headed shear studs under tensile force, namely concrete breakout failure, pull-out failure, and steel plate punching failure as presented in Yan et al. (2014a). Consequently, it is irrational to assume that the shear studs would yield which is one of the failure modes that depend upon the specific conditions (e.g., dimensions and material strength) of shear studs. Considering the different failure modes of headed shear studs in the concrete, the second term in Eq. (2) could be replaced by

ncp X hc i¼1

s

Ft

1 u1 hc

sin αi

ð6Þ

where ncp is the amount of shear connectors linking the shear cracks which equals to the number of shear studs attached to the inner plate within the critical perimeter u1 subtracting the number of shear studs under the loading area; s is the stud spacing; hc is the effective height of concrete core calculated by Eq. (5); αi is the angle between each stud axis and horizontal axis, which can be calculated by   π n s αi ¼  i ni ¼ 1; 2; …; ncp ð7Þ 2 R s is the stud spacing; R is the radius of the arch. F t is the tensile resistance of shear stud embedded in concrete, which can be obtained by the minimum value of concrete breakout resistance, pullout resistance, stud tension failure resistance and plate punching shear resistance as proposed in Yan et al. (2014a) 8 pffiffiffiffiffiffi F cb ¼ 0:33 f ck AN > > > > < F ¼ 0:9φf e d pl ck h ð8Þ F t ¼ min > F u ¼ ϕAse f ut > > p ffiffiffi > :F ¼A f = 3 ps

v u

where the projected  area of  cone surface to the free concrete surface 2 AN ¼ πhef 1 þ ðdh Þ= hef ; φ ¼ 1:4 for an anchor located in a region of a concrete member where analysis indicates no cracking, otherwise φ ¼ 1:0; eh is the distance from the inner shaft of a stud (bolt) to the outer tip of the stud (bolt), and 3d0 r eh r4:5d0 ; d is the diameter of stud; ϕ is the reduction factor of the steel; Ase and f ut are the crosssectional area and the ultimate strength of headed shear stud; Av ¼ πdt and f u are the punching area and ultimate strength of steel plate. 5.2.4. Effect of fibre In addition, Eq. (3) could be modified according to Majdzadeh et al. (2006) if fibres are added into the concrete core, to which vRd;c is obtained by  1=3 vRd;c ¼ C lRd;c kη1 100ρ1 f lck þ kf τf ;FRC ð9Þ where modification factor kf ¼ 0:29 is used for synthetic fibres; and τf ;FRC ¼ 4:23V f is used conservatively as suggested by Mirsayah and Banthia (2002) for flat ended fibres with circular cross section in which V f is the percentage of fibre volume faction. 5.2.5. Membrane effect (second peak strength) From the experimental investigation, the tension membrane action of outer plate contributes to the second peak strength of the sandwich shell. It is determined by punching shear of either the outer face plate

Z.-Y. Huang et al. / Ocean Engineering 102 (2015) 146–161

159

Table 11 Comparison of predictions with the test results by Marshall et al. (2012), Yan (2012) and Authors. Test data

Specimen

Marshall et al. (2012) Yan (2012)

Authors

SA1 SA2 SB1 SB2 SB3 SB4 SB5 SB6 SB7 SCSS-1 SCSS-2

Eurocode 2

Proposed model

(mm) uEC2 1

P EC2 (kN) 1

P1 P EC2 1

upro (mm) 1

P pro (kN) 1

P1 P pro 1

U (mm)

(kN) P pro 2

P2 P pro 2

2167.6 2167.1 2363.6 2237.2 2177.4 2212.1 2177.5 2312.6 2212.1 2781.1 2781.1

1698.4 2502.3 2289.8 2078.7 2428.3 1093.6 3148.6 2374.8 2053.5 2718.0 2729.2

0.56 0.58 0.47 0.66 0.72 1.06 0.98 0.49 0.59 0.44 0.51 0.64 0.20

1935.0 1934.7 2059.6 1979.3 1941.3 1963.3 2149.6 1902.2 1893.8 2550.7 2550.7

263.9 1351.3 1051.5 1262.5 1520.3 1265.4 3191.4 1050.4 1140.2 1143.0 1225.8

3.57 1.07 1.03 1.08 1.14 0.91 0.96 1.11 1.06 1.04 1.13 1.05 0.07

500.0 500.0 500.0 500.0 500.0 500.0 500.0 500.0 500.0 1600.0 1600.0

1245.9 1317.8 685.9 1238.4 1873.5 1075.6 1238.4 1238.4 1114.6 1135.2 1135.2

0.98 1.23 1.06 1.22 1.08 1.10 1.11 1.02 0.99 0.90 1.07 1.07 0.10

Mean value Std. dev.

U¼ final control perimeter of outer plate; P pro 2 ¼predicted second peak load by proposed model.

Mean: 1.07 Std.Dev: 0.09

Test results P (kN)

60

40

Mean: 0.69 Std.Dev: 0.14

20

EC2 Proposed model

0 0

20

40

60

Prediction (kN) Fig. 15. Comparison between EC 2 & proposed model. (18 tests by Shukry and Goode, 1990).

P -Proposed model

Test results P (kN)

P -Proposed model

Test-to-prediction Mean: 1.05(1.07) Std.Dev: 0.07(0.10)

2000

10

1

0.1 0.1

1

10

100

Contact area A (m2) Fig. 17. Test load v.s. ISO ice load (ISO19906, 2010).

where the first term represents the failure of inner plate fracture initiated by shear studs while the second term represents the shear fracture failure of outer plate; n0cp is the amount of shear studs that along the concrete punched through; ds is the diameter of shear stud; f u is the ultimate strength of steel; U ¼ 2ðla þ lb Þ is the perimeter of loading area, in which la ; lb are the original length of rectangular loading area, respectively.

P -EC 2

3000

Local ice pressure pL(MPa)

100

Test-to-prediction

5.3. Verification of the proposed formulae

1000 Mean: 0.64 Std.Dev: 0.20

0 0

1000 2000 Prediction (kN)

3000

Fig. 16. Comparison between EC 2 & proposed model. (11 tests by Marshall et al., 2012; Yan, 2012) and authors).

or inner face plate fracture initiated by shear studs, which is smaller. The load transferring mechanism can be shown in Fig. 14. The local tension membrane action of outer face plate provides the strength hardening. Therefore, the second peak load can be obtained by pffiffiffi pffiffiffi P 2 ¼ min f2ncp πds tf u = 3; f u Ut= 3g ð10Þ

Section 5.2 develops an analytical solution for predicting the punching shear resistance of SCS sandwich shell, on the basis of the observed failure modes and force transfer mechanism. Tables 10 and 11 summarises the test results and calculated punching shear resistance of 29 SCS sandwich shells. It is shown that the predicted results are in good agreement with the test values, except for some underestimations for specimen SA1. The average test-to-prediction ratio for 29 specimens is 1.06 with a standard deviation of 0.08. Figs. 15 and 16 also show the scatter plot for comparison between test and prediction. For specimen SA1, separation and local snap-through of the inner steel plate were observed when the ultimate load was reached, and the failure of concrete led to the loss of structural integrity. Table 11 also shows the comparison of predicted loads at large deflection (over 30 mm deflection) with the test loads. Predictions of the second peak resistance agree well with the ultimate loads. The mean value of P 2 =P pro 2 ratio is 1.07 with a standard deviation of 0.1, showing a slightly conservative predictions.

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Z.-Y. Huang et al. / Ocean Engineering 102 (2015) 146–161

Compared to Eurocode 2 method, it is found that directly using Eurocode 2 formulae could over-predict the punching resistance of sandwich shell by around 34% because a punching control perimeter with a distance of 2hc away from the loading area is used. While the proposed method uses the more rational control perimeter considering the arch effect and outer steel plate effect for prediction which is more realistic judged by the investigation. On the other hand, Eurocode 2 approach is incapable of estimating the second peak resistance. Therefore, the proposed analytical method offers close prediction of the test results, which can be recommended to calculate the punching shear resistance of SCS sandwich composite shells. Fig. 17 also compares the performance of tested specimens with a non-hydrostatic ice loading pattern which can be inferred from ISO 19906 (2010) pressure-vs-area guidelines. The test loads were found to satisfy the ISO requirements when scaled up fourfold to a prototype size. Punching shear was remarkably successful in developing the capacity of the arch span, even after the concrete core had disbonded and spalled. Nonetheless, problems of insufficient data of specimens subject to large contact area still exist, which needs more research dedication to this area.

6. Procedure to calculate punching shear resistance of SCS sandwich shell The prediction procedure of punching shear resistance for SCS sandwich composite shell can be summarised as follows: (1) Determine the location of inflection point in the arch strut where the bending moment equal to zero based on first order analysis (see Appendix Fig. A1 and Fig. A2). Determine punching length La ¼ 2x by making sectional bending moment M arch ðxÞ ¼ 0, and determine punching length in width direction Lb ¼ lb þ ð2hc = tan θwid Þ; (2) Determine the control perimeter u1 of the punched concrete frustum based on Eq. (4); (3) Determine the angle αi between each stud axis and horizontal axis by Eq. (7); (4) Calculate the punching shear resistance from concrete vRd;c based on Eq. (9); (5) Calculate the tensile resistance of headed shear studs embedded in the concrete based on the lowest strength by Eq. (8) as,

the transportation and installation of pre-filled structures in the Arctic region. Headed shear connectors have been proposed to improve the composite action between the steel face plate and the cement grout. These developments are necessary to form a robust and safe structure which is strong enough to resist ice forces. Two scaled SCS sandwich shell specimens subject to patch load, which simulating the high pressure zone by ice force was tested. From the tests and analytical investigations in the previous sections, the following findings are drafted: (1) The load–deflection curve behaviour exhibits two peak strength. The SCS sandwich composite shells fail in punching failure of concrete core at the first peak strength. A punched frustum was developed in concrete core followed unloading. After that, the load increased again until getting to the second peak strength due to tension membrane action of outer face plate. (2) Directly using Eurocode 2 approach may over-estimate the punching shear resistance of SCS shell due to its assumption of control perimeter with a distance of 2hc away from the loading area. A modification of Eurocode 2 approach is developed to predict the punching resistance of SCS shell both for the first peak and second peak strength. A close agreement between the test results and the predictions has been achieved. (3) The superior performance of SCS sandwich shell is demonstrated subject to ISO 19906 ice load. Compared to ISO design load, the proposed SCS sandwich shell possesses satisfactory punching shear resistance. Further researches should extend by conducting more tests on SCS sandwich shell subject to patch loads. (4) A step-by-step design method for predicting the punching shear resistance of SCS sandwich composite shell is provided as well.

Acknowledgements The research described in this paper was financially supported by the Maritime and Port Authority of Singapore (MPA), American Bureau of Shipping (ABS) and National University of Singapore (NUS) under R-302-501-002-490. This funding support is gratefully acknowledged by authors.

F t ¼ min fF cb ; F pl ; F u ; F ps g Appendix (6) Calculate the punching shear resistance P 1 of SCS sandwich composite shell by Eqs. (1), (4)–(9); (7) Calculate the second peak resistance P 2 of SCS sandwich composite shell by Eq. (10).

7. Conclusions Beginning with presenting the background and challenges in Arctic offshore structures, a steel–concrete–steel platform using SCS sandwich filled with ULCC has been proposed to resist the ice load. The platform can be constructed by fabricating two concentric steel shells, cylindrical at the bottom and conical towards the top. The shells are constructed onshore in the south where it can benefit from lower costs, existing construction yards and the ability to construct all year round. The platform is buoyant and can be towed to site. Once arrived, it can be ballasted down until it grounds on the seabed, and the space between the two shells is then filled with ultralightweight high strength cement composite grout. This will benefit

Calculation of internal force of fixed end arch: (1) Choose an equivalent model with a rigid arm element ðEI ¼ 1Þ; (2) Cut the rigid arm element and establish the compatibility equations at point C; y ¼ R cos φ; x ¼ R sin φ; ds ¼ Rdφ; sin Z Z φ0 ¼ L=2R; ys ¼ y=EIds= ð1=EIÞds 8 > < δ11 X 1 þ Δ1P ¼ 0 δ22 X 2 þ Δ2P ¼ 0 > : δ X þΔ ¼ 0 33

3

3P

where Z 2 M1 1 ds; δ22 ds ¼ EI EI Z Z 2 2 M2 F N2 ds þ ds ¼ EI EI Z

δ11 ¼

ðA:1Þ

Z.-Y. Huang et al. / Ocean Engineering 102 (2015) 146–161

P

P

= A

B

C O

EI= ∝

A

B

Fig. A1. Equivalent model for fixed end arch.

Fig. A2. Basic determined model subject to forces X 1 , X 2 and X 3 .

2 Z Z  y  ys cos 2 φ ds; ds þ EI EI Z 2 Z 2 M3 x δ33 ¼ ds ¼ ds; EI EI Z M1 MP ds; Δ1P ¼ EI Z Z M2 MP M3 MP ds; Δ3P ¼ ds: Δ2P ¼ EI EI ¼

M P is the bending moment in a basic determined structure subject to outer force P; for arch member subject to uniform load, M P ¼  ðq=2Þx2 ; f or arch member subject to point load, M P ¼  ðP=2Þx; for arch member subject to patch load, M P ¼  ðqc2 =2Þ  qcx. (3) Solve X 1 X 2 X 3 and substitute them to the internal force equations resulting in:   ðA:2Þ M ¼ X 1 þ X 2 y ys þ X 3 x þ M P F Q ¼ X 2 sin φ þ X 3 cos φ þ F Q P

ðA:3Þ

F N ¼  X 2 cos φ þ X 3 sin φ þ F NP

ðA:4Þ

Let Mj x ¼ 0, the position of inflection point x can be solved.

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