Analysis and design of steel-concrete composite sandwich systems subjected to extreme loads

Abstract

This paper presents the design guide based on analytical, numerical and experimental investigation of Steel-concrete-steel (SCS) sandwich structural members comprising a lightweight concrete core with density ranged from 1300 to 1445 kg/m³ subjected to static, impact and blast loads. The performance of lightweight sandwich members is also compared with similar members with normal weight concrete core and ultra high strength concrete core (f_c = 180 MPa). Novel J-hook shear connectors were invented to prevent the separation of face plates from the concrete core under extreme loads and their uses are not restricted by the concrete core thickness. Flexural and punching are the primary modes of failure under static point load. Impact test results show that the SCS sandwich panels with the J-hook connectors are capable of resisting impact load with less damage in comparison than equivalent stiffened steel plate panels. Blast tests with 100 kg TNT were performed on SCS sandwich specimens to investigate the key parameters that affect the blast resistance of SCS sandwich structure. Plastic yield line method is proposed to predict the plastic capacity and post peak large deflection of the sandwich plates. Finally, an energy balanced model is developed to analyze the global behavior of SCS sandwich panels subjected to dynamic load.

Keywords

blast load / composite structure / impact load / lightweight concrete / sandwich plate / J-hook connector

Introduction

Steel-concrete-steel (SCS) sandwich structures are becoming popular in offshore, bridge and other civil engineering constructions because of their higher specific strength and better stiffness. This form of construction may be used as an alternative to either conventional stiffened steel plate or reinforced concrete construction [1-3]. Zuk [4] and Bergan et al. [5] carried out further work to realize its potential for application as lightweight deck structures and for strengthening of weakened areas in ship structures. The apparent advantages of the system are that the external steel face plates act as both primary reinforcement and permanent formwork, and also as impermeable, impact and blast resistant membranes.

Sandwich structure comprises three major structural parts: face plates, sandwich core, and mechanisms to transfer shear between face plates and core. If a structure is potentially subject to significant bending moment, cyclic loading and large impact loading arising from hazardous environment, the SCS sandwich system serves as an appealing alternative to existing stiffened steel plate structures. The advantages of SCS include, but not limited to, the following: 1) economical and optimized design to achieve highs stiffness and strength; 2) improved impact resistance, especially leakage control after punching failure of the steel plates; 3) compared with stiffened plate, the exposed steel surface area is less and hence the amount of the protection coating can be reduced; 4) require less stiffeners and therefore less welding which eventually leads to improved fatigue performance; 5) concrete core provides good acoustic and thermal insulation; and 6) prefabrication and modular construction reduce construction time.

To improve the performance, adhesive, angle shear connector, and stud shear connectors were used in SCS sandwich structures by Solomon et al. [6], Malek et al. [7] and Tomlinson et al. [8]. Further modification in SCS sandwich construction was done and named as Bi-Steel [9]. SCS sandwich structure with adhesive bonding was not ideal in resisting shear force because there was no vertical shear reinforcement. The sandwich structure with angle shear connectors performed rather poorly in shear and separation of face plates occurs when it was subjected to impact loading. Headed studs could not provide through connection between the face plates and thus separation of face plates due to accidental impact load led to significant reduction in load carrying capacity. The overlap length and close stud spacing could lead to difficulty in concrete casting or grouting. Furthermore, research done by Liew et al. [2] showed that the shock wave generated by impact and blast loads tend to push the face plate out from the core leading to tensile separation as shown in Fig. 1. Bi-steel connectors (Fig. 2) proposed by Pryer and Bowerman [9] limit the core thickness to be at least 200 mm and the friction welding of the connectors must be carried out in workshop involving the use of proprietary equipment.

To overcome all the above mentioned disadvantages a novel method of connecting the two face plates using J-hook connector was developed by Liew et al. [10]. The J-hooks can direct connect the top and bottom steel face plates as shown in Fig. 3, and their uses are not restricted by the concrete core thickness. The proposed novel SCS sandwich system offers significant advantages for applications involving extreme loadings. Examples of such applications are as blast protective barriers and vehicle impact barriers as shown in Fig. 4. In this paper, the structural performance of SCS sandwich system with various concrete materials subject to static patch load, impact and blast loads is studied based on both experimental and analytical investigations. The key parameters, which include sandwich core strength, face plate thickness, and employment of shear connectors, affecting the structural performance are investigated.

Sandwich composite panels with J-hook connectors

For weight sensitive marine, offshore and some civil structures, the core thickness of the sandwich panel shall be optimized. In addition, to minimize the dependence on the welding equipment and to introduce flexibility in construction and repair, novel shear connectors named J-hook connectors and associated construction methods were invented by Liew and Sohel [1]. Generally, the construction process of SCS sandwich panels with J-hook connectors can be divided into two stages: 1) fabrication of steel plates and shear connectors and 2) filling of concrete between the plates.

In the first stage, the J-hook connector can be fabricated by bending a steel bar or through forging and machining. The diameter and height of the J-hook connectors depend on the strength requirement and are subject to the limit of core thickness. For small core thickness, the diameter of the J-hook connectors is limited by its bending radius. The J-hook connectors can be welded to the face plates by using commercially available shear stud arc welding equipment as shown in Fig. 3(a). After welding of J-hooks, two plates are hooked together by applying a light tension force to the plates before filling concrete in between the gap of the two steel plates [1]. The SCS sandwich panel can be assembled easily and efficiently as shown in Fig. 3(b).

Such J-hook shear connectors can effectively ensure composite action between steel face plates and concrete core under normal design loads. They also constrain the local buckling of steel face plates. Under extreme loadings, such as impact loading, the J-hook connectors prevent separation of steel the face plates and ensure both face plates act compositely with the concrete core. This connection technology together with the use of lightweight concrete core would reduce overall weight of the SCS sandwich system and make it a competitive choice for marine and offshore structures.

Analysis of SCS sandwich structures under static load

The potential failure mechanisms are shown in Fig. 5 and the design formulae to predict the ultimate resistance of various failure modes are described below.

Flexural resistance

The plastic moment resistance of a composite SCS sandwich section can be determined by assuming a rectangular plastic stress block of depth x_c for the concrete (Fig. 6). The concrete beneath the neutral axis (NA) is assumed to be cracked. The forces in the steel plates depend on the yield strength and shear strength of material used for the connectors in resisting interfacial shear stresses in between the steel plate and the concrete core. It is also assumed that sufficient shear connectors are provided to prevent local bucking of the steel plate in compression.

The nominal compressive force in concrete (N_cu) is given by

(1)N_{\mathrm{c}\mathrm{u}}={\displaystyle \frac{\mathrm{0.85}{f}_{\mathrm{c}}}{{\gamma }_{\mathrm{c}}}}b{x}_{\mathrm{c}},

where b, ƒ_c and γ_c are the beam width, concrete cylinder strength, and partial safety factor for concrete respectively. The plastic neutral axis position can be obtained by equating the compression force to the total tension force

(2)N_{\mathrm{c}}+N_{\mathrm{c}\mathrm{u}}=N_{\mathrm{t}}\mathrm{.}

Putting N_c = σ_ybt_c, N_t = σ_ybt_t and N_cu from Eq. (1) in Eq. (2),

(3)x_{\mathrm{c}}=\mathrm{1.176}{\gamma }_{\mathrm{c}}{\sigma }_{\mathrm{y}}(t_{\mathrm{t}}-t_{\mathrm{c}})/f_{\mathrm{c}},

where γ_c = 1.5 as recommended by Eurocode 2 [11] for design purposes; N_c and N_t are the compressive and tensile forces in the top and bottom steel plates, respectively.

By taking moments about the center of the compression steel plate, the plastic moment of resistance of the sandwich section is:

(4)M_{\mathrm{p}\mathrm{l}}={\sigma }_{\mathrm{y}}b{t}_{\mathrm{t}}\left(h_{\mathrm{c}}+{\displaystyle \frac{t_{\mathrm{c}}}{\mathrm{2}}}+{\displaystyle \frac{t_{\mathrm{t}}}{\mathrm{2}}}\right)-{\displaystyle \frac{\mathrm{0.85}{f}_{\mathrm{c}}b{x}_{\mathrm{c}}}{{\gamma }_{\mathrm{c}}}}\left(\mathrm{0.5}{x}_{\mathrm{c}}+{\displaystyle \frac{t_{\mathrm{c}}}{\mathrm{2}}}\right)\mathrm{.}

When the steel plates are of equal thickness and strength, the SCS sandwich beams can be treated as an under reinforced concrete beam. Since an under reinforced beam fails in a ductile manner, the SCS sandwich beam deflected extensively and usually developed extensive and wide cracks in the final loading stages [12]. After yielding of tension steel plate, the cracking of the concrete will continue to rise toward the compression steel plate. In this case, the strain at the bottom plate is very large compared to top steel plate. The moment capacity of the beam is reached when the neutral axis moves near to the lower surface of the compression plate (i.e. x ≈ 0) and the bottom plate is fully yielded.

Therefore, in case of t_c = t_t = t, the moment of resistance of the sandwich section becomes

(5)M_{\mathrm{p}\mathrm{l}}=N_{\mathrm{t}}(h_{\mathrm{c}}+t)\mathrm{.}

For fully composite beam (N_t = σ_ybt_t, in which σ_y is the yield strength of the steel plate), the number of J-hook connectors welded in the bottom or top face plate between the points of zero and maximum moment should be, n_s = σ_ybt_t/(κP_R) in which κ is the reduction factor for concrete. Therefore, Eq. (5) becomes

(6)M_{\mathrm{p}\mathrm{l}}={\sigma }_{\mathrm{y}}b{t}_{\mathrm{t}}(h_{\mathrm{c}}+t)\mathrm{.}

If the number of J-hook connectors is reduced, the beam will be partially composite and the moment resistance of the partially composite beam will also be reduced correspondingly. For partially composite beam,

(7)N_{\mathrm{t}}=n_{\mathrm{p}}(\kappa P_R),

in which n_p is the number of shear connectors between the points of zero and maximum moment for partial composite beam. Therefore, Eq. (5) can be written as

(8)M_{\mathrm{p}\mathrm{l}}=n_{\mathrm{p}}(\kappa P_R)(h_{\mathrm{c}}+t)\mathrm{.}

For SCS sandwich slabs, the flexural capacity of the slab can be evaluated using the yield line theory. Figure 7 shows the fracture pattern of yield lines in a square slab, simply supported at four edges and subjected to a concentrated patch load. From the virtual work principle, the flexural capacity of the slab may be evaluated using the equation proposed by Rankin and Long [13],

(9)F_{\mathrm{p}}=\mathrm{8}{m}_{\mathrm{p}\mathrm{l}}\left({\displaystyle \frac{L_{\mathrm{s}}}{L-c}}-\mathrm{0.172}\right),

where m_pl is the plastic moment capacity per unit length along the yield line, c is the side length of the loading area, L_s is the dimension of the slab specimen; L is the span between the supports.

Punching shear resistance

Figure 8(a) illustrates the failure pattern of a SCS sandwich slab showing the formation of a cone due to a punching load from the top. The punching shear resistance within the concrete core around the loaded perimeter of the SCS sandwich slab may be calculated using Eurocode 2 [11] or CEB-FIP [14] approach, on the basis that the slab behaves similarly to conventional reinforced concrete members with shear reinforcement in the punching shear zone. It should be noted that: 1) the method is for reinforced concrete slabs with re-bars in the tension side of the slab, which differs from the SCS sandwich slabs having top and bottom steel face plates. 2) The load factor, strength-reduction factor, and material factors have been taken as unity. The actual test values of the material (concrete and steel) properties were used in the model. 3) In the SCS sandwich slab, the top plate participates in transferring the punching load to the concrete. Therefore, the punching perimeter (Fig. 8(b)) may be calculated as

(10)u_{\mathrm{1}}=\mathrm{4}c+\mathrm{2}\mathrm{\pi }(\mathrm{2}{h}_{\mathrm{c}}+\mathrm{2}n{t}_{\mathrm{c}}),

in which n = E_s/E_c, where E_s and E_c are the modulus of elasticity of steel and concrete respectively.

The punching resistance of the composite sandwich slab is obtained by summing the shear resistance provided by the concrete core and the contribution from the shear connectors as

(11)V_{\mathrm{p}\mathrm{u}\mathrm{n}}=V_{\mathrm{c}}+V_{\mathrm{s}}\mathrm{.}

V_c is the shear resistance of the concrete core obtained as Eurocode 2 [11]:

(12)V_{\mathrm{c}}=\left[C_{\mathrm{c}}{k}_{\mathrm{c}}{\eta }_{\mathrm{1}}{(\mathrm{100}{\rho }_{\mathrm{1}}{f}_{\mathrm{c}\mathrm{k}})}^{\raisebox{1ex}{$\mathrm{1}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{3}$}\right.}\right]u_{\mathrm{1}}{h}_{\mathrm{c}},

where k_{\mathrm{c}}=\mathrm{1}+\sqrt{\mathrm{200}/h_{\mathrm{c}}}\le \mathrm{2} with h_c in mm, ρ₁ = t_t/h_c ≯ 0.02, C_c = 0.18/γ_c for normal weight concrete and C_c = 0.15/γ_c for LWC, η₁ = 0.4+ 0.6ρ/2200≮1.0 in which ρ is the density of concrete (kg/m³), γ_c is the partial safety factor for concrete. If fibers are added into the concrete core, the shear resistance of the concrete may be modified as (Majdzadeh et al. [15]),

(13)V_{\mathrm{c}}=\left[C_{\mathrm{c}}{k}_{\mathrm{c}}{\eta }_{\mathrm{1}}{(\mathrm{100}{\rho }_{\mathrm{1}}{f}_{\mathrm{c}\mathrm{k}})}^{\raisebox{1ex}{$\mathrm{1}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{3}$}\right.}+k_{\mathrm{f}}{\tau }_{\mathrm{f},\mathrm{F}\mathrm{R}\mathrm{C}}\right]u_{\mathrm{1}}{h}_{\mathrm{c}},

where k_f = 0.216 for steel fiber (hook end), limited to a maximum of 1% volume fraction; k_f = 0.290 for synthetic fibers; and τ_f,FRC = τ_FRC-τ_plain in which τ_FRC and τ_plain are the shear strength of FRC and plain concrete, respectively, as determined by direct shear test. In the present study τ_f,FRC = τ_FRC - τ_plain = 4.23V_f is used conservatively as suggested by Mirsayah et al. [16] for flat ended fibers with circular cross section in which V_f is the percentage of fiber volume faction.

V_s is the contribution of the J-hook connectors for punching resistance, i.e.,

(14)V_{\mathrm{s}}=n_{\mathrm{c}\mathrm{p}}{F}_{\mathrm{t}},

where n_cp is the number of J-hook connector attached to the bottom plate within the critical perimeter u₁ subtracting the number of J-hooks under the loading area; F_t is the tensile capacity of each J-hook connector obtained from direct tensile test of interconnected J-hooks within a concrete block. From the tensile tests [17], it was observed that the maximum tensile strength reached before any significant elongation of hook or cracking of concrete. Therefore, it can be assumed that the hook connector is fully engaged while concrete core develops its full shear strength.

SCS sandwich slabs under patch load—Experimental verification

Eight tests were conducted on two way spanning SCS sandwich slabs with a square aspect ratio. The span length was 1.0 m. The slabs were simply supported on all four edges using fixed bars on two adjacent sides and loose bars on the other sides. Load was applied through 100 mm square solid column. The differences among the test specimens are core thickness, steel plate thickness, J-hook diameter and concrete types (see Table 1). Figure 9(a) shows the test arrangement of the SCS sandwich slab.

The load-deflection behavior of SCS slabs under concentrated load is shown in Fig. 10. The behavior of all the slabs followed a pattern at the initial stage of loading. First a linear reaction with some slight tension cracking and the lifting of the corners which was expected. Secondly, the onset of slip, bucking of upper plate and possibly the failure of one or more connectors occurred. An explanation of this may be as follows. Initially the slab behaves in a fully composite way with full adhesion between concrete and steel and thus no slip was observed. Once the bond fails the connectors are required to carry all the shear forces.

The load deflection behaviors were different between the slabs with normal weight concrete and lightweight concrete as shown in Fig. 10. After the first peak, the slabs with normal weight concrete showed rapid reduction in load capacity. The reason is that the slab failed by punching of concrete core. After the local punching failure, the load capacity again increased due to membrane action of the steel plates. In the cases of the slabs with lightweight concrete cores, the load gradually increased with deflection after flexural yielding due to the membrane action of the steel plates. At the final stage of loading, the failure was governed by either buckling of top steel plate or cracking and crushing of the concrete core. From the test results, the general load-deflection behavior of the SCS sandwich slabs under concentrated load is illustrated in Fig. 11.

The comparisons of the ultimate loads are given in Table 2. Experimental shear capacity of the J-hook connectors was used to predict the ultimate load carrying capacity of the slabs in this study. In case of lightweight concrete, 90% of the experimental ultimate shear capacity of J-hook connector was used because push-out tests conducted by Liew and Sohel [1] showed that the load-slip behavior of J-hook connectors in the lightweight concrete was very ductile with the strength of the connector fluctuating in the region of about 8% to 10% of the maximum load.

The maximum difference between test and calculated flexural load carrying capacity of the SCS sandwich slabs is within 17% (Table 2). The predicted flexural load capacity is generally conservative except for slab SCS4-100 with thin steel face plates with a thickness of 4 mm. In this case, punching failure occurred in both concrete and top steel plate.

Table 3 compares the calculated punching load capacity of the slabs obtained from Eqs. (11) to (14) with the predicted flexural resistance. The punching capacity of the concrete core is considered to be reached when the load-deflection curve begins to descend from the first peak as shown in Fig. 10. Only the slabs with normal weight concrete cores show this behavior. The ratio of the predicted flexural load to the calculated punching load (F_p/V_pun) for the slabs with normal weight concrete core ranged from 0.91 to 1.30 with an average value of 1.14.

Behavior of SCS sandwich panels subject to impact loads

Test specimens

Two SCS sandwich specimens A and B were prepared (Fig. 12). Both specimens utilized 6 mm thick S275 steel plates. The dimensions of two specimens were the same (2400 mm×1000 mm). The concrete core thickness was 100 mm. Two sides along the length of the panel were temporarily closed by C-channel during concrete grouting. Both ends along the width of the panel were permanently closed by steel plates with continuous welding. During test, the side channels along the length of the panels were removed. Lightweight aggregate concrete with a density of 1400 kg/m³ was used for panel A and lightweight concrete with a density of 1300 kg/m³ and strength of 43 MPa was used for panel B. Details of the panels are given in Table 4. For comparison, one equivalent stiffened steel plate was prepared for impact test. All the SCS sandwich panels are simply supported at both ends (Fig. 12(b)). But, Stiffened steel plate (SP) was bolted at two ends with the support (see Fig. 13(b)).

Test set-up

Impact tests were conducted by an instrumented drop-weight impact test machine as shown in Fig. 13. A 7.5 meter tall steel frame was constructed and firmly bolted on the concrete base to increase the rigidity of the entire frame. The SCS sandwich panel was simply supported on a base frame over a span of 2000 mm. A central impact in the vertical direction was achieved by means of smooth rollers so that the projectile can drop freely along the guide rails. A mechanical hoisting system (winch) which is controlled by a hydraulic system was used to raise the projectile to the required height. A photodiode system, comprising two laser emitters and two photodiodes, was set near the specimen to record the incident and rebound velocities of the projectile. When the projectile crosses the first photodiode, the data acquisition system was triggered and the data captured over a period of 500 milliseconds (ms) which was enough to capture the full impact event. In this study, the drop height was fixed at 4 m and the projectile mass was 1246 kg. The hemispherical projectile head diameter was 90 mm. When the projectile reached the specimen, the velocity, V₀ was approximately 95% of its free fall velocity as shown in Table 4. Five percent loss of free fall velocity was due to friction in the hoisting winch and friction between the rollers and the guide rails. Periodic checks on the tup indicated that negligible permanent deformation had occurred as a result of repeated use.

For this experiment, both the projectile and the specimens were instrumented in order to capture the damage and response of the specimens. Quartz force rings of total capacity 1050 kN were attached near the projectile tip as a load cell in order to measure the impact force. Five linear potentiometers were attached to the bottom surface of the slab at the center, and 100, 200 and 300 mm away from the center of the panel, respectively (Fig. 13(c)). They were used to determine the deflection of the panel during impact. A 16-channel digital oscilloscope with an adjusted scan rate of 1 MHz per channel was used for data acquisition. A high speed camera which was capable of capturing 1000 frames per second was used to observe the central deformation and projectile movement during the impact. The pictures obtained from the high speed camera were used for measuring the projectile displacement during impact.

Under impact testing, electrical noise may be generated due to the electronic systems used and the mechanical system adopted. The recorded signals were digitally filtered using a low-pass second-order Butterworth filtering software. A filtering frequency of 5 kHz cut-off was found to be suitable to avoid unwanted noise without affecting the signal. The same projectile was used for all the impact tests described in this paper.

Test results

Damage pattern due to the impact was almost similar for all the SCS sandwich panels with major deformation occurred at the impact point (see Fig. 14). When the projectile struck the panel, very high stress was developed at the point of the impact. This stress caused local indentation and crushing of the concrete core below the impact point. The impact stress waves traveled from the impact point to the supports and induced cracks in the concrete core. The panel gained momentum as the projectile traveled downward causing larger displacements which further induced more damage to the concrete core due to the formation of flexural cracks in the concrete core. The bottom steel plate experienced impact pressure due to large local indentation and tends to move downward and separate from concrete core as shown in Fig. 15. The separation of the bottom plate was prevented by the J-hook connectors which connected both the top and bottom steel plates. The J-hook connectors prevented the buckling of the top steel face plate which was in compression due to flexural action.

Test results show that J-hook shear connectors are effective in preventing tensile separation of the steel face plates, thus reducing the overall beam deflection and maintaining the structural integrity despite the presence of flexural and shear cracks in the concrete core. The SCS sandwich panels experienced permanent deformation after the impact and the permanent deformation shapes are given Fig. 16(a). The force-displacement curves are shown in Fig. 16(b).

From these figures, it is seen that higher strength of the concrete core helps to reduce the deformation. In the case of stiffened steel plate (SP), maximum and permanent deformation was 156 and 116 mm respectively (Table 5). Whereas, for the SCS sandwich panel A, these values were 142.7 and 106.5 mm, respectively. Although, the impact velocity is lower in case of panel SP than other SCS sandwich panels, the panel SP experienced the highest deformation. This phenomenon indicates that the SCS sandwich panels with J-hook connectors can withstand higher impact load with less deformation than the stiffened steel plates.

SCS sandwich structures subject to blast load

A series of military explosive tests was carried out under the funding of the Defense Science and Technology Agency (DSTA) in collaboration with the Centre of Protective Technology (CPT) at the National University of Singapore (NUS) to investigate the blast response of simply-supported steel-concrete composite sandwich panels. Different configurations of these panels were tested in order to evaluate the effectiveness of such structures in resisting the blast loading. Total of 6 specimens were fabricated for 3 blast tests. Two specimens were tested in each blast test. The configuration and notations of the specimens are illustrated in Fig. 17. Each specimen has a length of 1200 mm and a width of 495 mm. The core thicknesses are all 70 mm. Specimen CSP was constructed as a cellular structure with internal web as stiffeners connecting two face plates. Specimen CSP and SCSN4 were designed in such a way that both have similar level of bending moment capacity and stiffness. As shown in Table 6, only specimens of CSP and SCSN4 employed 4 mm-thick steel plates as face plates, whereas the other specimens used 3mm steel plates. J-hook shear connectors with a diameter of 10 mm were employed in specimens other than CSP and SCSNE. The connector spacing in both directions is 100 mm. All side plates and end plates were fillet welded to adjacent structural components.

All the steel plates were of grade S275 with yielding strengths of 275 to 300 MPa from the tensile coupon tests. Three different structural grades of concrete materials were employed as sandwich core: normal weight concrete (NWC), lightweight aggregate concrete (LWC) and ultra-high strength concrete (HSC). The properties of these three concrete materials were tested according to relevant ASTM standards [18,19] and summarized in Table 7. These properties are also used in the numerical study.

The reinforced concrete (RC) support structure was designed to support two specimens during each blast test. It was also designed so that the amount of equalizing pressure acting on the backside of specimens can be minimized. The larger base of the RC support was submerged in the soil to ensure stability. The specimens were secured by brackets at two ends. The brackets were secured to the RC support by 8 bolts, which were welded to the reinforcement cage.

As shown in Fig. 18, five 20 kg TNT (100 kg in total) military crater charges were arranged in an annular pattern and were placed at a standoff distance of 5 m from the specimens. The same arrangement and position of the charges were maintained in all three blasts.

The permanent deformation of all six specimens were measured and tabulated in Table 6. In blast 1, it is interesting to observe that specimen CSP experienced very large permanent deformation. Comparison between CSP and SCSN4 is shown in Fig. 19. Local buckling was observed for specimen CSP. The main failure mode is flexural. Specimen SCSN4, which subject to the same blast load, experienced relatively less damage. The maximum permanent mid-span deformation is 27 mm. Considering that the two specimens were designed with the same face plate thickness, stiffness, and static flexural capacity, the difference is mainly attributed to the concrete core that added mass and rigidity of the structural system. This demonstrated the effectiveness of the SCS sandwich composite compared with stiffened plate in terms of maintaining structural integrity and residual capacity. Comparing SCSN4 (with 4 mm face plate) and SCSN (with 3 mm face plate), it can be observed that the face plate thickness, which contributes most part to the flexural resistance of the panel, indeed plays crucial role in resisting blast load. This is due to the fact that the structural response to blast is dominated by flexure. On the contrary, it is interesting to note that specimen SCSL (with lightweight core) had a different failure mode as shown in Fig. 20. Transverse shear failure led to the formation of plastic mechanism. The excessive shear and plastic hinge developed at support during the blast caused the shear buckling of the side plates and rupture at edge. The tearing mark of shear connector was also observed at the back side of the SCSL panel as shown in Fig. 21.

It should be noted that the side plates contributed significantly to the performance of the SCS sandwich panels subject to the blast loading. Due to small core thickness and width of the SCS sandwich, which were determined by the detonation capacity, side plates contributed significantly to the overall structural integrity of the SCS panel. Therefore, specimen SCSNE without shear connectors had relatively small permanent deformation. Another phenomenon observed was that the employment of high strength concrete core did not lead to smaller permanent deformation. This may be related to the brittle nature of the ultra high strength concrete. Further research is currently on-going to improve the ductility of the ultra high strength concrete.

Energy balance model to predict the impact and blast response

When a normal structural member is subjected to an accidental impact from a falling object, it may suffer considerable damage. Depending upon possible frequency of such accidents, a decision has to be made whether to construct a heavy but expensive structure which can resist the impact load without significant damage, or a more economical one which may absorb the impact energy without collapse, but the structure may be repaired or retrofitted.

Usually, when considering heavy impact loading of the type discussed, the deflection of a member will be well outside the elastic range. The static load-deflection (R-w) curve for a sandwich beam is similar to the idealized elastic-plastic case shown in Fig. 22, where R_u is the maximum load and w_m is the deflection corresponding to point C on the curve. The area ABCD is the energy absorbed at deformation level C which is designated as E_d.

In the energy balance model, the kinetic energy of the impacting mass will be converted into strain and fracture energy due to flexure, shear, and local indentation of the panel, plastic yielding of the steel plates and crushing and cracking of the concrete core. The energy losses from material damping, surface friction, and higher modes of vibration are assumed to be negligible, and therefore not considered in the energy equations.

The impact energy absorbed by a panel in flexural response can be expressed as:

(15)E_{\mathrm{i}\mathrm{m}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{t}}=E_{\mathrm{e}}+E_{\mathrm{p}}+E_{\mathrm{m}}+E_{\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{a}\mathrm{l}},

where E_e = (1/2)R_uw_e is the maximum elastic energy (recoverable); E_p = F_p(w_p - w_e) is the plastic work (irrecoverable) when the system deflected beyond w_e; and E_m is the energy for membrane stretching of the panel (in case of fixed ended panels).

When the impact energy delivered is small, i.e., E_impact<E_e + E_local, the deflection occurs within the elastic range (w<w_e) and the panel can survive the impact without global permanent damage.

For moderate levels of impact energy E_e + E_local<E_impact<E_e + E_p + E_local, plastic deformation is induced but the maximum displacement is within the range of w_e and w_p. The SCS sandwich panels can still withstand the impact with some local damage and global plastic deformation. The magnitude of maximum plastic deformation depends on how much plastic work is needed to dissipate the impact energy.

When the impact energy is large, i.e., E_impact>E_e + E_p + E_local, the panel is unable to dissipate the total impact energy, resulting in failure. US Department of the Army [20] recommends that for a simply supported doubly reinforced concrete beam, it may be designed to attain large deflections corresponding to a support rotation of about 8 degrees which corresponds to a span to deflection ratio of L/w≤14 under dynamic loading. This criterion may be applied to SCS sandwich beams as their flexural behaviors are similar to those of doubly reinforced concrete beams. Doubly reinforced concrete beams can achieve large deflection with ductile mode of failure. Similarly, test observations [1] showed that SCS sandwich beams also can achieve large deflection with ductile deformation. In addition, SCS sandwich beam also contains steel reinforcing on both top and bottom sides of the beam which is resemble to doubly reinforced concrete beam. Hence, the deflection criteria of doubly reinforced concrete beam are adopted for SCS sandwich beam in the absence of any other guidelines available in the literature.

To ensure structural integrity of the panel, adequate number of J-hook connectors must be provided to permit ductile deformation and redistribution of forces in the connectors. However, when safety for personnel and equipment are required, a limiting deflection ratio of L/w≤53 or a limiting ductility ratio of 10, whichever governs, is specified as a reasonable estimate of the absolute magnitude of the beam deformation as suggested by US Department of the Army [20].

To use this energy balance model, the force-displacement curve (i.e. resistance function) of the structure should be known. Plastic moment resistance and deflection of SCS sandwich panel can be determined analytically which is discussed in section 3.1. Using the plastic method, the resistant function for a simply supported SCS sandwich panels as Fig. 22 can be obtained.

If the panel is fixed at both ends, tensile membrane force is activated at large-deflection of the beam. The membrane force is related to the deflection of the beam. It is assumed that the tensile membrane force is carried out by the steel face plates only. Using this assumption and in light of Wang et al. [21] considerations, for a beam with a span L, width b, and plate thickness t, and deformed Δ at its mid-span, the load carrying capacity (by membrane action) can be approximately formulated as following:

(16)F_{\mathrm{m}\mathrm{e}\mathrm{m}}=\mathrm{8}{\sigma }_{\mathrm{0}}bt{\displaystyle \frac{\mathrm{\Delta }}{L}},

where σ₀ is the yield strength of the steel plate.

In case of impact loading, dynamic effect on material strength needs to be considered. The yield strength (σ₀) in Eq. (16) needs to be modified to consider the strain rate effect. The mean uniaxial strain rate {\dot{ϵ}}_{\mathrm{d}} for impact velocity V₀ may be estimated by means of the Perrone and Bhadra’s [22] approximation which is further simplified by Jones [23] as {\dot{ϵ}}_{\mathrm{d}}=\mathrm{4}{w}_{\mathrm{m}}{V}_{\mathrm{0}}/(\mathrm{3}\sqrt{\mathrm{2}}{L}^{\mathrm{2}}) for beams, where w_m = maximum deflection in mm, and L = length of the beam in mm. The Cowper-Symonds equation has been widely used [23] to estimate the dynamic yield strength, f_yd, of the steel plate from the static yield strength, f_y, with known {\dot{ϵ}}_{\mathrm{d}} as given in Eq. (3).

Table 8 shows the calculated moment and static load carrying capacity of the SCS sandwich panels. Using equations in section 3, these parameters were calculated. Elastic deformation at ultimate static load was calculated using standard beam equation for SCS sandwiches as described elsewhere [1]. From these calculated parameters, resistance curve were drawn. Table 8 compares the calculated maximum deflection during impact and the experimental deformation. In these calculations, the contact energy was ignored because of its small value compared to the bending energy. It can be observed that the energy balance method overestimates the maximum deflection compared with the experimental results for both panels. The ratio between analysis and test ranged from 1.03 to 1.17. In view of the approximations involved in the analysis, the prediction by analytical modeling can be considered reasonably accurate for design purposes.

Conclusions

This paper discusses the behavior, analysis and design of novel SCS sandwich system with J-hook connectors subject to static, impact and blast loads. In general, SCS sandwich panels with J-hook connectors exhibit ductile behavior when they are subjected to static loads. The use of J-hook connectors effectively improves the punching and impact resistance of concrete core due to the confinement effect and they defer the crack propagation during loading. The J-hook connectors prevent the local buckling of the face plates and enhance the resistance due to tensile separation of the face plates. Analytical solutions have been proposed to predict failure modes observed from the tests including punching shear failure, shear connectors failure, flexural and yielding of steel plates. If the patch load is applied on a small area, punching failure was found to be the dominant mode of failure. The J-hook connector was found to be effective not only in resisting the transverse shear but also the vertical shear. Using the plastic yield line analysis, an upper bound solution for predicting the ultimate flexural strength of SCS sandwich slabs can be obtained.

Compared to stiffened plate panels of the same stiffness and static flexural capacity, the SCS sandwich panels show better structural performance under blast loads. Based on the permanent deformation, it is found that the steel face plate thickness is crucial to increase the structural resistance of the SCS panels to blast loads. When normal strength concrete is used, flexural failure dominates the structural resistance. Therefore, increased steel face plate thickness enhances blast resistance of the SCS sandwich panel. When the concrete core has lower strength and density (such as lightweight concrete), failure of the SCS sandwich panel is dominated by shear. The use of ultra-high strength concrete core does not improve the overall structural performance of the SCS sandwich panel due to the brittleness of the concrete. When large deformation is considered, higher density concrete core (or the mass of the sandwich structure) has some beneficial effect in reducing the permanent deformation due to blast load.

An energy balance method was applied to analyze the global response behavior, especially the energy absorption capacity of the SCS sandwich panels. Using this approach, the maximum deformation of the panel during impact can be estimated with reasonable accuracy for a given impact energy and panel configuration.

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