The use of precast concrete sandwich panels has

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1 Load-arrying apaity of omposite preast onrete sandwih panels with diagonal fiber-reinfored-polymer bar onnetors Ehab Hamed The failure modes of omposite preast onrete sandwih panels made with diagonal shear onnetors made of fiber-reinfored-polymer (FRP) bar are investigated in this paper. A mathematial model that was previously developed by the author is further enhaned and used for the analysis, whih is also ompared with test results from the literature. A parametri study that investigates key parameters in the design of preast onrete sandwih panels is presented, inluding the diameter of the diagonal FRP bars, the diameter of the steel reinforement in the wythes, and the grade of onrete. The use of preast onrete sandwih panels has inreased signifiantly in the past few years due to their superior thermal and aousti insulation properties. They are omposed of two reinfored onrete layers (wythes) separated by a layer of rigid foam insulation. Unlike traditional nonomposite panels that rely only on the interior wythe to resist the load, omposite sandwih panels rely on the omposite ation between the wythes, whih an be ahieved by using shear onnetors that are mainly made from nonmetalli, diagonal fiber-reinfored-polymer (FRP) materials. FRP onnetors are preferred by many manufaturers over traditional steel onnetors beause of their exellent thermal insulation properties and their orrosion resistane. The result of suh a ombination of materials is an energy-effiient sandwih panel that has a thinner inner wythe than a nonomposite wall, whih an be used in many more appliations than its ounterpart nonomposite wall. 1 In the past, the full advantages of preast onrete sandwih panels have not been realized due to the lak of appropriate design guidelines. This was highlighted in the PCI ommittee report 1 in 211, whih indiated the need for future researh in this area. Although many studies have foused on the partial omposite behavior of preast onrete sandwih panels at the servieability limit state, few studies have investigated their load-arrying apaity. Einea et al. 2 tested panels made with FRP bent bars as the shear onnetors. Results of this researh indiated a dutile behavior of the panels though the FRP material was 34 PCI Journal July August 217

2 linear. Salmon et al. 3 presented test results of panels under a uniformly distributed load. A finite element analysis was onduted, and it was shown that the partial omposite behavior an be desribed by a linear analysis that aounts for the elasti response of the diagonal shear onnetors and the flexural response of the reinfored onrete wythes as beams. Benayoune et al. 4 presented an experimental investigation of six eentrially loaded preast onrete sandwih panels with different slenderness ratios. The results exhibited a large satter in terms of strength, stiffness, and dutility, whih made it diffiult to establish a behavior pattern or trend. Hassan and Rizkalla developed simplified design proedures for preast onrete sandwih panels made with arbon-fiber-reinfored polymer (CFRP) grids as shear onnetors. Naito et al. 6 tested preast onrete sandwih panels with different types of ontinuous and disretely plaed shear ties under diret shear. The results showed that the different strengths and stiffnesses of the ties an signifiantly influene the postraking stiffness of the entire preast onrete sandwih panel but have only a small influene on its ultimate strength. Cuypers and Wastiels 7 highlighted the importane of arefully onsidering the assumptions made for analyzing preast onrete sandwih panels beause onrete raking leads to shifting of the global neutral axis; hene, lassial sandwih theories annot be used. Comprehensive double lap-shear testing of preast onrete sandwih panels were onduted by Choi et al. 8 and Jang et al. 9 In this paper, a theoretial model that was previously developed by the author 1 is further enhaned and used to alulate the load-arrying apaity of preast onrete sandwih panels made with diagonal FRP bar onnetors. The model in Hamed 1 aounts for raking and tension stiffening only, but it is improved here to aount for the material nonlinearity of the onrete in ompression, as well as yielding of the steel reinforement. A numerial example is presented and followed by a parametri study and a omparison of the model with test results from the literature. Model, onstitutive laws, and failure riteria For brevity, the details of the mathematial model used for the analysis are not shown here, but they an be found in detail in Hamed. 1 Figure 1 shows the sign onvention of the model. The reinfored onrete wythes are modeled as Euler-Bernoulli beams. The insulation layer is assumed to possess shear and through-the-thikness normal stiffness K (w - w ) w Insulation layer Reinfored onrete wythe Steel mesh N i N i K (u - u ) u L R Diagonal bar N i +1 N i+1 V N M N V 2 M Figure 1. Mathematial model and sign onventions of preast onrete sandwih panels. Note: K u spring stiffness in height diretion; K w spring stiffness in out-of-plane diretion; M internal bending moment in the inner reinfored onrete wythe; M internal bending moment in the outer reinfored onrete wythe; N i axial fore in the ith diagonal bar; N i + 1 axial fore in the i + 1 diagonal bar; N internal axial fore in the inner reinfored onrete wythe; N internal axial fore in the outer reinfored onrete wythe; u L longitudinal displaement at the left interfae of the middle line of the insulation layer; u R longitudinal displaement at the right interfae of the middle line of the insulation layer; V internal shear fore in the inner reinfored onrete wythe; V internal shear fore in the outer reinfored onrete wythe; w out-of-plane displaement of the inner reinfored onrete wythe; w out-of-plane displaement of the outer reinfored onrete wythe. PCI Journal July August 217 3

3 σ ε lim ε f tm ε Compression E 1 f tm E Tension f m σ ε r 2 ε r ε Figure 2. Constitutive laws of onrete. Note: E modulus of elastiity of onrete; f m mean ompressive strength of onrete; f tm mean tensile strength of onrete; α 1 parameter for tension stiffening; α 2 parameter for tension stiffening that depends on reinforement ratio and dimensions; ε strain at peak ompressive stress in onrete; ε r raking strain in onrete; ε ultimate ompression strain in onrete; lim ε onrete normal strain; σ onrete normal stress. with negligible in-plane rigidity. The insulation layer is onsidered to be two halves that are eah onneted to the adjaent reinfored onrete wythe with linear strain distribution through the thikness. In this sense, its rigidities are introdued through springs loated at the middle of its thikness (Fig. 1). The onnetion of the two reinfored onrete wythes via the diagonal FRP bar onnetor reates a truss mehanism. The reinfored onrete wythes arry the bending moment by a fore ouple, while the shear fore is arried by axial fores in the diagonal bars. Hene, for simpliity, the diagonal bars are assumed to transfer axial fores N i only. The following failure modes are onsidered in the analysis: flexural failure (either by onrete rushing or yielding of the steel) bukling of the diagonal FRP bars rupture or rushing of the diagonal FRP bars To aount for the first mode of failure, a nonlinear iterative analysis that is based on the seant modulus approah was onduted. 1 For this, eah reinfored onrete wythe was divided into a number of layers through its thikness and the stresses were examined at eah point through the height of the panel for the determination of raking, tension stiffening, and material softening in ompression. The onstitutive relation in Eq. (1) for the onrete in ompression follows Euro-International Conrete Committee (CEB) International Federation for Prestressing (FIP) 11 and adopts the model proposed by Torres et al. 12 to aount for the tension-stiffening effet (Fig. 2). where σ onrete normal stress E modulus of elastiity of onrete ε onrete normal strain f m mean ompressive strength of onrete ε strain at peak ompressive stress in onrete ε lim σ 2 ε E ε + f m ε 1 E ε + 2 f ε m ε E ε ultimate ompressive strain in onrete α 2 parameter for tension stiffening that depends on reinforement ratio and dimensions for for ε lim < ε ε ε r α 2 ε r ε α ( α f tm for ε r < ε α 2 ε r )ε r otherwise (1) 36 PCI Journal July August 217

4 ε r raking strain in onrete (determined based on the mean tensile strength as f tm /E ) 133 kn 133 kn f tm mean tensile strength of onrete α 1 parameter for tension stiffening.4 Following CEB-FIP, 11 all onrete mehanial properties (that is, E, f m, ε, ε, and f ) an be determined based on lim tm the onrete grade (harateristi strength). The onstitutive relation of the steel reinforement under both tension and ompression assuming an elasti perfetly plasti behavior is given by Eq. (2) E s ε s for ε s ε y σ s E s ε y for ε y < ε s E s ε y for ε s < ε y (2) 2.7 m mm In 4 q Out Cross setion mm diameter at 2 mm Fiber-reinforedpolymer onnetor with 1 mm diameter where σ s s ε s ε y stress of steel reinforement elasti modulus of steel reinforement strain of steel reinforement yielding strain of steel reinforement It was shown by Zong et al., 13 who investigated the bukling response of steel bars embedded in onrete, that their stress-strain urve is linear up to the yield stress, whereas bukling atually ours at the inelasti range and is haraterized by a gradual softening or hardening that depends on a number of parameters. For simpliity, the postbukling response is not aounted for here, and only an elasti perfetly plasti response is onsidered. Bukling of the diagonal FRP bars of the shear onnetor is assumed to our one the axial ompression load exeeds the Euler bukling load of the bars N r, whih is alulated by Eq. (3). where b b b N r π 2 E b I b L b 2 modulus of elastiity of the diagonal bars (3) geometrial moment of inertia of the diagonal bars bukling length of the diagonal bars 133 kn Figure 3. Geometry and loading of investigated preast onrete sandwih panel. Note: All dimensions are in millimeters unless otherwise indiated. q lateral load on the panel. 1 mm.394 in.; 1 m 3.28 ft; 1 kn.22 kip. The bukling length is taken as the distane between the onnetion points of the bars to the reinfored onrete wythes at their interfaes assuming fixed onnetions. This follows the experimental observations in Bush and Stine, 14 where push-out tests indiated no deformation of the truss diagonals within the length embedded in the onrete. Rupture or rushing of the diagonal bars is assumed to our one the stress exeeds the tensile or ompressive strength as follows: Ni fu A > b (4) where A b ross-setional area of diagonal bars f u tensile or ompressive strength of diagonal bars Numerial example A preast onrete sandwih wall that is subjeted to uniformly distributed lateral loading was investigated (Fig. 3). The spaing between the truss onnetors was 8 mm (31 in.), and therefore the analysis was onduted on a representative 8 mm width of the panel with one truss onnetor only. The panel was assumed to be simply supported at the top and bottom edges of the inner reinfored onrete wythe. Deformed steel bars of 6. mm (.24 in.) PCI Journal July August

5 Lateral load, kn/m Fully omposite Craking of outer wythe Craking of inner wythe Full raking of inner wythe Nonomposite Defletion, mm Figure 4. Load-defletion urve of preast onrete sandwih panel. Note: 1 mm.394 in.; 1 kn/m.68 kip/ft. diameter with spaing of 2 mm (8 in.) that were loated at the middle of the thikness of eah reinfored onrete wythe were used. The elasti modulus of steel was taken as 2 GPa (29, ksi), and the yielding strain was.2%. The diagonal bars were made from FRP with a bar diameter of 1. mm (.394 in.) and an inlination angle of 4 degrees. The elasti modulus of the FRP was taken as 4 GPa (6 ksi), and the tensile strength was 97 MPa (14 ksi), following Maximos et al. 1 The insulation layer was taken as expanded polystyrene with an elasti modulus of MPa (.7 ksi) and a shear modulus of 2.27 MPa (.329 ksi). The onrete had a mean ompressive strength of 38 MPa ( psi) and a tensile strength of 2.9 MPa (42 psi). The onrete properties that are used in Eq. (1) are as follows: E ε.23% ε lim.3% α 1.4 α GPa (487 ksi) To simulate real appliations of load-bearing omposite wall panels, the wall was subjeted to a ombined axial ompression fore and lateral loading. The axial fore desribes the loads that are transferred from the superstruture, suh as floors or load-arrying beams onneted to the wall. The lateral load may result from wind, hydrostati pressure, or other ation. For simulating the results, the axial load of 266 kn (9.8 kip) that was shared between the two wythes is kept onstant, while the lateral load was assumed to be applied quasi-statially and to gradually inrease until failure. Figure 4 shows the load-defletion urve of the sandwih panel along with preditions that are based on elasti fully omposite and nonomposite ations. The results reveal that first raking of the inner wythe ours at a load level Height, m Defletion, mm 1 Height, m Outer wythe Inner wythe Bending moment, knm 1 Height, m Outer wythe 2 Inner wythe Shear fore, kn 3 Height, m Outer wythe Inner wythe 1 2 Axial fore, kn 3 Figure. Strutural response under a load level of 2 kn/m (137 lb/ft). Note: 1 mm.394 in.; 1 m 3.28 ft; 1 kn.22 kip; 1 kn-m.738 kip-ft. 38 PCI Journal July August 217

6 Figure 6 shows the distribution of stresses at midheight through the thikness of the inner and outer reinfored onrete wythes at three different load levels that orrespond to first raking of the inner wythe, raking of the outer wythe, and failure. The nonlinear stress distributions obof 13.1 kn/m (.897 kip/ft), followed by raking of the outer wythe at a load of 22.1 kn/m (1.1 kip/ft). The drasti redution in stiffness that is observed at a load level of 29.3 kn/m (2.1 kip/ft) is attributed to full raking of the inner wythe, whih leads to a signifiant loss of the omposite ation in the panel. The panel loses its moment-arrying apaity shortly after full raking of the inner wythe by yielding of the steel reinforement at a load level of 32 kn/m (2.2 kip/ft), indiating a typial flexural failure. Due to onvergene issues governed by the load-ontrol approah of the analysis, the analysis was stopped at the yield point of the reinforement. Beause of the flexibility of the shear onnetors, the response of the panel annot be predited with simple models that are based on fully omposite or nonomposite ations. These aspets highlight the importane of using refined models that properly aount for the layered strutural onfiguration of sandwih panels and the interation between the layers through the shear onnetors. The failure load predited by assuming full omposite ation using typial flexural-strength design methods, whih onsists of a retangular stress blok in the onrete and yielding of the steel and an approximated lever arm of.9 times the effetive depth, equals 27.4 kn/m (1.8 kip/ft). This is slightly less than the predited failure load using the proposed detailed model. Hene, as was also shown by Salmon et al., 3 the strength of sandwih panels an be approximately and onservatively omputed assuming a full omposite panel when the failure mode is dominated by flexure. Figure shows the distribution of the deformations and internal fores through the height of the panel at a load level of 2 kn/m (1.37 kip/ft). The distributions of the fores and moments show the sharp hanges at the loations of the diagonal bar onnetions, whih also lead to the development of negative moments in the outer reinfored onrete wythe near the edges. The results quantitatively show the portion of the moment that is arried by loal bending in the reinfored onrete wythes, and the portion of the moment that is arried in terms of a fore ouple between the reinfored onrete wythes. The total bending moment equals /8, whih equals 18 kn-m (13 kip-ft). The loal bending moment in the inner and outer reinfored onrete wythes (Fig. ) equals 1.4 kn-m (1. kip-ft) and 3.4 kn-m (2. kip-ft), respetively, whih in sum are only about 26% of the total bending moment. The remaining 74% of the moment is arried in terms of a fore ouple between the reinfored onrete wythes with a lever-arm length that is equal to the thikness of the insulation layer plus half the thikness of eah wythe. Figure shows that the reinfored onrete wythes are subjeted to different axial fores due to the ombination of the applied axial ompression fore and the overall bending due to lateral loading. As mentioned, the inner reinfored onrete wythe is already raked under this load level due to bending, whih leads to a signifiant redution in its ability to arry bending moments. Figure also shows that beause the inner wythe is the one that is supported laterally, the shear fore in the outer reinfored onrete wythe drops to zero at the edges, while all of the shear fores are transferred to the supports via the inner wythe. These aspets of behavior annot be obtained using simple equivalent beam analysis that assumes full or no omposite ation. σ, MPa Craking of inner wythe Craking of outer wythe Failure 1 1 z, mm 2 3 σ, MPa Craking of inner wythe Craking of outer wythe Failure 1 1 z, mm 2 3 Figure 6. Stress distributions through the thikness of the reinfored onrete wythes at different stages. Note: z horizontal distane from the middle thikness of the inner wythe (positive to the left); z horizontal distane from the middle thikness of the outer wythe (positive to the left); σ stress in the inner reinfored onrete wythe; σ stress in the outer reinfored onrete wythe. 1 mm.394 in.; 1 MPa.14 ksi. PCI Journal July August

7 tained by the model show that the maximum ompression stress at the outer wythe is still less than the ompressive strength. Craking propagates through the entire depth of the inner wythe at the maximum load level and the raks extend to almost half the depth of the outer wythe. These observations indiate that simplified models, whih assume raking of the inner wythe only, an lead to inaurate results. The main reason for raking of both wythes is the ombined axial and bending ations of the wythes, where the external moment is arried by a fore ouple and loal bending of eah wythe. Parametri study Three main parameters that may govern the load-arrying apaity of preast onrete sandwih panels are investigated here: diameter of the fiber-reinfored polymer diagonal bars, diameter of the steel reinforement, and onrete grade. The sandwih panel investigated in the numerial study is used as a referene, and when one of the parameters is hanged, the other two are kept the same as in the referene panel. Figure 7 shows the influene of hanging the diameter of the diagonal bars on the load-defletion urve of the panel. The results are also ompared with the response obtained assuming full and nonomposite ations of the panel. The sandwih panel that ontained 6 mm (.2 in.) diameter diagonal bars failed by bukling of the ritial bars. Nevertheless, inreasing the diameter of these diagonal bars from 8 to 12 mm (.3 to.47 in.) inreases the panel stiffness but does not have an influene on its failure load, whih is a typial flexural one in this ase. This was also notied in the test results reported in Naito et al., 6 who tested different types of shear ties and indiated only a small influene of the type of shear tie on the flexural strength of the sandwih panel but with signifiant influene on the postraking response. This observation is important beause it indiates that as long as diagonal-bar shear onnetors are used and a reasonable diameter of the diagonal bars is hosen so that no bukling ours. In most ases, engineers an onservatively use simplified models that are based on full omposite ation for the strength design of preast onrete sandwih panels. Nevertheless, the preraking and postraking response at the servieability limit state is always haraterized by a partial shear interation (Fig. 7), whih requires the use of advaned models for its haraterization. Figure 8 shows the influene of hanging the diameter of the internal steel reinforement from to 12 mm (.2 to.47 in.) on the load-defletion urve of the panel. All panels failed by typial flexural failure. Unlike the influene of the diameter of the diagonal bars (Fig. 7), inreasing the diameter of the steel mesh reinforement does not influene the stiffness of the sandwih panel but signifi- Load, kn/m Fully omposite 12 mm 1 mm 8 mm 6 mm Nonomposite Defletion, mm Figure 7. Influene of the diameter of the fiber-reinfored polymer diagonal bars on the load-arrying apaity of preast onrete sandwih panels. Note: 1 mm.394 in.; 1 kn/m.68 kip/ft. Load, kn/m mm 1 mm 8 mm 6 mm mm Defletion, mm Figure 8. Influene of the diameter of the steel reinforement on the load-arrying apaity of preast onrete sandwih panels. Note: 1 mm.394 in.; 1 kn/m.68 kip/ft. Load, kn/m MPa 6 MPa 4 MPa 3 MPa 2 MPa Defletion, mm Figure 9. Influene of the grade of onrete on the loadarrying apaity of preast onrete sandwih panels. Note: 1 mm.394 in.; 1 kn/m.68 kip/ft; 1 MPa.14 ksi. 4 PCI Journal July August 217

8 antly inreases the failure load. An inrease of about 4% is expeted by inreasing the diameter of the steel mesh from to 12 mm, thereby inreasing the reinforement ratio from.16% to.92%. As expeted, the stiffness of the panel after full raking of the inner wythe at a load level of about 3 kn/m (2.1 kip/ft) is also influened by the reinforement ratio. Figure 9 shows the influene of hanging the design onrete ompressive strength from 2 to 6 MPa (29 to 87 psi) on the load-defletion urve of the panel. All panels failed by typial flexural failure. Inreasing the onrete strength slightly inreases the stiffness after first raking of the inner wythe at a load level that ranges from 12 to 1 kn/m (.82 to 1. kip/ft). Inreasing the onrete strength an also inrease the ultimate load, yet the inrease is less signifiant ompared with hanging the reinforement ratio. Comparison with test results A omparison with the test results of Salmon et al. 3 inludes the testing of two idential panels that were simply supported and tested vertially under a uniformly distributed lateral load. Due to the lak of other well-reported test results, only these test results are used for the validation of the model. The height of the sandwih panels was 914 mm (36 in.), and their width was 244 mm (96.1 in.). The thikness of the reinfored onrete wythes was 63. mm (2. in.), and that of the insulation layer was 76.2 mm (3. in.). Eah reinfored onrete wythe inluded a 6 6 (W4 W4) welded-wire steel reinforement mesh of.7 mm (.22 in.) diameter with spaing of 12 mm (.98 in.) loated at the middle of the thikness. Five 9. mm (.37 in.) nominal diameter prestressing Applied pressure, kpa Model Panel 1 test Panel 2 test Peak defletion, mm Figure 1. Theoretial and experimental load-defletion urves. Note: 1 mm.394 in.; 1 kpa.14 psi. Soure: Data from Salmon et al. (1997). strands were used in eah wythe. Prestressing was introdued in the model as an axial load, and the area of the strands was aounted for as additional reinforement with initial strain due to prestressing. The ultimate tensile strength of prestressing strands f pu was 186 MPa (27 ksi), with a jaking stress of.8f pu and a reported total prestress loss of 3%. The elasti modulus of steel was taken as 2 GPa (29, ksi), and the yield strain was.26%. The shear onnetors were made from FRP with a diameter of 9. mm (.37 in.) and an inlination angle of degrees. The modulus of elastiity of FRP was GPa (7 ksi), and its tensile strength was 41 MPa (8.2 ksi). Six rows of shear onnetors were used in the third of the span near the supports and three rows in the entral third. The insulation layer was taken as expanded polystyrene with an elasti modulus of MPa (.7 ksi) and a shear modulus of 2.27 MPa (.329 ksi). The onrete had a ompressive strength of 34. MPa ( psi), a tensile strength of 3.3 MPa (.48 ksi), and an elasti modulus of 3.44 GPa ( ksi). The strain at peak ompressive stress ε was.23%, and the ultimate strain used for the onstitutive law ε was.3%.11 lim Figure 1 shows the predited and measured load-defletion urves of the panels. The atual behavior of the two idential sandwih panels that were tested under the same onditions differed signifiantly after raking, whih shows the sensitivity of these strutures to unertain imperfetions and to other parameters that depend on the onstrution proedure and that an be different between the two panels. The predited response agreed well with the response of panel 1 at the preraking and postraking stages, as well as the ultimate load. Craking of the inner wythe was predited at an applied pressure of 3. kpa (.1 psi), whih propagated rapidly through the entire depth of the inner wythe and led to its full raking at a pressure of 4.21 kpa (.611 psi) with signifiant redution in stiffness. Craking of the outer wythe ourred at an applied pressure of.46 kpa (.792 psi). The predited flexural failure pressure by steel yielding was 6.22 kpa (.92 psi), whih agreed well with that of panel 1, whih is 6.96 kpa (1.1 psi). A similar omparison to these test results was onduted in Hamed 1 but with less orrelation beause the model in Hamed did not aount for the material nonlinearity of the onrete in ompression nor for the yielding of the steel. Conlusion This study shows that typial omposite preast onrete sandwih panels that are made with diagonal FRP bar onnetors are dominated by a flexural mode of failure that is governed by yielding of the steel reinforement. No FRP rupture was observed, and only one ase out of the thirteen PCI Journal July August

9 examined ases exhibited bukling of the diagonal bars. As suh, the diameter of the diagonal bars of the shear onnetor has a minor influene on the load-arrying apaity of the sandwih panel but signifiantly influenes its stiffness and the degree of shear interation at the servieability limit state. Alternatively, it was shown that the reinforement ratio and the onrete strength ould signifiantly inrease the load-arrying apaity. It was also shown that simple strength design approahes an be effetively and onservatively used to predit the failure load of omposite sandwih panels. Based on this study, only the thermal and orrosion harateristis of the shear onnetor should be a onern for hoosing the appropriate material (steel or FRP). It appears that dutility of the shear onnetor is not needed beause the panel will eventually fail by omplete raking and yielding of the steel reinforement before yielding or rupture of the shear onnetor ours. Hene, it is reommended that FRP onnetors be used for these appliations beause of their superior thermal and orrosion resistane despite being a linear elasti material. The overall behavior of preast onrete sandwih panels would still exhibit some level of nonlinear behavior that is mainly attributed to raking, tension stiffening, and yielding of the steel reinforement. The model presented in this study was solved by a omputationally effiient in-house omputer ode developed by the author. It an be further used to investigate additional parameters and to present design aids in terms of harts and simple equations in the future. Aknowledgments The work reported in this paper was supported by the Australian Researh Counil through Disovery Projet DP Referenes 1. PCI Committee on Preast Sandwih Wall Panels State of the Art of Preast/Prestressed Conrete Sandwih Wall Panels. PCI Journal 6 (2): Einea, A., D. C. Salmon, M. K. Tadros, and T. D. Culp A New Struturally and Thermally Effiient Preast Sandwih Panel System. PCI Journal 34 (4): Salmon, D. C., A. Einea, M. K. Tadros, and T. D. Culp Full Sale Testing of Preast Conrete Sandwih Panels. ACI Strutural Journal 94 (4): Benayoune, A., A. A. A. Samad, D. N. Trikha, A. A. Abang Ali, and A. A. Ashrabov. 26. Strutural Behaviour of Eentrially Loaded Preast Sandwih Panels. Constrution and Building Materials 2 (9): Hassan, T. K., and S. H. Rizkalla. 21. Analysis and Design Guidelines of Preast, Prestressed Conrete Composite Load-Bearing Sandwih Wall Panels Reinfored with CFRP Grid. PCI Journal (2): Naito, C., J. Hoemann, M. Bearaft, and B. Bewik Performane and Charaterization of Shear Ties for Use in Insulated Preast Conrete Sandwih Wall Panels. Journal of Strutural Engineering 138 (1): Cuypers, H., and J. Wastiels Analysis and Verifiation of the Performane of Sandwih Panels with Textile Reinfored Conrete Faes. Journal of Sandwih Strutures and Materials 13 (): Choi, K.-B., W.-C. Choi, L. Feo, S.-J. Jang, and H.- D. Yun. 21. In-Plane Shear Behavior of Insulated Preast Conrete Sandwih Panels Reinfored with Corrugated GFRP Shear Connetors. Composites Part B: Engineering, no. 79: Jang, S.-J., and H.-D. Yun. 21. Effets of Insulation Types on In-Plane Shear Behavior of Insulated Conrete Sandwih Wall Panels with GFRP Shear Connetor. Contemporary Engineering Sienes 8 (-8): Hamed, E Modeling, Analysis, and Behavior of Load-Carrying Preast Conrete Sandwih Panels. Journal of Strutural Engineering 142 (7). doi:1.161/(asce)st x CEB-FIP Code-Type Models for Strutural Behaviour of Conrete, Bakground of the Constitutive Relations and Material Models in the fib Model Code for Conrete Strutures 21. Lausanne, Switzerland: International Federation for Strutural Conrete (fib). 12. Torres, L., F. Lopez-Almansa, and L. M. Bozzo. 24. Tension-Stiffening Model for Craked Flexural Conrete Members. Journal of Strutural Engineering 13 (8): Zong, Z., S. Kunnath, and G. Monti Material Model Inorporating Bukling of Reinforing Bars in RC Columns. Journal of Strutural 42 PCI Journal July August 217

10 Engineering 14 (1). doi:1.161/(asce)st x.88. N internal axial fore in the outer reinfored onrete wythe 14. Bush, T. D., and G. L. Stine Flexural Behavior of Composite Preast Conrete Sandwih Panels with Continuous Truss Connetors. PCI Journal 39 (2): q u L lateral load on the panel longitudinal displaement at the left interfae of the middle line of the insulation layer 1. Maximos, H. N., W. A. Pong, and M. K. Tadros. 27. Behavior and Design of Composite Preast Prestressed Conrete Sandwih Panels with NU- Tie. Researh report, University of Nebraska Linoln. Notation u R longitudinal displaement at the right interfae of the middle line of the insulation layer V internal shear fore in the inner reinfored onrete wythe V internal shear fore in the outer reinfored onrete wythe A b E b E ross-setional area of diagonal truss bars modulus of elastiity of diagonal truss bars modulus of elastiity of onrete w w out-of-plane displaement of the inner reinfored onrete wythe out-of-plane displaement of the outer reinfored onrete wythe E s f m f tm modulus of elastiity of steel mean ompressive strength of onrete mean tensile strength of onrete z z horizontal distane from the middle thikness of the inner wythe (positive to the left) horizontal distane from the middle thikness of the outer wythe (positive to the left) f pu ultimate tensile strength of prestressing strands α 1 parameter for tension stiffening f u I b tensile strength of diagonal truss bars geometrial moment of inertia of diagonal truss bars α 2 ε parameter for tension stiffening that depends on reinforement ratio and dimensions strain at peak ompressive stress in onrete K u spring stiffness in height diretion ε r raking strain in onrete K w spring stiffness in out-of-plane diretion ε s strain of steel reinforement L b bukling length of diagonal truss bars ε y yielding strain of steel reinforement M internal bending moment in the inner reinfored onrete wythe M internal bending moment in the outer reinfored onrete wythe ε lim ε σ ultimate ompression strain in onrete onrete normal strain stress in the inner reinfored onrete wythe N r Euler bukling load of the diagonal bars σ stress in the outer reinfored onrete wythe N i axial fore in the ith diagonal bar σ s stress in steel reinforement N i + 1 axial fore in the i + 1 diagonal bar σ onrete normal stress N internal axial fore in the inner reinfored onrete wythe PCI Journal July August

11 About the author Ehab Hamed, PhD, is a senior leturer in the Shool of Civil and Environmental Engineering at the University of New South Wales and a member of its Centre for Infrastruture Engineering and Safety in Sydney, Australia. He reeived his PhD from the Tehnion Israel Institute of Tehnology. His researh interests inlude modeling and analysis of onrete strutures, reep, sandwih strutures, and the retrofitting of steel and onrete strutures with omposite materials. Abstrat The failure modes of omposite preast onrete sandwih panels made with diagonal shear onnetors made of fiber-reinfored-polymer (FRP) bar are investigated in this paper. A mathematial model that was previously developed by the author is further enhaned and used for the analysis, whih is also ompared with test results from the literature. The model aounts for raking; tension stiffening; nonlinear softening of the onrete in ompression; yielding of the steel reinforement; and rupture, rushing, and bukling of the FRP diagonal bars. A parametri study investigates key parameters in the design of onrete sandwih panels, inluding the diameter of the diagonal FRP bars, the reinforement ratio in the wythes, and the grade of onrete. The results explain the strutural behavior of onrete sandwih panels and provide reommendations and a basis for their design. Keywords Composite ation, failure, FRP, fiber-reinfored polymer, partial interation, sandwih panel. Review poliy This paper was reviewed in aordane with the Preast/Prestressed Conrete Institute s peer-review proess. Reader omments Please address reader omments to journal@pi.org or Preast/Prestressed Conrete Institute, /o PCI Journal, 2 W. Adams St., Suite 21, Chiago, IL 666. J 44 PCI Journal July August 217