FEM models of composite timber-lightweight concrete floor systems

Transcription

1 FEM models of composite timber-lightweight concrete floor systems Rajcic, Vlatka. 1, Zagar, Zvonimir 2 ABSTRACT Paper presents the main principals in designing wood-lightweight concrete composite floor structures using FEM models. All design-related analyses are performed by means of the FEA COSMOS/M program. Paper emphasises some important details in FEM model design (how to choose appropriate finite elements for different types of materials, how to connect concrete slab and timber beams to work together as they really works in nature). The results obtained by COSMOS/M FEM model are compared with the results from full- scale laboratory floor test on the real model with the same geometry, boundary conditions and loads. Compared to real measured values of stresses and displacements, the FEM models show very good accuracy. They could be therefore recommended in design of composite structures. 1. INTRODUCTION One of the possible good solutions in designing new, and especially in reconstruction of old wooden floors, is usage of composite construction wood-lightweight concrete. Such constructions are made of timber beams and concrete slabs connected with shear connectors. It is important that they satisfy with their resistance, durability and serviceability as well as for seismic criteria. Since designing of such structures is not subject of any norm, only literatures are articles with experimental works with the various results for different types of connectors. We also tried to compare experimental researches for two types of connecting: discontinuous and continuous, with results from FEM modelling. That s the way to find out if the modelling is successful enough. 2. CALCULATION MODEL WITH DISCONTINUOUS TYPE OF SHEAR CONNECTORS (STEEL BOLTS) Calculation FEM model for composite floor system composed with steel bolts φ 20 was made by program package COSMOS/M at Dept. of wooden construction on Faculty of Civil Engineering in Zagreb. As could be seen on Figure 1, only one quarter of system is modelled using symmetry about x and z-axis with proper boundary conditions. Timber beams are 10 cm wide and 20 cm high, made for monolith timber (fir). Reinforced concrete slab was made from lightweight concrete with expanded granules of polystearen. During modelling, effective width of flanges is taken as distance of beam axis, what is confirmed as correct on figures of Sigma_Z stresses in concrete slab. Because the contact between two materials was made using shear connectors (steel bolts), we modelled gap of 1 mm between finite elements with timber material properties and finite elements with concrete material properties. Those elements act like couplers that take over tension or compression. We could define friction between two materials but we didn t because PVC folio was put between them. Composite action between timber a concrete slab was carried out trough steel bolts φ 20 mm. Those discontinuous shear connectors were modelled as linear elastic straight PIPE elements. They were at the constant distance of 24 cm, which satisfy Croatian Standards HRN. U. C and propositions of STEP/EUROFORTECH 13. Pipe elements are one-axis elements and they are specific case of 3D elastic BEAM elements. PIPE elements are connected to both timber and concrete finite elements. Steel bolts are 10 cm deep in the timber beams and 4 cm deep in concrete slab. Timber beams and concrete slab are modelled with SOLID elements defined by eight keypoints. While defining real constants of these elements, it s important to define material axis. Of course, main axis of SOLID element was defined in direction of timber grains (global Z-axis). SOLID element is three-dimensional element. It was defined as 1 Assistant, Mr.sc., Dept. of Wood design, Faculty of Civil Engineering, Kacic Str. 26, Croatia 2 Professor Dr., Dept. of Wood design, Faculty of Civil Engineering, Zagreb, Kacic26, Croatia

2 orthotropic for timber and isotropic for concrete material characteristics. Values of physical and mechanical properties of two materials are got from laboratory tests on proper epruvetes: Modulus of elasticity: (timber: EX=11500 MPa, EY= 300 MPa, EZ=300 MPa) (lightweight concrete: EX=EY=EZ= MPa) Poisson s coefficient: (timber: NUXY=NUXZ=NUYZ=0.3) (lightweight concrete: NUXY=NUXZ=NUYZ=0.2) Density (timber: DENS=6 kn/m 3, concrete: DENS=15.0 kn/m 3 ) Shear modulus: (timber: GXY=500 MPa, GXZ= 500 MPa, GYZ=500 MPa) (lightweight concrete: GXY=GXZ=GYZ=4300 MPa) Material characteristic for steel bolts, PIPE elements are following: (steel Fe 235, EX= MPa, NUXY=0.3, DENS=78.5 kn/m 3 ) Real model at the laboratory full-scale test was loaded using hydraulic press, across metal rail, which was modelled as THICK SHELL element. Load was according to EUROCODE 5. Boundary conditions of the model are: - fixed displacements UX and UY on the supports - longitudinal condition of symmetry, all keypoints are fixed for UZ and for rotations RX and RY - transverse symmetry conditions, all keypoints are fixed for UX displacements and for RZ and RY rotations Boundary conditions are shown on the Figure 1 where single arrow means fixed displacement and double arrow, fixed rotation about axis. Load was set as a force at node with the value of one quarter of selfweight plus imposed load. It was defined in the node of metal rail, which was on the real model at laboratory to transfer load uniformly on the composite structure. Selfweight was taken into account with option GRAVITY while activating R-STATIC analysis. Linear static analyse is carried out and results show that all the elements satisfy for set load for both stresses and deformations. From Figure 5 it could be seen that deflection due to load g+p in half of the span is 4.85 mm, that is L/625, while limit deformation is about L/300. Stress analyses shows that all the stresses are less then design values of the strengths. COSMOS/M enable calculation and graphic presentation of 10 different stresses: 1. Sigma_X, main stress in X direction 2. Sigma_Y, main stress in Y direction 3. Sigma_Z, main stress in Z direction 4. Tau_XY, shear stress in XY plane 5. Tau_YZ, shear stress in YZ plane 6. Tau_XZ, shear stress in XZ plane 7. Princ_1, first principle stress 8. Princ_2, second principle stress 9. Princ_3, third principle stress 10.Von Mises, complex stress according to Mises s theory As dominant stress, Sigma_Z is shown on Figure 4. It represents stresses due to bending. Maximal compression stress in concrete slab is 3.2 MPa and maximal tension stress in half of span is 1.5 MPa, which is taken over by reinforced mesh. Maximal tension stress in half of the span on the lower edge of timber beam is 5.2 MPa and design tension strength is 10.0 MPa. For complex state of stress (von Mises s), it could be seen that those stresses are also lower than adequate designed strength. The biggest influence on von Mises stresses come from Sigma_Z and Tau_XY stresses. Maximal Tau_XZ in concrete slab are 0.32 MPa and, in this case, it was taken over by steel bolts. Shear stresses in timber beams are less than designed shear strength. Figure 2 shows shear forces on the steel bolts. Maximal shear force on one steel bolt is 6.15 kn, while its design shear resistance is kn. 3.COMPARISON OF THE RESULTS FROM FULL-SCALE TEST AND CALCULATION MODEL OF DISCONTINUOS TYPE OF SHEAR CONNECTORS For brief comparison of the results made with calculation model and the results from full-scale laboratory test we used Figure 3 with lines of deflections for four different ways of composing structure made from two materials, with the same dimensions. There are results from laboratory test shown with thick line (real, measured data), and given with COSMOS/M. They are very close.

3 Also for comparison we put the theoretical results for ideally absolutely composion of two materials, and for uncomposed materials where deflection is calculated only for timber beams. Figure 4 shows Sigma_Z bending stresses in the most strained cross section. It could be seen that the lines of stress are with the close to the values that were measured in the laboratory full-scale test for both of materials concrete and timber. So we can conclude that this way of modelling of composite structure we get results close to the real, measured ones got from laboratory, and it is very good way of design this kind of structures. 4. CALCULATION MODEL WITH CONTINUOUS TYPE OF SHEAR CONNECTOR (STEEL PLATE) Calculation model for composite floor system composed with continuous steel plate 2 mm thick was modelled in whole size as it was tested in laboratory. It has 7928 finite elements and 9105 nodes.timber beams and concrete slab are with the same dimensions as in the last case. (beams 10/20 cm, and slab 8 cm high and 140 cm wide) Dimensions of composite structure are modelled according to model in the laboratory test.it means that whole structure is modelled. In this case, all elements from real model are included in FEM model. Timber beams and concrete slab were modelled by SOLID elements. Vertical steel plate 2 mm thick with slashes for reinforced mesh, which is also shear connector, was modelled with SHELL4 elements. Reinforced mesh put into slashes of steel plate was modelled with TRUSS3D elements. During modelling all characteristic cross sections are modelled with PLANE2D elements. Connection between two materials was achieved only with vertical steel plate, which was glued in groves of the timber beams. Gap between two material was 0.1 mm. Contact was modelled again by GAP elements to take over compression and tension on the edge. Shear forces from conjugation of two entities were taken over by steel plate. Three different types of material properties are defined for timber, steel and lightweight concrete. The values of physical and mechanical material properties are preliminary tested in laboratory on small specimens of built in materials. Material properties were: - for timber (EX=EY=EZ=11500 MPa NUXY=NUXZ=NUYZ=0.3) (GXY=GXZ=GYZ=5000MPa DENSITY=4.48 kn/m 3 ) - for lightweight concrete (EX=EY=EZ=18200 MPa NUXY=NUXZ=NUYZ=0.25) (GXY=GXZ=GYZ=7300 Mpa DENSITY=18.5 kn/m 3 ) - for steel (EX=EY=EZ= MPa NUXY=NUXZ=NUYZ=0.3) (GXY=GXZ=GYZ=84000 MPa DENSITY= 78.5 kn/m 3 ) Boundary conditions were defined as simply supported beam. The supports are translated 15 cm from the beginning and the end of the timber beams. First support is line support with all the displacement fixed, and the second support is also line support with fixed UX and UY displacements. Loads are put as forces at nodes on the first line at 1.4 m and second line on 2.8 m so that the diagram of bending moment between this two line is constant and shear force is zero. Total value of load is kn divided in 2x36 nodes as incommodes load plus selfweight, which was taken with, option GRAVITY. After STATIC analysis, we got following results: On the Figure 6, there are resultant displacements of the structure. Maximal displacement is, as it could be seen, 0.11 cm in the middle of the span, while laboratory measured results for the deflection in the middle of the span gives the result of 0.14 cm. Dominant stresses were Sigma_Z shown on the Figure 7 and Figure 8 for timber beams and lower edge of concrete slab and for upper edge of concrete slab. Maximal tension stress measured in the laboratory test were 8.4 MPa, while here on the Figure 7 it is 8.05 MPa. Lower part of the concrete slab, was in laboratory test in tension with stress of 1.7 MPa taken over by reinforced mesh. Upper edge of the concrete in compression with stress of 3.3 MPa. Similar values are got using FEM modelling. 5. CONCLUSION Using FEM package COSMOS/m and modelling composite structure with different kinds of shear connectors, we got very similar results of deformations and stresses in the structures as those achived on real full-scale testes on the same real structure. Therefore, this kind of desing is warmly recomanded for such type of structure. Also, there is a possibility of parametric design and finally using of the neural network.

4 REFERENCES: 1. COSMOS/M User Guide, Structural Researc and Analysis Corporation, Santa Monica, Blaβ, H.J., van der Linden and Schlager, M Trag-und Verformungsverhalten von Holz-Beton- Verbundkonstruktionen, STEP 3, 14/1 14/25 3. Van der Linden, Ir.M.R Load-sharing of timber-concrete composite floor system, TU Delft, Giuriani, e. and Gelfi, P Stud shear connectors in wood-concrete composite beams, 1 st Int. RILEM Symposium on Timber Engineering, Stocholm, 65-78

5 Figure 1: Boundary conditions of composite structure, only quatre is modelled Figure 2: Diagram of shear forces on steel bolts

6 LOADS (kn) REAL,MEASURED DATAS TIMBER BEAMS IDEALY COMPOSED COSMOS/M DEFLECTION (m m ) Figure 3: Comparrison of the results of deflections in the middle of the span Figure 4: Path diagram of Sigma_Z stresses in the middle of the span in marked cross section

7 Figure 5: Deformation plot with the biggest value of 4.85 mm in the middle of the span Figure 6: Resultant displacement of composite structure

8 Figure 7: Picture of Sigma_Z stresses on timber beams and lower edge of concrete slab Figure 8: Sigma_Z stresses on the upper edge of concrete slab