University of Sheffield The development of finite elements for 3D structural analysis in fire

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1 The development of finite elements for 3D structural analysis in fire Chaoming Yu, I. W. Burgess, Z. Huang, R. J. Plank Department of Civil and Structural Engineering StiFF 05/09/2006

2 3D composite structures Concrete-filled steel tube columns Bi-Steel panels

3 Why 3D brick elements? Complicated 3D problems. The elevated-temperature concrete material models used in a series of finite element programs, such as ABAQUS and Ansys, are too inefficient to converge. In theory, triaxial concrete failure criteria at high temperatures were still problems.

4 The development of 3D brick elements There were only slab, beam-column, spring and shear-connector elements in Vulcan. A new 3D brick element had to be developed and implemented into Vulcan. Both geometric and material non-linearities were considered.

5 The procedure 3D brick element 3D Nonlinear material law Steel Concrete Verifications Parametric studies

6 3D geometric model Static finite element equilibrium equation t t t+ t ( K + K U = R ) 0 L 0 NL t T 0 0 K L = 0 BL C B d t t 0 0 L 0V t T t 0 K NL = 0 BNL 0 S B V t t 0 0 NL 0V t T F = B Sˆ d t t L 0 0V V d V 0 t F K L, K NL are respectively the linear-strain incremental stiffness matrix and the nonlinear-strain incremental stiffness matrix; U is the vector of increments in the nodal point displacements; R is the vector of externally applied nodal point loads; F is the vector of nodal point forces equivalent to the element stresses at time t z y x t s r

7 Triaxial steel model The von Mises criterion was chosen as the yield function of steel. It changes with the temperature. Plastic theory 2 f ( J 2 ) = J 2 k = 0 k = σ 0 3 J 2 is the second invariant of the deviatoric stress tensor; k is material constant; σ 0 is the uniaxial yield stress.

8 3D concrete model The Drucker-Prager function Material degradation considered Plastic theory f ( I, J 2 ) = α I1 + J 2 k 1 = 1 α = 3 k 2 = 3 f f f f c c c c + + f f f t f t t t 0 I 1 is the first invariant of the stress tensor; α and k are material constants; f c is the uniaxial compressive strength; f t is the uniaxial tensile strength.

9 Post-failure definitions for concrete model Assumptions: After the initiation of cracking in a single principal direction, concrete is treated as an orthotropic material. Cracks can close in terms of the development of principal stresses. For the crushing failure mode, the material is assumed to lose its loadcarrying capacity completely.

10 Post-failure definitions for concrete model First cracking Crushing Symmetric σ 1 σ 1 σ 3 /f c σ 2 /f c Second cracking Crushing

11 Post-failure definitions for concrete model After the second cracking happened, the third principal stress is used to determine the next failure mode. If σ 3 f t, the third cracking occurs. If σ 3 f c, it reaches to the crushing failure.

12 No. 1 Specimen label Han-1 Dimensions h b t (mm) Validations of the developed 3D models 4 tests, which were stub concretefilled steel columns at ambient temperature, have been simulated by a series of 3D eight-noded brick elements in Vulcan. Length (mm) 300 Steel properties Yield strength (MPa) 228 Young's modulus (MPa) Concrete properties Compressive strength (MPa) 49.3 Young's modulus (MPa) Han Stephen-S Stephen-R

13 Validations of the developed 3D models

14 Comparisons with elevatedtemperature tests The fire behaviours of two concrete-filled steel columns were modelled by the developed brick elements, and presented here. Specimen label Han-R-1 Chabot- SQ-22 Dimensions h b t (mm) Bar ratio (%) Length (mm) Steel yield strength (MPa) Concrete compressive strength (MPa) Test load (kn) Fail mode Crush Crush

15 Comparisons with elevatedtemperature tests

16 Case study-bi-steel At ambient temperature, the structural behaviour of Bi- Steel panels has been studied during recent years. However, there have been few research of the behaviour in fire of Bi-Steel components or structures. In the building fire resistance context, it is necessary to do some detailed research in this field. For Bi-Steel panels, the calculation of fire resistance involves the determination of temperature distribution, deformation and stress under various types of loading.

17 3D heat transfer simulation A Bi-Steel panel without additional fire protection, exposed to the standard ISO 834 fire, is presented for thermal analysis. The finite element analysis software ABAQUS was used to generate temperature information. Because of the inherent symmetry of the case, only a cube of Bi-Steel panel was considered here. Temperature plot at mid-plane

18 3D heat transfer simulation

19 The influence of thermal parameters Effect of heat flux Fig.1 Temperature distributions along the steel bar connector Effect of steel bar connectors Fig.2 Temperature variation at mid-plane

20 The influence of thermal parameters Effect of the moisture content of concrete Fig.3 Concrete temperature variation at mid-plane Effect of the emissivity of the fire Fig.4 Temperatures at hot plate

21 3D structural analysis L Cross section view h c Parameters: Plate thickness (mm) 10 Fire ISO834 / Hydrocarbon Load ratio 0.3 / 0.5 S Boundary condition Yield strength of steel plates (MPa) 355 Bar diameter (mm) 25 Yield strength of Bars (MPa) 370 Fire Fire H c (mm) S (mm) 200 Ambient Ambient L (mm) 3140 Compressive strength of concrete (MPa)

22 The analysis of mesh sensitivity Fire At ambient temperature Ambient Total node number Total element number At elevated temperatures Finest mesh Fine mesh Medium mesh Coarse mesh

23 Structural responses of Bi-Steel in ISO834 fire

24 Comparisons in different fires Fire Ambient

25 Conclusions The developed brick element works well. Thermal behaviours of Bi-Steel panels. Structural fire behaviours of Bi-Steel panels. Underpin the theoretical basis of Bi- Steel structures. Further studies on the Bi-Steel panels.

26 Thank you! Any questions?

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