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Fire Technology

, Volume 53, Issue 3, pp 1147–1170 | Cite as

Behavior of Steel–Concrete Partially Composite Beams Subjected to Fire—Part 2: Analytical Study

  • Weiyong Wang
  • Kang Wang
  • Michael D. Engelhardt
  • Guoqiang Li
Article

Abstract

This paper presents the development of an analytical model of steel–concrete partially composite beams subjected to fire. The model includes consideration of temperature dependent material properties, temperature dependent interface slip between concrete and steel, non-uniform temperature distributions throughout the cross-section and the effect of different rates of thermal expansion at the concrete–steel interface. Model predictions showed good agreement with the results of fire tests on two composite beams reported in an earlier companion paper as well as with limited experimental data published in literature. An extensive parametric study was undertaken by using the proposed model. Parameters considered in this study included geometric dimensions of the composite beam, material grades of steel and concrete, shear connection ratio, reinforcing steel ratio in the concrete slab, and load level on the beam. The parametric study clearly shows that shear connection ratio and load level significantly influence the fire performance of partially composite beams. The critical temperatures with shear connection ratio of 50%, 75% and 100% are 645°C, 602°C and 548°C, respectively, under load level of 0.6. The critical temperatures under load ratio of 0.5, 0.6 and 0.7 are 468°C, 553°C and 633°C respectively, with a shear connection ratio of 50%.

Keywords

Composite beams Analytical approach Partially composite Fire resistance 

List of Symbols

\( \sigma_{c,T} \)

Stress of concrete at elevated temperature

\( f_{c,T} \)

Ultimate stress of concrete at elevated temperature

\( \varepsilon_{c,T} \)

Strain of concrete at elevated temperature

\( \varepsilon_{c1,T} \)

Strain at the ultimate stress of concrete at elevated temperature

\( \varepsilon_{cu1,T} \)

Ultimate strain of concrete at elevated temperature

\( E_{c,T} \)

Elastic modulus of concrete at elevated temperature

\( E_{c} \)

Elastic modulus of concrete at room temperature

\( T_{c} \)

Temperature of concrete

\( \sigma_{s,T} \)

Stress of steel at elevated temperature

\( \varepsilon_{s} \)

Strain of steel

\( f_{p,T} \)

Proportional limit of steel at elevated temperature

\( f_{y,T} \)

Yield stress of steel at elevated temperature

\( E_{s,T} \)

Elastic modulus of steel at elevated temperature

\( \varepsilon_{y,T} \)

Strain of steel at elevated temperature

\( \varepsilon_{p,T} \)

Strain at the proportional limit

\( \varepsilon_{t,T} \)

Limiting strain for yield stress

\( \varepsilon_{u,T} \)

Ultimate strain of steel at elevated temperature

\( V_{T} \)

Shear load on the stud at elevated temperatures

\( V_{u} \)

Shear resistance of the stud at room temperatures

\( m \)

Material dependant parameters of shear stud

\( n \)

Material dependant parameters of shear stud

\( s \)

Slip of the stud at elevated temperatures

\( s_{u} \)

Ultimate slip of the stud at elevated temperatures

\( V_{\hbox{max} } \)

Maximum shear force of stud

\( s_{\hbox{max} } \)

Maximum slip of stud

\( V_{\hbox{min} } \)

Minimum shear force of stud

\( s_{\hbox{min} } \)

Minimum slip of stud

\( V_{j} \)

Shear force on the shear stud j

\( M_{c} \)

Interior bending moment of concrete slab

\( M_{s} \)

Interior bending moment of steel beam

\( h_{c} \)

Thickness of concrete slab

\( h_{s} \)

Height of steel beam

\( \varphi_{s,T} \)

Curvature of steel beam at elevated temperature

\( \varphi_{c,T} \)

Curvature of concrete slab at elevated temperature

\( \varepsilon_{ct,T} \)

Concrete strain at the top boundary of slab

\( \gamma \)

Relative height of compressive area of concrete slab

\( \varphi_{c,th} \)

Curvature of concrete slab results by non-uniform temperature

\( \varepsilon_{{s{\text{t}},T}} \)

Steel strain at top boundary of steel beam

\( \varepsilon_{cb,T} \)

Concrete strain at bottom boundary of slab

\( \varepsilon_{th} \)

Difference of thermal strain between steel and concrete

\( \varepsilon_{sd,T} \)

Steel strain at bottom boundary of steel beam

\( \alpha_{s} \)

Thermal expansion coefficient of steel

\( \alpha_{c} \)

Thermal expansion coefficient of concrete

\( T_{s,tf} \)

Temperature of top flange of steel beam

\( T_{c,b} \)

Temperature of concrete slab at the bottom boundary

\( A_{s} \)

Sectional area of steel beam

\( \varphi_{s,th} \)

Thermal curvature of steel beam result by non-uniform temperature

R

Load ratio of composite beam

η

Shear connection ratio of composite beam

α

Enforcing steel ratio in concrete slab

Q

Grade of steel

C

Grade of concrete

\( b_{\text{eff}} \)

Effective width of concrete slab in composite beam

Notes

Acknowledgments

This material is based upon the work supported by the Open Research fund of State Key Laboratory for Disaster Reduction in Civil Engineering (Grant number:SLDRCE-MB-05). The assistance of the staff in Ferguson Structural Engineering Laboratory in the University of Texas at Austin, and the support of China Scholarship Council are also greatly acknowledged.

References

  1. 1.
    Ranzi G, Bradford MA (2007) Composite beams with both longitudinal and transverse partial interaction subjected to elevated temperatures. Eng Struct 29:2737–2750CrossRefGoogle Scholar
  2. 2.
    Kwon G, Engelhardt MD, Klingner RE (2011) Experimental behavior of bridge beams retrofitted with postinstalled shear connectors. J Bridge Eng 16 (4):536–545CrossRefGoogle Scholar
  3. 3.
    EN 1994-1-2 (2006) Eurocode 4: design of composite steel and concrete structures-part 1–2: general rules—structural fire design. European Committee for Standardization, BrusselsGoogle Scholar
  4. 4.
    British Standards Institution (1990) BS 5950: Part 3, Section 3.1. Code of practice for design of simple and continuous composite beams. LondonGoogle Scholar
  5. 5.
    CECS200: 2006 (2006) Technical Code for Fire safety of Steel Structure in Buildings, Chinese Planning Press, BeijingGoogle Scholar
  6. 6.
    Wang W, Engelhardt MD, Li GQ et al. (2016) Behavior of steel–concrete partially composite beams subjected to fire—Part 1:Experimental study. Fire Technol. doi:  10.1007/s10694-016-0618-y.Google Scholar
  7. 7.
    Loh HY, Uy B, Bradford MA (2004) The effects of partial shear connection in the hogging moment regions of composite beams Part II—analytical study. J Constr Steel Res 60(6):921–962CrossRefGoogle Scholar
  8. 8.
    Santos HAFA, Silberschmidt VV (2014) Hybrid equilibrium finite element formulation for composite beams with partial interaction. Compos Struct 108(2):646–656CrossRefGoogle Scholar
  9. 9.
    Benedetti A, Mangoni E (2007) Analytical prediction of composite beams response in fire situations. J Constr Steel Res 63(2):221–228CrossRefGoogle Scholar
  10. 10.
    Hozjan T, Saje M, Srpcic S et al. (2011) Fire analysis of steel–concrete composite beam with interlayer slip. Comput Struct, 89(1–2):189–200CrossRefGoogle Scholar
  11. 11.
    Li GQ, Wang WY (2013) A simplified approach for fire-resistance design of steel–concrete composite beams. Steel Compos Struct 14(3):295–312CrossRefGoogle Scholar
  12. 12.
    Selden K L, Varma AH (2016) Flexural capacity of composite beams subjected to fire: fiber-based models and benchmarking. Fire Technol 52:995–1014CrossRefGoogle Scholar
  13. 13.
    Wu DY, Zhang M, Ling ZB (2010) Mechanics property analysis of steel–concrete composite beams based on relative interface slip. J East China Jiaotong Univ 21(6):27–35Google Scholar
  14. 14.
    Chen LZ (2014) The Structural Behavior of Composite Beams in Fire Considering Interface Slip and Uplift Effects. Ph.D. thesis, Tongji University, ChinaGoogle Scholar
  15. 15.
    ENV 1992-1-2 (2004) Eurocode 2: design of concrete structures, Part1-2: general rules-structural fire design, European Committee for Standardization, BrusselsGoogle Scholar
  16. 16.
    Guo ZH, Li W (1993) Deformation testing and constitutive relationship of concrete under different stress-temperature paths. J Civil Eng 26(5):58–69Google Scholar
  17. 17.
    ENV 1993-1-2 (2006) Eurocode 3: design of steel structures, Part1-2: general rules-structural fire design. European Committee for Standardization, BrusselsGoogle Scholar
  18. 18.
    Mirza O, Uy B (2009) Behavior of headed stud shear connectors for composite steel–concrete beams at elevated temperatures. J Constr Steel Res 65(3):662–674CrossRefGoogle Scholar
  19. 19.
    Wang H (2004) Experimental and theoretical study on external prestressed steel concrete composite beam. Master thesis, Tongji University, ChinaGoogle Scholar
  20. 20.
    Zhang SZ (1997) A study on the behavior of stud-connector under cyclic loading. J Harbin Inst Archit Eng 30(5):187–192.Google Scholar
  21. 21.
    Benedetti A, Mangoni E (2007) Analytical prediction of composite beams response in fire situations. J Constr Steel Res 63: 221–228CrossRefGoogle Scholar
  22. 22.
    Wainman DE, Kirby BR (1987) Compendium of UK Standard Fire Test Data, Unprotected Structural Steel-1, British Steel CorporationGoogle Scholar
  23. 23.
    MATLAB (2005) MATLAB user manual version 7.1 (R14). Math Works Incorporation, NatickGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Weiyong Wang
    • 1
    • 2
  • Kang Wang
    • 1
  • Michael D. Engelhardt
    • 3
  • Guoqiang Li
    • 2
  1. 1.College of Civil EngineeringChongqing UniversityChongqingPeople’s Republic of China
  2. 2.State Key Laboratory for Disaster Reduction in Civil EngineeringTongji UniversityShanghaiPeople’s Republic of China
  3. 3.Department of Civil, Architectural and Environmental EngineeringUniversity of Texas at AustinAustinUSA

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