Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Second-order analysis of planar steel frames considering the effect of spread of plasticity

  • Leu, Liang-Jenq (Department of Civil Engineering, National Taiwan University) ;
  • Tsou, Ching-Huei (Department of Civil Engineering, National Taiwan University)
  • Published : 2001.04.25
⟨ Previous Next ⟩

Abstract

This paper presents a method of elastic-plastic analysis for planar steel frames that provides the accuracy of distributed plasticity methods with the computational efficiency that is greater than that of distributed plasticity methods but less than that of plastic-hinge based methods. This method accounts for the effect of spread of plasticity accurately without discretization through the cross-section of a beam-column element, which is achieved by the following procedures. First, nonlinear equations describing the relationships between generalized stresses and strains of the cross-section are derived analytically. Next, nonlinear force-deformation relationships for the beam-column element are obtained through lengthwise integration of the generalized strains. Elastic-plastic flexibility coefficients are then calculated by differentiating the above element force-deformation relationships. Finally, an elastic-plastic stiffness matrix is obtained by making use of the flexibility-stiffness transformation. Adding the conventional geometric stiffness matrix to the elastic-plastic stiffness matrix results in the tangent stiffness matrix, which can readily be used to evaluate the load carrying capacity of steel frames following standard nonlinear analysis procedures. The accuracy of the proposed method is verified by several examples that are sensitive to the effect of spread of plasticity.

Keywords

Acknowledgement

Supported by : National Science Council of the Republic of China

References

  1. Attalla, M.R., Deierlein, G.G., and McGuire, W. (1994), "Spread of plasticity: Quasi-plastic-hinge approach", J. of Struct. Eng., ASCE, 120(8), 2451-2473. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:8(2451)
  2. Attalla, M.R. (1995), "Inelastic torsional-flexural behavior and three-dimensional analysis of steel frames", Ph.D. Dissertation, Cornell University, Ithaca, N.Y., USA.
  3. Clarke, M.J., Bridge, R.Q., Hancock, G.J., and Trahair, N.S. (1992), "Advanced analysis of steel building frames", J. of Constr. Steel Res., 23, 1-29. https://doi.org/10.1016/0143-974X(92)90034-C
  4. El-Zanaty, M.H., Murray, D.W., and Bjorhovde, R. (1980), "Inelastic behavior of multistory steel frames", Struct. Engrg. Rep. No. 83, Univ. of Alberta, Edmonton, Alberta, Canada.
  5. Galambos, T.V., and Ketter, R.L. (1959), "Columns under combined bending and thrust", J. of the Eng. Mech. Div., ASCE, 85(2), 1-30.
  6. Kanchanalai, T. (1977), "The design and behavior of beam-columns in unbraced steel frames", CESRL Report No. 77-2, Univ. of Texas, Austin, Texas.
  7. King, W.S., White, D.W., and Chen, W.F. (1992), "Second-order inelastic analysis methods for steel-frame design", J. of Struct. Eng., ASCE, 118(2), 408-428. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:2(408)
  8. Liew, J.Y.R., White, D.W., and Chen, W.F. (1993a), "Second-order refined plastic-hinge analysis for frame design. Part I", J. of Struct. Eng., ASCE, 119(11), 3196-3216 https://doi.org/10.1061/(ASCE)0733-9445(1993)119:11(3196)
  9. Liew, J.Y.R., White, D.W., and Chen, W.F. (1993b), "Second-order refined plastic-hinge analysis for frame design. Part II", J. of Struct. Eng., ASCE, 119(11), 3217-3237. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:11(3217)
  10. Liew, J.Y.R., White, D.W., and Chen, W.F. (1994), "Notional-load plastic-hinge method for frame design", J. of Struct. Eng., ASCE, 120(5), 1434-1454. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:5(1434)
  11. McGuire, W., Gallagher, R.H., and Ziemian, R.D. (2000), Matrix Structural Analysis, John Wiley & Sons, New York.
  12. Yang, Y.B., and Chiou, H.T. (1987), "Rigid body motion test for nonlinear analysis with beam elements", J. of Eng. Mech., ASCE, 113(9), 1404-1419. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:9(1404)
  13. Yang, Y.B., and Shieh, M.S. (1990), "Solution method for nonlinear problems with multiple critical points", AIAA J., 28(12), 2110-2116. https://doi.org/10.2514/3.10529
  14. Yang, Y.B., and Kuo, S.R. (1994), Theory and Analysis of Nonlinear Framed Structures, Prentice-Hall, Singapore.
  15. Teh, L.H., and Clarke, M.J. (1999), "Plastic-zone analysis of 3D steel frames using beam elements", J. of Struct. Eng., ASCE, 125(11), 1328-1337. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:11(1328)
  16. Tsou, C.H. (1997), "Second-order analysis of planar steel frames considering the effect of spread of plasticity", M.S. Thesis, Department of Civil Engineering, National Taiwan University, Taipei, Taiwan, ROC (in Chinese).
  17. White, D.W. (1993), "Plastic hinge methods for advanced analysis of steel frames", J. of Constr. Steel Res., 24(2), 121-152. https://doi.org/10.1016/0143-974X(93)90059-2
  18. White, D.W., Liew, J.Y.R., and Chen, W.F. (1993), "Toward advanced analysis in LRFD", Plastic Hinge Based Methods for Advanced Analysis and Design of Steel Frames, White, D.W. and Chen, W.F., eds., SSRC, Lehigh University, Bethlehem, PA.
  19. Wolfram, S. Mathematica: A System for Doing Mathematics by Computer, 2nd ed., Addison-Wesley, Redwood City, CA.
  20. Zhou, S.P., and Chen, W.F. (1994), "Plastic-zone analysis of beam-columns and portal frames", Advanced Analysis of Steel Frames: Theory, Software, and Applications, Chen, W.F. and Toma, S., eds., CRC press, Boca Raton, FL.

Cited by

  1. Second-order flexibility-based model for nonlinear inelastic analysis of 3D semi-rigid steel frameworks vol.136, 2017, https://doi.org/10.1016/j.engstruct.2017.01.040
  2. Explicit Inelastic Stiffness for Beam Elements with Uniform and Nonuniform Cross Sections vol.134, pp.4, 2008, https://doi.org/10.1061/(ASCE)0733-9445(2008)134:4(608)
  3. An application of large displacement limit analysis to frame structures vol.33, pp.2, 2009, https://doi.org/10.12989/sem.2009.33.2.159