Reliability, Brittleness, Covert Understrength Factors, and Fringe Formulas in Concrete Design Codes
Publication: Journal of Structural Engineering
Volume 132, Issue 1
Abstract
The paper analyzes the reliability consequences of the fact that the current design codes for concrete structure contain covert (or hidden) understrength (or capacity reduction) factors. This prevents distinguishing between different combinations of separate risks due to the statistical scatter of material properties, the error of the design formula, and the degree of brittleness of failure mode, and also makes any prediction of structural reliability (or survival probability) impossible. The covert formula error factor is implied by the fact that the design formula was calibrated to pass not through the mean but through the fringe (or periphery, margin) of the supporting experimental data. The covert material randomness factor is the ratio of the reduced concrete strength required for design to the mean of the strength tests. As a remedy, the covert understrength factor of design formula should be made overt, its coefficient of variation (based on the supporting test data) should be specified, and the type of probability distribution (e.g., Gaussian or Weibull) indicated (which then also implies the probability cutoff). Alternatively, the code could give the mean formula, specify its coefficient of variation and type of distribution, and either prescribe the probability cutoff or overtly declare the understrength factor. The mean of strength tests required for quality control should be figured out from the required design strength on the basis of a specified probability cutoff and the coefficient of variation of these tests. Furthermore, it is proposed that the currently used empirical understrength factor, which accounts mainly for the risks of structural brittleness (or lack of ductility), should be based on the expected maximum kinetic energy that could be imparted to the structure. The reliability integral taking into account the randomness of both the load and structural resistance is generalized for the case of multiple (statistically independent) understrength factors. Finally, it is pointed out that the currently assumed proportionality of the tensile and shear strengths to the square root of compressive strength of concrete is realistic only for the mean, but grossly underestimates the scatter of tensile and shear strengths.
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Acknowledgments
Financial support by the Infrastructure Technology Institute of Northwestern University under Grant No. 0740-357-A466 is gratefully acknowledged. The theoretical background studies were supported by National Science Foundation Grant No. NSFCMS-0301145 to Northwestern University.
References
ACI-ASCE Committee 326. (1962). “Shear and diagonal tension.” ACI J., Proc. 59, 1–30 (Jan.),
277–344 (Feb.),
352–396 (March).
American Concrete Institute (ACI). (2002). Building code requirements for structural concrete (ACI 318-02) and commentary (ACI 318R-02), Farmington Hills, Mich.
Ang, A. H.-S., and Tang, W. H. (1984). Probability concepts in engineering planning and design. Vol II. Decision, risk and reliability, Wiley, New York.
Angelakos, D., Bentz, E. C., and Collins, M. P. (2001). “Effect of concrete strength and minimum stirrups on shear strength of large members.” ACI Struct. J., 98(3), 290–300.
Bažant, Z. P. (1976). “Instability, ductility, and size effect in strain-softening concrete.” J. Eng. Mech. Div., 102(2), 331–344;
and discussions in (1977), 103, 357–358,
775–777,
104,
501–502.
Bažant, Z. P. (2002). Scaling of structural strength, Hermes Penton Science (Kogan Page Science), London;
and 2nd Ed., Elsevier, London, 2005.
Bažant, Z. P. (2003). “Probability distribution of energetic-statistical size effect in quasibrittle fracture.” Probab. Eng. Mech., in press.
Bažant, Z. P., and Becq-Giraudon, E. (1999). “Effects of size and slenderness on ductility of fracturing structures.” J. Eng. Mech., 125(3), 331–339.
Bažant, Z. P., and Cedolin, L. (1991). Stability of structures: Elastic, inelastic, fracture and damage theories, Oxford Univ., New York; and 2nd Ed., 2003, Dover, New York.
Bažant, Z. P., and Frangopol, D. M. (2002). “Size effect hidden in excessive dead load factor.” J. Struct. Eng., 128(1), 80–86.
Bažant, Z. P., and Kim, Jenn-Keun (1984). “Size effect in shear failure of longitudinally reinforced beams.” ACI J., 81, 456–468.
Bažant, Z. P., and Pang, S.-D. (2005). “Revision of reliability concepts for quasibrittle structures and size effect on probability distribution of structural strength.” Proc., 9th Int. Conf. of Structural Safety and Reliability, Univ. of Rome, Italy, in press.
Bažant, Z. P., Pijaudier-Cabot, G., and Pan, J.-Y. (1987). “Ductility, snapback, size effect, and redistribution in softening beams and frames.” J. Struct. Eng., 113(12), 2348–2364.
Bažant, Z. P., and Planas, J. (1998). Fracture and size effect in concrete and other quasibrittle materials, CRC, Boca Raton, Fla.
Bažant, Z. P., and Sun, H-H. (1987). “Size effect in diagonal shear failure: Influence of aggregate size and stirrups.” ACI Mater. J., 84(4), 259–272.
Bažant, Z. P., and Yu, Q. (2003). “Designing against size effect on shear strength of reinforced concrete beams without stirrups.” Struct. Eng. Rep. No. 03-02/A466s, Northwestern Univ., Evanston, Ill.
Bažant, Z. P., and Yu, Q. (2005a). “Designing against size effect on shear strength of reinforced concrete beams without stirrups: I. Formulation.” J. Struct. Eng., 131(12), 1877–1885.
Bažant, Z. P., and Yu, Q. (2005b). “Designing against size effect on shear strength of reinforced concrete beams without stirrups: II. Verification and calibration.” J. Struct. Eng., 131(12), 1886–1897.
Collins, M. P., and Kuchma, D. (1999). “How safe are our large, lightly reinforced concrete beams, slabs and footings.” ACI Struct. J., 96(4), 482–490.
Freudenthal, A. M., Garrelts, J. M., and Shinozuka, M. (1966). “The analysis of structural safety.” J. Struct. Div. ASCE, 92(1), 619–677.
Fuchs, W., Eligehausen, R., and Breen, J. (1995). “Concrete capacity design (CCD) approach for fastening to concrete.” ACI Struct. J., 92(1), 73–93
[with Discussion, (6), 787–802].
Haldar, A., and Mahadevan, S. (2000). Probability, reliability and statistical methods in engineering design, Wiley, New York.
Jacobsen, B., and Rosendahl, F. (1994). “The Sleipner platform accident.”Struct. Eng. Int. (IABSE, Zurich, Switzerland), 4(3), 190–193.
Madsen, H. O., Krenk, S., and Lind, N. C. (1986). Methods of structural safety, Prentice-Hall, Englewood Cliffs, N.J.
Nawy, E. C., (2003). Reinforced concrete: A fundamental approach, 5th ed., Prentice Hall (Pearson Education), Upper Saddle River, N.J. (Fig. 6.6).
Novák, D., and Bažant, Z. P. (2002). “Interaction of size effect andreliability of design: Case study of flexural strength of concrete.” First Int. Conf. on Bridge Maintenance, Safety and Management (IABMAS), Universitat Politècnica de Catalunya, Barcelona, 1–8.
Park, R., and Paulay, T. (1975). Reinforced concrete structures, Wiley, New York (Fig. 7.13).
Wang, C.-K., and Salmon, C. G. (1998). Reinforced concrete design, 6th Ed., Addison-Wesley (Longman), Menlo Park, Calif., (Fig. 5.5.1).
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 132 • Issue 1 • January 2006
Pages: 3 - 12
Copyright
© 2005 ASCE.
History
Received: Feb 9, 2004
Accepted: Mar 22, 2005
Published online: Jan 1, 2006
Published in print: Jan 2006
Notes
Note. Associate Editor: Shahram Sarkani
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