Singularities in RC Beam Elements with Finite-Length Hinges
Publication: Journal of Structural Engineering
Volume 121, Issue 1
Abstract
Several models have been presented in the literature for reinforced concrete (RC) beam elements with finite-length hinges to facilitate analyses of the inelastic response of reinforced-concrete frame structures. Such models are considered an improvement on the conventional zero-length hinge (point hinge) model, which seems an unrealistic representation of RC elements undergoing inelastic deformations and is viewed as theoretically inconsistent. This paper identifies two singularities that could arise in the formulation of member models with finite-length hinges. The singularities are more likely to be encountered in frame analysis under cyclic loads (earthquake), than under monotonically increasing loads. Two singularity points are identified in the formulation of the model. One singularity point is due to the direction dependency of the stiffness, and can be avoided if an additional condition is imposed in the formulation to take care of this factor. The other singularity point has physical significance and corresponds to the critical softening parameter, beyond which a member cannot sustain equilibrium.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Anagnostopoulos, S. A.(1981). “Inelastic beams for seismic analyses of structures.”J. Struct. Engrg., ASCE, 107(7), 1297–1312.
2.
Barnard, P. R. (1964). “The collapse of reinforced concrete beams.”Proc., Int. Symp. on the Flexural Mech. of Reinforced Concrete, ACI SP-12, Am. Concrete Inst. (ACI), Detroit, Mich., 501–520.
3.
Barnard, P. R., and Johnson, R. P. (1965). “Plastic behavior of continuous composite beams.”Proc., I.C.E., Instn. of Civ. Engrs. (ICE), London, England, Vol. 32, 180–187.
4.
Bazant, Z. P.(1976). “Instability, ductility and size effect in strain-softening concrete.”J. Engrg. Mech. Div., ASCE, 102(2), 331–344.
5.
Corley, W. G.(1966). “Rotational capacity of reinforced concrete beams.”J. Struct. Engrg., ASCE, 92(5), 121–126.
6.
Cranston, W. B. (1965). “A computer method for inelastic analysis of plane frames.”Tech. Rep. TRA/386, Cement & Concrete Assoc., Cement and Concrete Association, London, England.
7.
Darvall, P. L.(1984a). “Critical softening of hinges in portal frames.”J. Struct. Engrg., ASCE, 110(1), 157–162.
8.
Darvall, P. L.(1984b). “Load-deflection curves for elastic-softening beams.”J. Struct. Engrg., ASCE, 110(10), 2536–2541.
9.
Darvall, P. L.(1985). “Stiffness matrix for elastic-softening beams.”J. Struct. Engrg., ASCE, 111(2), 469–473.
10.
Darvall, P. L., and Mendis, P. A.(1985). “Elastic-plastic-softening analysis of plane frames.”J. Struct. Engrg., ASCE, 111(4), 871–888.
11.
Mattock, A. H. (1964). “Rotational capacity of hinging regions in reinforced concrete beams.”Proc., Int. Symp. on the Flexural Mech. of Reinforced Conc., ACI SP-12, Am. Concrete Inst. (ACI), Detroit, Mich., 143–181.
12.
Mendis, P. A. (1986). “Softening of reinforced concrete structures,” PhD thesis, Dept. of Civ. Engrg., Monash Univ., Clayton, Victoria, Australia.
13.
Meyer, C., Roufaiel, M. S. L., and Arzoumanidis, S. G. (1983). “Analysis of damaged concrete frames for cyclic loads.”Earthquake Engrg. and Struct. Dynamics, Vol. 11, 207–228.
14.
Park, R., Priestley, M. J. N., and Gill, W. D.(1982). “Ductility of square-confined concrete columns.”J. Struct. Engrg., ASCE, 108(4), 929–950.
15.
Rosenblueth, E., and Diaz de Cossio, R. (1964). “Instability considerations in limit design of concrete frames.”Proc., Int. Symp. on the Flexural Mech. of Reinforced Conc., ACI SP-12, Am. Concrete Inst. (ACI), 439–463.
16.
Roufaiel, M. S. L., and Meyer, C.(1987). “Analytical modeling of hysteretic behavior of R/C frames.”J. Struct. Engrg., ASCE, 113(3), 429–444.
17.
Sanjayan, G., and Darvall, P. L.(1988). “Discussion of `Analytical modeling of hysteretic behavior of R/C frames,' by M. S. L. Roufaiel, and C. Meyer,”J. Struct. Engrg., ASCE, 114(9), 2174–2175.
18.
Sanjayan, G. (1988). “Dynamic response of reinforced concrete structures with softening behavior,” PhD thesis, Dept. of Civ. Engrg., Monash Univ., Clayton, Victoria, Australia.
19.
Tse, D., and Darvall, P. L. (1988). “Softening hinges in reinforced concrete beams.”Res. Rep. No. 3/1988, Dept. of Civ. Engrg., Monash Univ., Clayton, Victoria, Australia.
20.
Wood, R. H. (1968). “Some controversial and curious developments in the plastic theory of structures,”Engrg. Plasticity, J. Heyman and F. A. Leckie eds., Cambridge University Press, London, England, 665–691.
Information & Authors
Information
Published In
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Jan 1, 1995
Published in print: Jan 1995
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.