Analytical study is made of an elastic-perfectly plastic bar under repeated axial loading. A previous formulation on a pin-ended bar is extended here to include the effects of load eccentricity and rotational constraint at the bar ends. Basic equations are derived, based on the assumptions of planar and small deflection, and of symmetry with respect to the bar center. The end spring is allowed to yield. Numerical examples are presented to demonstrate the application of the basic equations, and adequacy is shown for any specified history of axial displacement. Diagrammatical representation of state variation provides a better understanding of the hysteretic behavior as well as the applicability of the basic equations.
Issue Section:
Technical Papers
1.
Nonaka
, T.
, 1973
, “An Elastic-Plastic Analysis of a Bar Under Repeated Axial Loading
,” Int. J. Solids Struct.
, 9
, pp. 569
–580
, (with Erratum in No. 10).2.
Nonaka
, T.
, 1977
, “Approximation of Yield Condition for the Hysteretic Behavior of a Bar Under Repeated Axial Loading
,” Int. J. Solids Struct.
, 13
, pp. 637
–643
.3.
Nonaka
, T.
, 1977
, “An Analysis for Large Deformation of an Elastic-Plastic Bar Under Repeated Axial Loading, Part—I Derivation of Basic Equations
,” Int. J. Mech. Sci.
, 19
, pp. 619
–627
.4.
Nonaka
, T.
, 1977
, “An Analysis for Large Deformation of an Elastic-Plastic Bar Under Repeated Axial Loading, Part—II Correlation with Small Deformation Theory
,” Int. J. Mech. Sci.
, 19
, pp. 631
–638
.5.
Nonaka
, T.
, 1983
, “Closed Form Formulation for the Hysteretic Behavior of a Bar Under Repeated Axial Loading, Part 1—Derivation of Basic Equations
,” Trans. Arch. Inst. Jpn.
, No.334
, pp. 1
–8
(in Japanese).6.
Nonaka
, T.
, 1984
, “Closed Form Formulation for the Hysteretic Behavior of a Bar Under Repeated Axial Loading, Part 2—Analytic Solution
,” Trans. Arch. Inst. Jpn.
, No. 338
, pp. 29
–35
(in Japanese).7.
Nonaka
, T.
, 1984
, “Closed Form Formulation for the Hysteretic Behavior of a Bar Under Repeated Axial Loading, Part 3—Plastic Straining and Characteristic Features
,” Trans. Arch. Inst. Jpn.
, No. 343
, pp. 42
–50
(in Japanese).8.
Prathuangsit
, P.
, Goel
, S. C.
, and Hanson
, R. D.
, 1978
, “Axial Hysteresis Behavior With End Restraints
,” J. Struct. Div. ASCE
, 104
, No. ST6
, pp. 2261
–2277
.9.
Fukuta
, T.
, and Yamanouchi
, H.
, 1986
, “Post-Buckling Behavior of Steel Braces With Elastically Restrained Ends
,” J. Struct. Construct. Eng., Trans. Arch. Inst. Jpn.
, No. 364
, pp. 10
–22
(in Japanese).10.
Mitani
, I.
, 1978
, “An Elastic-Plastic Analysis of a Restrained Steel Bar Under Repeated Eccentrical Axial Loading
,” Trans. Arch. Inst. Jpn.
, No.274
, pp. 65
–73
(in Japanese).11.
Higginbotham
, A. B.
, and Hanson
, R. D.
, 1976
, “Axial Hysteresis Behavior of Steel Members
,” J. Struct. Div. ASCE
, 102
, No. ST7
, Proc. Paper 12245, pp. 1365
–1381
.12.
Kahn
, L. F.
, and Hanson
, R. D.
, 1976
, “Inelastic Cycles of Axially Loaded Steel Members
,” J. Struct. Div. ASCE
, 102
, No. ST5
, Proc. Paper 12111, pp. 947
–959
.1.
Nonaka, T., 1972, “A Kinematic Approach to the Plastic Collapse Load of a Rectangular Frame With Consideration of Axial Forces,” Proc., Symposium on Plastic Analysis of Structures, Iassy, Rumania, Sept., pp. 192–220;
2.
Theoretical and Applied Mechanics, Vol. 23, University of Tokyo Press, Tokyo, pp. 301–315.
1.
Nonaka, T., and Iwai, S., 1989, “Failure of Bar Structures Under Repeated Loading,” Structural Failure, T. Wierzbicki and N. Jones, ed., John Wiley and Sons, New York, pp. 389–433.
2.
Iwai, S., Nonaka, T., Park, Y.-S., and Kameda, H., 1993, “Experimental Observation on Fatigue of Steel Members and Elements Under Very Low Load Cycles,” Structural Dynamics-Eurodyn’93 (Proc. 2nd Euro. Conf. on Structural Dynamics, Tronheim), Vol. 2, A. A. Balkema, Rotterdam, pp. 771–778.
3.
Nonaka
, T.
, 1989
, “Elastic-Plastic Bar Under Changes in Temperature and Axial Load
,” Jour. of Structural Engineering, ASCE
, 115
, No. 12
, pp. 3059
–3075
.4.
Wakabayashi, M., Nonaka, T., Nakamura, T., Morino, S., and Yoshida, N., 1973, “Experimental Studies on the Behavior of Steel Bars Under Repeated Axial Loading—Part 1, Rectangular Cross-Section,” Bulletin, Disaster Prevention Research Institute, Kyoto University, No. 16B, pp. 113–125.
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