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Stress and strain variation in the section of a beam for different positions of neutral axis in the elastic-plastic model. (a) Case I (1r k 0 rk 1 ); (b) Case II (0rk 0 r1); (c) Case III (1r k 0 r1).
Source publication
This article derives bending moment-axial force (M-P) interaction curves for mild steel by considering elastic-plastic and strain hardening idealisations with linear and parabolic strain hardening characteristics.
Contexts in source publication
Context 1
... are three cases for this perfectly plastic model, which depend upon the position of the neutral axis. Two cases are associated with the neutral axis lying inside the cross-section and one for it lying outside the section, as shown in Fig. 3. The relations obtained for these cases are given below. The proof of Case I is given in Appendix A. Other expressions can be derived in a similar ...
Context 2
... the first case, the neutral axis is inside the section (Fig. 3a) and there is an elastic-plastic state in tension as well as one in compression, i.e. 1rk 0 rk 1 . The M-P interaction relation obtained for this case ...
Context 3
... a large value of k, the value of the shape factor given by the above equation, approaches 1.5, which is equal to the plastic shape factor of a rectangular section. In the second case, the neutral axis is also inside the section (Fig. 3b), but the compression remains elastic, i.e. 0 rk 0 r1, whereas it is elastic-plastic in tension. The M-P interaction relation obtained for this case ...
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... the third case, the neutral axis is outside the section (Fig. 3c) so that the tension zone is in the elastic-plastic state, i.e. 0 rk 0 r1 and becomes fully plastic when k 0 ¼1. The M-P interaction relation obtained for this case ...
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... The elastic-plastic interaction curve for k¼ k 1 is close to the rigid, perfectly plastic curve for large values of the yield strains (k 1 Z10). There are three parts in the elastic-plastic curve arising due to the three positions of the neutral axis in Fig. 3. The third case, i.e. with the neutral axis outside the section in Fig. 3, represents a small zone of the interaction curve with P 40:95 for large values of k 1 (say, k 1 Z10). (b) Cases III-V of the strain hardening models in Figs. 5 and 6 are required for a continuous curve, but from a practical perspective, the portion of the ...
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... The elastic-plastic interaction curve for k¼ k 1 is close to the rigid, perfectly plastic curve for large values of the yield strains (k 1 Z10). There are three parts in the elastic-plastic curve arising due to the three positions of the neutral axis in Fig. 3. The third case, i.e. with the neutral axis outside the section in Fig. 3, represents a small zone of the interaction curve with P 40:95 for large values of k 1 (say, k 1 Z10). (b) Cases III-V of the strain hardening models in Figs. 5 and 6 are required for a continuous curve, but from a practical perspective, the portion of the interaction curve represented by these cases is very small and could be ignored ...
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... as upper and lower bounds for the purposes of failure analysis of beams of rectangular section. A uniaxial tension test provides all the parameters, which are required for the idealisation of mild steel. However, the formulation could be used to develop the interaction curves of many other ductile materials. Similarly, the total tensile force in Fig. 3(a) ...
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... The plastic moment capacity varies if the axial force (P) is considered [44]. Because the H-shaped section is a special case, the axial load should be divided into two parts. ...
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概要
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