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By Colin OConnor,Peter A Shaw,NetLibrary, Inc.

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1979:7; Nadai 1950:20 etc; Neal 1977:5; Smith and Sidebottom 1965:12f, etc). This discussion is based on the behaviour of a rectangular steel beam, with the stress-strain curve shown in Fig. 1 (b) and the moment-curvature relationship of Fig. 7. For the typical mild steel used in structural members, the ductility is large, with strains to strain-hardening of the order of 10–20 times the elastic strain at first yield. The final elongations at failure are typically much larger again, of the order of 25–30%, with an ultimate stress higher than sy.

Consider this situation: (a) Sections around D and B have experienced moments well above My in the moment curvature diagram shown in Fig. 7, with tension in the lower fibres at D and in the upper fibres at B. (b) Unloading has occurred as W approaches B and for W at B, these locked-in reactions and bending moments will cause some negative bending moments throughout the member. (c) As the load advances into the second span, it will tend to cause negative bending moments at both D and B—see Fig. 13 (c) and (d).

Consider the notched specimen shown in Fig. 21 (a). The notch is semicircular; a uniform tensile stress, s, applied to the ends of the member will cause an elastic stress concentration, of the order of 3s, at the base of the notch, the behaviour being not unlike that beside a hole in a tension member, as described by Timoshenko and Goodier (1970:90ff). Allen and Southwell (1949; see also Henrickson et al. 1958) developed an inelastic analysis for this member. 33sy. As s is increased, yield spreads slowly from the notch.

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