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The largest stress for which Hooke’s law applies£¨ÊÊÓã©or the highest point on the straight-line portion of the stress-strain diagram is the proportional limit£¨±ÈÀý¼«ÏÞ£©. The largest stress that a material can withstand without being permanently£¨ÓÀ¾ÃµØ£©deformed is called the elastic limit£¨µ¯ÐÔ¼«ÏÞ£©. This value is seldom actually measured and for most engineering materials including structural steel is synonymous with£¨Óë..Òâ˼Ïàͬ£©the proportional limit. For this reason the term proportional elastic limit is sometimes used.

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The stress at which there is a decided£¨Ã÷ÏԵģ©increase in the elongation or strain without a corresponding increase in stress is said to be the yield stress. It is the first point on the stress-strain diagram where a tangent to£¨..µÄÇÐÏߣ©the curve is horizontal. The yield stress is probably the most important property of steel to the designer, as so many£¨ºÜ¶àµÄ£©design procedures are based on this value. Beyond the yield stress there is a range in which a considerable increase in strain occurs without increase in stress. The strain that occurs before the yield stress is referred to as the elastic strain; the strain that occurs after the yield stress, with no increase in stress, is referred to as the plastic strain. Plastic strains are usually from 10 to 15 times the elastic strains.
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Yielding of steel without stress increase may be thought to be a severe disadvantage when£¨¶ø£©in actuality£¨Êµ¼ÊÉÏ£©it is a very useful characteristic. It has often performed the wonderful£¨³öÉ«µÄ£©service of preventing failure due to omissions£¨ºöÂÔ£©or mistakes on the designer’s part£¨ÔÚ..·½Ã棩. Should£¨µ¹×°£¬±íʾÈç¹û..£© the stress at one point in a ductile steel structure reach the yield point, that part of the structure will yield locally without stress increase, thus preventing premature failure. This ductility allows the stresses in a steel structure to be readjusted£¨ÖØе÷Õû£©. Another way of describing this phenomenon is to say that very high stresses caused by fabrication, erection, or loading will tend to equalize£¨Ê¹..ƽºâ£© themselves. It might also be said that a steel structure has a reserve£¨´¢±¸£©of plastic strain that enables it to resist overloads and sudden shocks. If it did not have this ability, it might suddenly fracture, like glass or other vitreous£¨²£Á§Öʵģ©substances.
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Following£¨ÔÚ..Ö®ºó£©the plastic strain there is a range in which additional£¨¶îÍâµÄ£©stress is necessary to produce additional strain. This is called strain-hardening. This portion of the diagram is not too important to today’s designer because the strains are so large. A familiar stress-strain diagram for mild or low-carbon structural steel is shown in Fig. 10-1. Only the initial part of the curve is shown here because of the great£¨ºÜ¶àµÄ£©deformation which occurs before failure. At failure in the mild steels the total strains are from 150 to 200 times the elastic strains. The curve will actually continue up to its maximum stress value and then “tail off”£¨¼õС£©before failure. A sharp£¨¼±¾çµÄ£©reduction in the cross section of the members takes place (called “necking”¾±Ëõ) followed by failure.
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The stress-stain curve of Fig.10-1 is typical of£¨¶Ô..ÊǵäÐ͵ģ©the usual ductile structural steel and is assumed to be the same for members in tension or compression. (The compression members must be stocky£¨´Ö¶ÌµÄ£©because slender compression members subjected to compression loads tend to bend laterally£¨²àÏòµØ£©, and their properties are greatly affected by the bending moments so produced.) The shape of the diagram varies with the speed of loading, the type of steel, and the temperature. One such variation is shown in the figure by the dotted line£¨ÐéÏߣ©marked upper yield£¨±êÃ÷Çü·þÉÏÏÞ£©. This shape stress-strain curve is the result when a mild steel has the load applied rapidly, while the lower yield is the case for slow loading.