one or more structural members. Estimation of load limits is one of the most important aspects of design and is commonly computed by one of two methods--classical design or limit analysis Classical Design. The conservative, classical method of design(assuming monotonic or static loading) assumes that failure occurs whenever the stress at any point in a structure exceeds the yield strength of the material. Except for members that are loaded in pure tension, the fact that yielding occurs at some point in a structure has little influence on the ability of the structure to support the load. However, yielding has long his classical approach inherently assumes that or fracture and is therefore a reasonable basis for limiting applied loads the stress to cause fracture is greater than the stress to cause yield. As fracture mechanics analysis clearly shows, this may not be the case. Fracture may occur at loads less than that required to cause yield if a sufficiently large imperfection is present in the material Classical design keeps allowable stresses entirely within the elastic region and is used routinely in the design of parts Allowable stresses for static service are generally set at one-half the yield strength for ductile materials and one-sixth for brittle materials, although other fractions may be more suitable for specific applications. For very brittle materials, there may be little difference between the yield"and ultimate strength, and the latter is used in design computations. The reason for using such low fractions of yield (or ultimate) strength is to allow for such factors as possible errors computational assumptions, accidental overload, introduction of residual stress during processing, temperature effects, variations in material quality(including imperfections), degradation(for example, from corrosion), and inadvertent local increases in applied stress resulting from notch effects Classical design is also used for setting allowable stresses in other applications, for example, where fracture can occur by fatigue or stress rupture. In these instances, fatigue strength or stress-rupture strength is substituted for yield strength as a point of reference, typically with different factors of safety Limit Analysis. The upper limit in design is defined as the load at which a structure will break or collapse under a single application of force. This load can be calculated by a method known as limit analysis(Ref 1, 2). With limit analysis, it is unnecessary to estimate stress distributions, which makes stress analysis much simpler by this method than by classical design. However, limit analysis is based on the concept of tolerance to yielding in the most highly stressed regions of the structure and therefore cannot be used in designing for resistance to fatigue or elastic buckling or in designing flaw- tolerant structures Limit analysis assumes an idealized material-one that behaves elastically up to a certain yield strength, then does not work harden but undergoes an indefinite amount of plastic deformation with no change in stress. The inherent safety of a structure is more realistically estimated by limit analysis in those instances when the structure will tolerate some plastic deformation before it collapses. Because low-carbon steel, one of the most common materials used in structural members behaves somewhat like the idealized material, limit analysis is very useful to the designer, especially in the analysis of statically indeterminate structures Figure 1 illustrates the relative stress-strain behavior of a low-carbon steel, a strain-hardening material, and an idealized material-all with the same yield strength(the upper yield point for the low-carbon steel and the stress at 0. 2% offset for the strain-hardening material ) Load limits for parts made of materials that strain harden significantly when stressed in the plastic region can be estimated by limit analysis, as can those for parts made of other materials whose stress-strain behavior differs from that of the idealized material. In these situations the designer bases his design calculations on assumed strength that may actually lie well within the plastic region for the material Strain-hardening Low-carbon ste Idealized moterial Strainone or more structural members. Estimation of load limits is one of the most important aspects of design and is commonly computed by one of two methods—classical design or limit analysis. Classical Design. The conservative, classical method of design (assuming monotonic or static loading) assumes that failure occurs whenever the stress at any point in a structure exceeds the yield strength of the material. Except for members that are loaded in pure tension, the fact that yielding occurs at some point in a structure has little influence on the ability of the structure to support the load. However, yielding has long been considered a prelude to structural collapse or fracture and is therefore a reasonable basis for limiting applied loads. This classical approach inherently assumes that the stress to cause fracture is greater than the stress to cause yield. As fracture mechanics analysis clearly shows, this may not be the case. Fracture may occur at loads less than that required to cause yield if a sufficiently large imperfection is present in the material. Classical design keeps allowable stresses entirely within the elastic region and is used routinely in the design of parts. Allowable stresses for static service are generally set at one-half the yield strength for ductile materials and one-sixth for brittle materials, although other fractions may be more suitable for specific applications. For very brittle materials, there may be little difference between the “yield” and ultimate strength, and the latter is used in design computations. The reason for using such low fractions of yield (or ultimate) strength is to allow for such factors as possible errors in computational assumptions, accidental overload, introduction of residual stress during processing, temperature effects, variations in material quality (including imperfections), degradation (for example, from corrosion), and inadvertent local increases in applied stress resulting from notch effects. Classical design is also used for setting allowable stresses in other applications, for example, where fracture can occur by fatigue or stress rupture. In these instances, fatigue strength or stress-rupture strength is substituted for yield strength as a point of reference, typically with different factors of safety. Limit Analysis. The upper limit in design is defined as the load at which a structure will break or collapse under a single application of force. This load can be calculated by a method known as limit analysis (Ref 1, 2). With limit analysis, it is unnecessary to estimate stress distributions, which makes stress analysis much simpler by this method than by classical design. However, limit analysis is based on the concept of tolerance to yielding in the most highly stressed regions of the structure and therefore cannot be used in designing for resistance to fatigue or elastic buckling or in designing flaw￾tolerant structures. Limit analysis assumes an idealized material—one that behaves elastically up to a certain yield strength, then does not work harden but undergoes an indefinite amount of plastic deformation with no change in stress. The inherent safety of a structure is more realistically estimated by limit analysis in those instances when the structure will tolerate some plastic deformation before it collapses. Because low-carbon steel, one of the most common materials used in structural members, behaves somewhat like the idealized material, limit analysis is very useful to the designer, especially in the analysis of statically indeterminate structures. Figure 1 illustrates the relative stress-strain behavior of a low-carbon steel, a strain-hardening material, and an idealized material—all with the same yield strength (the upper yield point for the low-carbon steel and the stress at 0.2% offset for the strain-hardening material). Load limits for parts made of materials that strain harden significantly when stressed in the plastic region can be estimated by limit analysis, as can those for parts made of other materials whose stress-strain behavior differs from that of the idealized material. In these situations, the designer bases his design calculations on an assumed strength that may actually lie well within the plastic region for the material