A uniaxial tension test is commonly used to determine the mechanical properties of steel, but it has no meaning for the response of the material in a structure. The test was developed as a consensus solution by producers, fabricators, designers and code writers, to have a standard by which similar materials could be compared to a common base. It does not represent the actual behavior of the steel in a structure, and was never intended to do so. To study the true behavior of the structure and how the material responds it would be better to determine the strains and deformations that will take place during actual service condition. Such characteristics reflect the real behavior, whether in the elastic or inelastic range. If stresses or forces are needed, these are easily determined by the value of the strain and the relevant material modulus, along with the type of cross section, whether elastic or inelastic. The paper addresses the properties of a range of structural steels, how these are incorporated into design standards and how the standards define deformation characteristics and demands for bolted and welded connections.
As a construction material, steel has significant advantages over many others: it offers high strength and stiffness, has adequate deformation capacity and stress redistribution ability for many applications; it does not crack or otherwise fracture under normal service conditions, and is available in several strengths and geometric forms. Finally, for most practical purposes it may also be regarded as isotropic, with resulting benefits.
On the other hand, many structures will experience “non-normal” conditions many times during fabrication, construction or service. A dynamically loaded structure such as a bridge will experience fatigue; seismic events impose major deformation demands on structural components and details; and fabrication methods such as punching of holes and all forms of welding place very high demands for local deformation ability of the steel in certain regions of the structure. The state of the art of computation technology is such that it is possible to incorporate many of these effects explicitly in the analysis phase, and the quality of fabrication and construction continues to improve as staff training and equipment are enhanced. However, much of the advanced software is not suitable for design purposes, and most of this work therefore continues to be strictly research-oriented.
It is a major problem that the material itself is not adequately understood by the professionals who specify its use for structural purposes. This includes the complexity of its chemical and metallurgical makeup, as well as the fact that the models that are used by codes to represent its mechanical response bear little resemblance to what the steel will experience under actual fabrication and service conditions. For one, it is known that steel is anisotropic, as a result of production operations as well as other plastic deformation effects. Although the anisotropy normally is of no particular consequence, it will affect the response of the steel in extreme loading and deformation demand situations. For another, the behavior of steel is a function of deformation history, to the effect that otherwise ductile steel may respond as a high strength, low ductility material, given the prior occurrence of large displacements.
In brief, the complex nature of the response is not generally appreciated. The common measures, namely, the data obtained from simple uniaxial tension tests, have no bearing on the in-structure performance. The tension test was developed as a consensus solution to have the convenience of a performance standard by which similar materials could be compared to a common base. This test does not represent the actual behavior of steel in a structure, and was never intended to.
Many designers tend to consider the requirements of the materials standards as reflecting actual performance ability. Two- and three-dimensional effects are not recognized, at least in part due to the inability of design standards to correlate such effects with the elementary material behavior models that are used. This is done in spite of the fact that multidimensional response is the key to the behavior of some of the most important regions of the structure. In particular, experience has shown that this is where problems tend to develop, much more than in any other areas of the structure [1-4].
Nevertheless, the focal point for designers continues to be the design codes. For rational decisions and proper recognition of material abilities, it is essential to appreciate the relationships between strength and deformation demands, and to assess which one governs the end result.
Basic material behavior representation
The uniaxial test uses engineering stress (current load divided by the original cross sectional area of the specimen) and strain (current deformation divided by the original gage length) to define the response of the steel, for convenience in measurement and because the test results are ultimately intended only for use in comparison with other steels and what the standard requires for the particular grade. Although convenient and suitable as representations of the steel behavior up to and slightly beyond yielding, these definitions do not recognize that the area changes as the load increases. This part of the response is recognized by the true stress and strain, which is not practical for use with practical applications. For most purposes, however, the engineering and the true strains are equal for small strains, and the stress-strain curves coincide up to and slightly beyond the yield stress. After this point the two curves will diverge, to the effect that the true stress will continue to increase until material rupture. Figure 1 illustrates the two forms of stress-strain representation.
The most common ductility measure for steel is the elongation at fracture, which is defined in terms of engineering strain. Somewhat inconveniently, this is a function of the gage length, and steel mill test reports must therefore report its magnitude as either of the commonly used 50 mm or 200 mm lengths. True strain is clearly a better ductility measure, since it reflects the total accumulated strain at the point of failure. For equal levels of engineering and true stress, the true strain is significantly smaller than the engineering strain. Conversely, for equal levels of engineering and true strain, the true stress is significantly higher than the engineering stress.
Uni- and multi-dimensional response characteristics
The preceding developments are always based on one-dimensional material behavior, with no restraint offered against deformations in the other orthogonal directions of the steel specimen. Once the yield stress is reached, plastic deformation takes place, and necking (transverse contraction) occurs in the area of the specimen where the failure ultimately will occur. For a more realistic assessment of the response of the steel under multi-dimensional restraint conditions, it has been shown that the true stress-true strain relationship is the appropriate representation, unless the yield criteria for multi-dimensional states of strain are utilized. However, this is not practical, especially in view of the need for fairly simple material definitions.
At the same time, the true stress and strain reflect the fact that the steel cannot supply the amount of deformation indicated by the results of the simple tension test. Even under minor restraint conditions, fracture takes place at strains that are significantly lower than those specified by the materials standards.
Complicating the issues further is the fact that the yield ratio has been shown to play a major role for the deformability of steel. Designating the yield ratio by Y, it is defined aswhere Fy and Fu are the mechanical properties utilized by all common materials standards. Examining a wide range of structural steels, Kato [5] showed that the deformability decreases with an increasing value of Y, and the decrease is especially pronounced for Y-values in excess of approximately 0.6. As an illustration, Table 1 gives the yield ratios and relevant mechanical properties for a number of the current American structural steels. The standard numbers are those of the American Society for Testing and Materials (ASTM); the relevant stress levels are given in units of MPa (N/mm2). These steels have very similar counterparts within European, Chinese, Japanese and Korean steelmaking practices, to mention some of the major steel production countries. Similarly, the standards published by the International Standards Organization (ISO) also reflect these types of materials.
It is clear that adequate structural performance cannot be guaranteed by basing the material choice only on the standards’ basic properties. In fact, Kato [5] recommended that in order to assure reasonable and reliable deformation capacity of steel members and connections, as a minimum, an upper limit of the yield stress and/or the yield ratio should be specified for each steel grade.
Based on the above recommendation as well as substantial research work performed in the aftermath of the 1994 Northridge earthquake, an enhanced 350 MPa steel grade was developed and marketed by steel mills in the United States, starting in 1997, using a maximum Y-value of 0.85 [6]. The specified minimum yield stress is 350 MPa; the standard also requires a maximum value of Fy of 450 MPa, and the minimum tensile strength is Fu = 450 MPa. Detailed chemistry requirements are provided, as is an upper limit on the carbon equivalent, to ensure a satisfactory weldability.
Additional response considerations
The preceding issues are further complicated by the way tension tests are performed and reported by steel producers. Specifically, the upper yield point is commonly given as the value of the representative Fy. Although the use of this property is understandable, from a production viewpoint, it is not a dependable, realistic value, since it relies heavily on the specifics of the method of testing. As noted by Lay Ref. [7], “the upper yield stress is not of relevance in design, as it is lost if small overloads or misalignments occur.” Specifically, utilizing dislocation theory as the basis for yielding or plastic deformation in steel, the upper yield point mobilizes dislocations, and the lower yield point maintains the “movement” of the dislocations. In essence, yielding is caused by crystal structure (lattice) defects, in the form of dislocations.
These issues have not been addressed by a number of studies, among them many seismic projects, their reports noting that “...50 percent of the material actually incorporated in a project will have yield strengths that exceed these mean values. For the design of facilities with stringent requirements for limiting post-earthquake damage, consideration of more conservative estimates of the actual yield strength may be warranted” [4]. The same reference notes that “Design professionals should be aware of the variation in actual properties permitted by the ASTM specifications. This is especially important for yield strength. Yield strengths for ASTM A36 material have consistently increased over the last 15 years....” [4]
As a result of these developments, the American seismic design code has specifically recognized the variability of the material properties beyond the use of a resistance factor [8]. The code has introduced the concept of the expected yield stress and the expected tensile strength, and these are used in design rather than the values provided by the material standards. As an example, the expected yield stress is given by the expression RyFy – the multiplier Ry reflects the variability of the yield stress of the particular steel grade, and this is applied in addition to the resistance factor for the relevant limit state. For example, for the most commonly used American structural steel today, A992, the value of Ry is 1.1, demonstrating that this steel grade has relatively small strength variability. For what used to be the most common structural steel, ASTM A36, with a yield stress of 250 MPa, the value of Ry is 1.5, emphasizing the very significant strength variability of this material. In fact, this level of variability was one of the reasons for the development of steel grade A992, since structural failures during the Northridge earthquake were prompted by overstrength A36 material in some members and connections. The designers realized that they could not depend on the yield stress being the specified minimum value, as given by the relevant ASTM standard, since unanticipated limit states (failures) governed the behavior of some members and connections.
Several other factors also play important roles, such as the steel production methods (e.g., conventional and thermo-mechanical control processes [9]). The changes that have taken place over the past 25 years in North America in going from iron ore and coke-based ingot steel to scrap-based continuous cast steel have resulted in materials that are significantly different, but have been clearly improved as far as metallurgy and mechanical properties are concerned. Steel chemistry and weldability, and especially the carbon and alloy contents further emphasize the complex problems facing the designer and the fabricator in the steel selection process. These issues were taken into account in the development of the criteria for what is now the most commonly used structural steel in the United States, the A992 steel [6].
Performance indications of current structural steels
Current structural steels in the United States span the range from the mild, carbon-manganese A36, to the high strength, quenched and tempered A514 and the quenched and self-tempered A913. For hot-rolled shapes the old methods have given way to continuous casting. For structural shapes in the United States, almost all production is based entirely on this technology. As a result, steel chemistry has changed perceptibly, such that steel now gains its strength less from carbon and more from a variety of alloying elements. The current steels have significantly lower levels of carbon than previous production runs. Values of C-content less than 0.10 percent are the norm; this contrasts with a carbon content of 0.2 percent and higher for earlier steels.
The lower carbon and higher alloying elements contents result in steels with acceptable strength and ductility characteristics, as defined by the material standards. Further, the lower carbon, in particular, means that weldability is significantly improved. Fracture toughness is improved as well, indicating that fatigue performance and resistance to brittle fracture are enhanced [9]. Nevertheless, localized effects of cold straightening, for example, continue to affect the performance of the steel, especially in connection regions. On the other hand, the issue of through-thickness strength and ductility, which used to be regarded as critical for the performance of seismic connections, for example, has been found to be much less important than originally conceived. In the extensive study by Dexter et al. [10] the through thickness limit state never governed the behavior. It is unfortunate that in spite of these findings, a major international design code like Eurocode 3 [11] maintains through thickness requirements that are not needed.
The basic quality and variety of structural steels available to designers and fabricators have therefore been improved significantly, yet problems persist. As demonstrated earlier in this paper, this has at least partly been caused by misinterpretation of materials standards and what they imply for the actual in-structure performance of the steel. Of equal importance are clearly functions that are controlled directly by the designer and the fabricator: it is unrealistic to expect the material to provide for all of the stiffness, strength and deformability that are needed by the structure under all expected service conditions.
An evaluation of the ductility and deformability requirements of the current American structural steel design specification for non-seismic applications [12] is provided in the following. It is emphasized that most of these requirements, where they exist, are implied rather than explicit. This has frequently been the result of an engineering tradition of focusing on stress and strength rather than strain and deformation. The AISC seismic code [8] obviously has very detailed deformation requirements, but these are necessitated by extreme performance needs and go far beyond the intent of this paper. However, a discussion of some of the seismic criteria will be provided in certain cases, since they have evolved from non-seismic requirements.
Deformation criteria for some elements and connections
General observations
Between structural strength, stiffness and deformability, the first two are supplied relatively easily, although improvements continue to be made through higher material strength and improved production methods for the steel. Further, many structures are controlled by the need for stiffness, in the form of deflection or drift limits or dynamic response characteristics. For these cases the use of higher strength steel is not advantageous. Framing system, high redundancy, well-defined load paths and less reliance on a limited number of structural elements are keys to successful performance.
Possibly of the greatest significance are the problems and solutions for the variety of connection types and details that are utilized in structures. These are the regions where the material will be exposed to the highest degrees of restraint and the highest local deformation demands, during shop fabrication and field erection, as well as during high-demand service conditions. The connections influence local ductility demands and framing performance, as evidenced by numerous examples from various fabrication and construction operations. Similarly, problems have developed during many of the earthquakes that have taken place in the past several years. Many reports of fractured welds and base metal details have been publicized. The basic concept that cyclic loads above yield for low-ductility steel will cause fracture after a few cycles (and conversely for a high-ductility steel) continues to be correct, but the problem is severely aggravated under multi-dimensional degrees of restraint.
The following examples examine some of the primary American design criteria for steel members and connections.
Tension members
Chapter D of the AISC Specification [12] detail the strength criteria for tension members. These are possibly the simplest structural elements, and the ones whose performance is closest to the uniaxial conditions of the basic tension test. The limit states of gross cross section yielding and effective net section fracture are well defined, although the reliability of the fracture case is less than that of the overall yield. The reason for this is the greater variability of the tensile strength (Fu) of the steel, as well as the influence of the geometry of the net section and the shear lag associated with the cross-sectional shape and the placement of the end connection.
Ductility is recognized through the reference to strain hardening, stress concentrations, and the importance of large deformations accompanying the yielding of the gross cross section. These observations are based on various full- and reduced-scale tension member tests, but no data are presented on actual deformation demands. However, in view of the relatively simple (other than within the end connection regions) condition of these members and their satisfactory behavior over the long-term, it is generally accepted that ductility and deformation needs have been assessed correctly. Deformation data are judged to be roughly comparable to tension specimen tests, although specific results in support of this finding are not presented. However, it is understood that the deformations that will occur in full-size tension members will be larger than those of the material tests, primarily due to residual stress, initial crookedness and eccentric application of the axial load.
Columns
Chapter E of the AISC Specification [12] gives the design criteria for columns and other compression members. Since column buckling is primarily a stability phenomenon that is not related to local or overall deformation demands, the questions of material performance are not central to the issues at hand.
Beams
Chapter F of the AISC Specification [12] addresses the design criteria for laterally supported and unsupported beams, and sections of Chapter B details local buckling and other compactness issues. Chapter I gives the criteria for composite members; these will not be examined here.
The overall behavior of beams is based on ultimate limit states involving in-plane or out-of-plane failure. For example, for a laterally supported, compact beam, the ultimate limit state is the development of a plastic hinge at the location of the maximum moment. The strength in this case is therefore governed by the fully plastic moment, Mp, of the cross section. As another example, for a laterally unsupported beam with an unbraced length larger than Lr, the ultimate limit state is governed by elastic lateral-torsional buckling.
However, in all of these cases there is no clear indication of a required deformation or rotation capacity. This is implied only through the criteria used to define compactness or the capacity of the cross section to rotate after reaching the fully plastic moment. Specifically, flange and web width-to-thickness ratios are established to allow full yielding in the cross section. In addition, the beam has to be capable of rotating a certain amount beyond what constitutes the theoretical full plastification rotation, θp, before local buckling or strain hardening occurs at the ultimate rotation value, θu. The deformation demand is therefore inelastic and concentrates on the ability of the compression flange to deform sufficiently longitudinally without buckling locally, and of the tension flange to deform sufficiently longitudinally before strain hardening or fracture occurs. The deformation capacity is therefore very much a function of the type of steel, or, in other words, the level of the yield stress as well as the shape of the stress-strain relationship. The rotation need also depends on the type of loading, to the effect that structures in seismically active areas must be capable of supplying significantly larger inelastic rotations. A summary of some of the key compactness criteria are given in Table 2.
Only the requirements for the flange of a W-shape are given in Table 2, as an example. It is interesting to note that the current seismic b/t-criterion was used for non-seismic applications as recently as the 7th edition of the allowable stress design specification of AISC (1970); the change of the constant from 0.30 to 0.38 was made in the 8th edition (1980).
In the table, the term ry is the y-axis radius of gyration; θu is the rotation developed before local buckling or strain hardening occurs; and θp is the rotation developed as the fully plastic moment is reached. The unbraced length criteria pertain to the maximum length that will allow the development of the fully plastic moment for a laterally unsupported beam. Since plastic design response characteristics are needed for seismic conditions, the requirements are much more demanding.
The key data in Table 2 are the rotation demand ratio, θu/θp. The original data for the non-seismic ratio are based on numerous beam tests, as reported by Yura et al. [13]. The history of the seismic deformation demand is not as clear; the demand ratio value of 7 to 9 is primarily based on studies by Popov and others, but specific references for this work cannot be cited.
For beams in 250 and 350 MPa yield stress steel, the rotation demand ratios are governed by the occurrence of local buckling or strain hardening in the compression flange. Limited studies have been made of higher strength steel, but research work at the US Steel Research Laboratory in the 1960s and early 1970s showed that for Fy = 700 MPa, tension flange fracture governed the beam behavior. At the time, US Steel was exploring the potential development of hot-rolled shapes in such high strength steel; this was unsuccessful as a result of the limited rotation capacity.
Studies of beams with yield stress values from 380 to 550 MPa are very limited at this time, and no definitive conclusions can be reached for such members. However, the practical utilization of higher strength beams is questionable, especially in seismic areas. This is in part caused by the “strong column, weak beam” concept, as well as the fact that beam size is frequently governed by stiffness, rather than strength. Since the modulus of elasticity is independent of the level of yield stress, using higher strength material for beams is unnecessary.
Connections
Welds and bolts are addressed in Chapter J of the AISC Specification and connection details are covered in Chapter K [12]. These are the most complex sections of the specification and the attention given to strength limit states as opposed to deformations is very substantial. This is done in spite of the fact that the deformation response often controls the actual ultimate limit state.
In the following only some of the requirements will be examined. However, in view of the severe deformation demands that are placed on many types of connections, it would seem important to assess all of these specification criteria in detail in order to gain a clear understanding of what is expected of the material when the connections are designed according to the Specification. This is especially important for many types of beam-to-column moment connections and some welded tension member splices, for which localized material deformation demands can be very high [2,3].
Welded splices in heavy shapes
The criteria for welded splices in very heavy wide-flange shapes are qualitative, but clear recognition is given to the fact that the combination of residual stress, localized high deformation demand due to fabrication operations, high localized hardness, and low fracture toughness in the core area of hot-rolled shapes have the potential for leading to cracks and propagation of cracks [2,3]. The event that caused this change in the AISC Specification was the bottom chord fracture in one of the trusses for the Orange County Civic Center in Orlando, Florida. The core area problem is much less important now, since continuous cast shapes have smaller and less pronounced cores. The shapes that cracked in the Florida structure were all ingot-based.
Overlap in fillet welded joints
Single lap welded joints will rotate when subjected to axial forces in the longitudinal direction, due to the eccentricity of one plate relative to the other. Figure 2 shows a typical connection example. The Specification recognizes the need for a certain length of overlap between the plates or members in the joint, equal to five times the thickness of the thinnest part, but not less than 25 mm. If this is satisfied, “… the resulting rotation will not be excessive....” [12]. Specifics are not given as regards to rotation magnitudes.
Short vs. long bolted joints
Short bolted joints generally deform in such a fashion that localized yielding allows for a redistribution of the bolt forces to load each bolt equally. This is not the case with long bolted joints, for which the non-uniform strain distribution leads to significant differences in the actual bolt loads. In particular, the outermost bolts will have the higher loads, leading to the potential for an “unzipping” type of failure. The AISC Specification recognizes this behavior by reducing the tabulated bolt strength values by 20 percent for connections longer than 1270 mm. However, the actual deformation demand is only accounted for qualitatively.
Bearing strength at bolt holes
This is one of the few cases where deformation and strength limit states are explicitly recognized. Research has shown that the hole deformation will increase beyond 6 mm when the nominal factored bolt load exceeds 2.4dtFu [12], where d is the bolt diameter, t is the thickness of the material and Fu is the tensile strength of the steel [14]. Under many circumstances this will be unacceptable, due to the contribution of such deformations to overall connection deformations. If the bolt load increases to 3dtFu, the limit state will be that of hole ovalization or “dishing.”
Beam-to-column connections
The criteria for the design of the details of beam-to-column connections are given in Chapter K of the AISC Specification [12]. The section provides extensive ultimate limit state criteria for local flange bending, local web yielding, web crippling, side sway web buckling, compression web buckling, panel zone web shear, unframed beam and girder ends, additional stiffeners requirements for concentrated forces, and additional doubler plate requirements for concentrated forces. It is only in the treatment of panel zone web shear that strength and deformation are explicitly recognized. It is formulated qualitatively, to the effect that different equations are used to determine the nominal strengths if panel zone deformations are considered in the frame stability analysis.
The Commentary for the Specification gives qualitative observations involving deformation needs, such as “... that flange must be sufficiently rigid to prevent deformation of the flange ......” [12]. A detailed evaluation is provided for the panel zone behavior and the importance of its deformation as regards to the story and overall drifts of the structure.
Summary
The paper has presented a discussion of issues related to performance demands for steel in structures, especially under high restraint and high dynamic load conditions. It is shown that the use of elementary materials standards requirements, which reflect uniaxial tension test response, is unacceptable as a means to assess the response of the steel in the structure during actual operating conditions.
Designers and fabricators must fully understand the material behavior. However, it is also clear that the steel cannot assure satisfactory behavior by itself. Only together, through 1) material choice, 2) local and overall structural design, and 3) shop and field fabrication techniques and operations, will overall performance demands be met. In all cases strict adherence to specified procedures is essential. Future developments may see improved material standards, particularly if upper and lower limits are placed on the specified yield stress values, as was done in the case of the steel grade ASTM A992, and/or yield ratios are defined and required.
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[2]
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[3]
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[10]
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