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A quantitative approach for determining weldability of steel is to calculate its carbon equivalent value. One definition of the carbon equivalent value Ceq is

(manganese + silicon) (copper + nickel) Ceq = Carbon H--~6--1--—-

H (chromium + molybdenum + vanadium + columbium) ^ ^

A steel is considered weldable if Ceq < 0.50% for steel in which the carbon content does not exceed 0.12% and if Ceq < 0.45% for steel in which the carbon content exceeds 0.12%.

Equation 4.1 indicates that the presence of alloying elements decreases the weldability of steel. An example of high-alloy steels is stainless steel. There are three types of stainless steel: austenitic, mar-tensitic, or ferritic. Austenitic stainless steel is the most weldable, but care must be exercised to prevent thermal distortion because heat dissipation is only about one third as fast as in plain carbon steel. Martensitic steel is also weldable but prone to cracking because of its high hardenability. Preheating and maintaining interpass temperature are often needed, especially when the carbon content is above 0.10%. Ferritic steel is weldable but decreased ductility and toughness in the weld area can present a problem. Preheating and postweld annealing may be required to minimize these undesirable effects.

4.2 Design Philosophy and Design Formats 4.2.1 Design Philosophy

Structural design should be performed to satisfy the criteria for strength, serviceability, and economy. Strength pertains to the general integrity and safety of the structure under extreme load conditions. The structure is expected to withstand occasional overloads without severe distress and damage during its lifetime. Serviceability refers to the proper functioning of the structure as related to its appearance, maintainability, and durability under normal, or service load, conditions. Deflection, vibration, permanent deformation, cracking, and corrosion are some design considerations associated with serviceability. Economy concerns with the overall material, construction, and labor costs required for the design, fabrication, erection, and maintenance processes of the structure.

4.2.2 Design Formats

At present, steel design in the United States is being performed in accordance with one of the following three formats.

4.2.2.1 Allowable Stress Design (ASD)

ASD has been in use for decades for steel design of buildings and bridges. It continues to enjoy popularity among structural engineers engaged in steel building design. In allowable stress (or working stress) design, member stresses computed under service (or working) loads are compared to some predesignated stresses called allowable stresses. The allowable stresses are often expressed as a function of the yield stress (Fy) or tensile stress (Fu) of the material divided by a factor of safety. The factor of safety is introduced to account for the effects of overload, understrength, and approximations used in structural analysis. The general format for an allowable stress design has the form

where Rn is the nominal resistance of the structural component expressed in unit of stress (i.e., the allowable stress), Qni is the service or working stresses computed from the applied working load of type i, FS is the factor of safety; i is the load type (dead, live, wind, etc.), and m is the number of load types considered in the design.

4.2.2.2 Plastic Design (PD)

PD makes use of the fact that steel sections have reserved strength beyond the first yield condition. When a section is under flexure, yielding of the cross-section occurs in a progressive manner, commencing with the fibers farthest away from the neutral axis and ending with the fibers nearest the neutral axis. This phenomenon of progressive yielding, referred to as plastification, means that the cross-section does not fail at first yield. The additional moment that a cross-section can carry in excess of the moment that corresponds to first yield varies depending on the shape of the cross-section. To quantify such reserved capacity, a quantity called shape factor, defined as the ratio of the plastic moment (moment that causes the entire cross-section to yield, resulting in the formation of a plastic hinge) to the yield moment (moment that causes yielding of the extreme fibers only) is used. The shape factor for hot-rolled I-shaped sections bent about the strong axes has a value of about 1.15. The value is about 1.50 when these sections are bent about their weak axes.

For an indeterminate structure, failure of the structure will not occur after the formation of a plastic hinge. After complete yielding of a cross-section, force (or, more precisely, moment) redistribution will occur in which the unyielded portion of the structure continues to carry some additional loadings. Failure will occur only when enough cross-sections have yielded rendering the structure unstable, resulting in the formation of a plastic collapse mechanism.

In PD, the factor of safety is applied to the applied loads to obtain factored loads. A design is said to have satisfied the strength criterion if the load effects (i.e., forces, shears, and moments) computed using these factored loads do not exceed the nominal plastic strength of the structural component. PD has the form where Rn is the nominal plastic strength of the member, Qni is the nominal load effect from loads of type i, g is the load factor, i is the load type, and m is the number of load types.

In steel building design, the load factor is given by the AISC Specification as 1.7 if Qn consists of dead and live gravity loads only, and as 1.3 if Qn consists of dead and live gravity loads acting in conjunction with wind or earthquake loads.

4.2.2.3 Load and Resistance Factor Design (LRFD)

LRFD is a probability-based limit state design procedure. A limit state is defined as a condition in which a structure or structural component becomes unsafe (i.e., a violation of the strength limit state) or unsuitable for its intended function (i.e., a violation of the serviceability limit state). In a limit state design, the structure or structural component is designed in accordance to its limits of usefulness, which may be strength related or serviceability related. In developing the LRFD method, both load effects and resistance are treated as random variables. Their variabilities and uncertainties are represented by frequency distribution curves. A design is considered satisfactory according to the strength criterion if the resistance exceeds the load effects by a comfortable margin. The concept of safety is represented schematically in Figure 4.2. Theoretically, the structure will not fail unless the load effect Q exceeds the resistance R as shown by the shaded portion in the figure. The smaller this shaded area, the less likely that the structure will fail. In actual design, a resistance factor f is applied to the nominal resistance of the structural component to account for any uncertainties associated with the determination of its strength and a load factor g is applied to each load type to account for the uncertainties and difficulties associated with determining its actual load magnitude. Different load factors are used for different load types to reflect the varying degree of uncertainties associated with the determination of load magnitudes. In general, a lower load factor is used for a load that is more predicable and a higher load factor is used for a load that is less predicable. Mathematically, the LRFD format takes the form m m

Frequency

Load effect

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