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1.1: Structural Design 3 chapter 1 Introduction 1.1 S truc tur al De si g n T he structural design of buildin...

1.1: Structural Design 3 chapter 1 Introduction 1.1 S truc tur al De si g n T he structural design of buildings, whether of structural steel or reinforced concrete, requires the determination of the overall proportions and dimensions of the supporting framework and the selection of the cross sections of individual members. In most cases the functional design, including the establishment of the number of stories and the floor plan, will have been done by an architect, and the structural engineer must work within the constraints imposed by this design. Ideally, the engineer and architect will collaborate throughout the design process to com- plete the project in an efficient manner. In effect, however, the design can be summed up as follows: The architect decides how the building should look; the engineer must make sure that it doesn’t fall down. Although this distinction is an oversimplifica- tion, it affirms the first priority of the structural engineer: safety. Other important considerations include serviceability (how well the structure performs in terms of appearance and deflection) and economy. An economical structure requires an efficient use of materials and construction labor. Although this objective can usually be accomplished by a design that requires a minimum amount of material, savings can often be realized by using more material if it results in a simpler, more easily constructed project. In fact, ­materials account for a relatively small portion of the cost of a typical steel structure as compared with labor and other costs. A good design requires the evaluation of several framing plans—that is, dif- ferent arrangements of members and their connections. In other words, several al- ternative ­designs should be prepared and their costs compared. For each framing plan investigated, the individual components must be designed. To do so requires the structural analysis of the building frames and the computation of forces and bending moments in the individual members. Armed with this information, the structural ­designer can then select the appropriate cross section. Before any analy- Bukhanovskyy/Shutterstock.com sis, however, a decision must be made on the primary building material to be used; it will usually be reinforced concrete, structural steel, or both. Ideally, alternative designs should be prepared with each. The emphasis in this book will be on the design of individual structural steel members and their connections. The structural engineer must select and evaluate the overall structural system in order to produce an efficient and economical design but 3 Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 4 Chapter 1: Introduction FIGURE 1.1 cannot do so without a thorough understanding of the design of the components (the “building blocks”) of the structure. Thus component design is the focus of this book. Before discussing structural steel, we need to examine various types of structural members. Figure 1.1 shows a truss with vertical concentrated forces applied at the joints along the top chord. In keeping with the usual assumptions of truss analysis— pinned connections and loads applied only at the joints—each component of the truss will be a two-force member, subject to either axial compression or tension. For simply supported trusses loaded as shown—a typical loading condition—each of the top chord members will be in compression, and the bottom chord members will be in tension. The web members will either be in tension or compression, depending on their location and orientation and on the location of the loads. Other types of members can be illustrated with the rigid frame of Figure 1.2a. The members of this frame are rigidly connected by welding and can be assumed to form a continuous structure. At the supports, the members are welded to a rect- angular plate that is bolted to a concrete footing. Placing several of these frames in parallel and connecting them with additional members that are then covered with roofing material and walls produces a typical building system. Many impor- tant ­details have not been mentioned, but many small commercial buildings are constructed essentially in this manner. The design and analysis of each frame in the ­system begins with the idealization of the frame as a two-dimensional struc- ture, as shown in Figure 1.2b. Because the frame has a plane of symmetry parallel to the page, we are able to treat the frame as ­two-dimensional and represent the frame members by their centerlines. (Although it is not shown in Figure 1.1, this same ­idealization is made with trusses, and the members are usually represented by their centerlines.) Note that the supports are represented as hinges (pins), not as fixed supports. If there is a possibility that the footing will undergo a slight rota- tion, or if the connection is flexible enough to allow a slight rotation, the support must be considered to be pinned. One assumption made in the usual methods of structural analysis is that deformations are very small, which means that only a slight rotation of the support is needed to qualify it as a pinned connection. Once the geometry and support conditions of the idealized frame have been ­established, the loading must be determined. This determination usually involves ­apportioning a share of the total load to each frame. If the hypothetical structure under consideration is subjected to a uniformly distributed roof load, the portion carried by one frame will be a uniformly distributed line load measured in force per unit length, as shown in Figure 1.2b. Typical units would be kips per foot. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  1.1: Structural Design 5 FIGURE 1.2 For the loading shown in Figure 1.2b, the frame will deform as indicated by the dashed line (drawn to a greatly exaggerated scale). The individual members of the frame can be classified according to the type of behavior represented by this ­deformed shape. The horizontal members AB and BC are subjected primarily to bending, or flexure, and are called beams. The vertical member BD is subjected to couples transferred from each beam, but for the symmetrical frame shown, they are equal and ­opposite, thereby canceling each other. Thus member BD is subjected only to axial compression arising from the vertical loads. In buildings, vertical compression members such as these are referred to as columns. The other two vertical members, AE and CF, must resist not only axial compression from the vertical loads but also a significant amount of bending. Such members are called beam-columns. In reality, all members, even those classified as beams or columns, will be subjected to both bending and axial load, but in many cases, the effects are minor and can be neglected. In addition to the members described, this book covers the design of connec- tions and the following special members: composite beams, composite columns, and plate girders. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 6 Chapter 1: Introduction 1.2 Loa ds The forces that act on a structure are called loads. They belong to one of two broad categories: dead load and live load. Dead loads are those that are permanent, includ- ing the weight of the structure itself, which is sometimes called the self-weight. In ­addition to the weight of the structure, dead loads in a building include the weight of nonstructural components such as floor coverings, partitions, and suspended ceilings (with light fixtures, mechanical equipment, and plumbing). All of the loads men- tioned thus far are forces resulting from gravity and are referred to as gravity loads. Live loads, which can also be gravity loads, are those that are not as permanent as dead loads. They may or may not be acting on the structure at any given time, and the location may not be fixed. Examples of live loads include furniture, equipment, and occupants of buildings. In general, the magnitude of a live load is not as well defined as that of a dead load, and it usually must be estimated. In many cases, a structural member must be investigated for various positions of a live load so that a potential failure condition is not overlooked. If a live load is applied slowly and is not removed and reapplied an excessive num- ber of times, the structure can be analyzed as if the load were static. If the load is ap- plied suddenly, as would be the case when the structure supports a moving crane, the effects of impact must be accounted for. If the load is applied and removed many times over the life of the structure, fatigue stress becomes a problem, and its effects must be accounted for. Impact loading occurs in relatively few buildings, notably i­ ndustrial buildings, and fatigue loading is rare, with thousands of load cycles over the life of the structure required before fatigue becomes a problem. For these reasons, all loading ­conditions in this book will be treated as static, and fatigue will not be ­considered. Wind exerts a pressure or suction on the exterior surfaces of a building, and ­because of its transient nature, it properly belongs in the category of live loads. Be- cause of the relative complexity of determining wind loads, however, wind is usually considered a separate category of loading. Because lateral loads are most detrimen- tal to tall structures, wind loads are usually not as important for low buildings, but uplift on light roof systems can be critical. Although wind is present most of the time, wind loads of the magnitude considered in design are infrequent and are not considered to be fatigue loads. Earthquake loads are another special category and need to be considered only in those geographic locations where there is a reasonable probability of occurrence. A structural analysis of the effects of an earthquake requires an analysis of the structure’s response to the ground motion produced by the earthquake. Simpler methods are sometimes used in which the effects of the earthquake are simulated by a system of horizontal loads, similar to those resulting from wind pressure, act- ing at each floor level of the building. Snow is another live load that is treated as a separate category. Adding to the ­uncertainty of this load is the complication of drift, which can cause much of the load to accumulate over a relatively small area. Other types of live load are often treated as separate categories, such as hydrostatic pressure and soil pressure, but the cases we have enumerated are the ones ­ordinarily encountered in the design of structural steel building frames and their members. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  1.4: Design Specifications 7 1.3 B u ild i n g Co de s Buildings must be designed and constructed according to the provisions of a build- ing code, which is a legal document containing requirements related to such things as structural safety, fire safety, plumbing, ventilation, and accessibility to the physi- cally disabled. A building code has the force of law and is administered by a gov- ernmental entity such as a city, a county, or, for some large metropolitan areas, a consolidated government. Building codes do not give design procedures, but they do specify the design requirements and constraints that must be satisfied. Of particular importance to the structural engineer is the prescription of minimum live loads for buildings. ­Although the engineer is encouraged to investigate the actual loading conditions and attempt to determine realistic values, the structure must be able to support these ­specified minimum loads. Although some large cities have their own building codes, many municipalities will modify a “model” building code to suit their particular needs and adopt it as modified. Model codes are written by various nonprofit organizations in a form that can be easily adopted by a governmental unit. Three national code organizations have ­developed model building codes: the Uniform Building Code (International Conference of Building Officials, 1999), the Standard Building Code (Southern Building Code Congress International, 1999), and the BOCA National Build- ing Code (BOCA, 1999). (BOCA is an acronym for Building Officials and Code ­Administrators.) These codes have generally been used in different regions of the United States. The Uniform Building Code has been essentially the only one used west of the Mississippi, the Standard Building Code has been used in the southeast- ern states, and the BOCA ­National Building Code has been used in the northeast- ern part of the country. A unified building code, the International Building Code (International Code Council, 2015), has been developed to eliminate some of the inconsistencies among the three national building codes. This was a joint effort by the three code orga- nizations (ICBO, BOCA, and SBCCI). These organizations have merged into the International Code Council, and the new code has replaced the three regional codes. Although it is not a building code, ASCE 7, Minimum Design Loads for Build- ings and Other Structures (American Society of Civil Engineers, 2016) is similar in form to a building code. This standard provides load requirements in a format suit- able for adoption as part of a code. The International Building Code incorporates much of ASCE 7 in its load provisions. 1. 4 De si g n Specifi c ati o n s In contrast to building codes, design specifications give more specific guidance for the design of structural members and their connections. They present the guidelines and criteria that enable a structural engineer to achieve the objectives mandated by a building code. Design specifications represent what is considered to be good engineer- ing practice based on the latest research. They are periodically revised and ­updated by the issuance of supplements or completely new editions. As with model building codes, design specifications are written in a legal format by nonprofit ­organizations. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 8 Chapter 1: Introduction They have no legal standing on their own, but by presenting design ­criteria and limits in the form of legal mandates and prohibitions, they can easily be adopted, by refer- ence, as part of a building code. The specifications of most interest to the structural steel designer are those published by the following organizations. 1. American Institute of Steel Construction (AISC): This specification pro- vides for the design of structural steel buildings and their connections. It is the one of primary concern in this book, and we discuss it in detail (AISC, 2016a). 2. American Association of State Highway and Transportation Officials (AASHTO): This specification covers the design of highway bridges and ­related structures. It provides for all structural materials normally used in bridges, including steel, reinforced concrete, and timber (AASHTO, 2014). 3. American Railway Engineering and Maintenance-of-Way Association (AREMA): The AREMA Manual for Railway Engineering covers the design of railway bridges and related structures (AREMA, 2016). This organization was formerly known as the American Railway Engineering Association (AREA). 4. American Iron and Steel Institute (AISI): This specification deals with cold-formed steel, which we discuss in Section 1.6 of this book (AISI, 2012). 1.5 S truc tur al S teel The earliest use of iron, the chief component of steel, was for small tools, in approximately 4000 b.c. (Murphy, 1957). This material was in the form of wrought iron, produced by heating ore in a charcoal fire. In the latter part of the eighteenth century and in the early nineteenth century, cast iron and wrought iron were used in various types of bridges. Steel, an alloy of primarily iron and carbon, with fewer ­impurities and less carbon than cast iron, was first used in heavy construction in the nineteenth century. With the advent of the Bessemer converter in 1855, steel began to displace wrought iron and cast iron in construction. In the United States, the first structural steel railroad bridge was the Eads bridge, constructed in 1874 in St. Louis, Missouri (Tall, 1964). In 1884, the first building with a steel frame was completed in Chicago. The characteristics of steel that are of the most interest to structural engineers can be examined by plotting the results of a tensile test. If a test specimen is subjected to an axial load P, as shown in Figure 1.3a, the stress and strain can be computed as follows: P DL f5 and « 5 A L where f = axial tensile stress A = cross-sectional area « = axial strain L = length of specimen DL = change in length Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  1.5: Structural Steel 9 FIGURE 1.3 If the load is increased in increments from zero to the point of fracture, and stress and strain are computed at each step, a stress–strain curve such as the one shown in Figure 1.3b can be plotted. This curve is typical of a class of steel known as ductile, or mild, steel. The relationship between stress and strain is linear up to the proportional limit; the material is said to follow Hooke’s law. A peak value, the upper yield point, is quickly reached after that, followed by a leveling off at the lower yield point. The stress then remains constant, even though the strain continues to increase. At this stage of loading, the test specimen continues to elongate as long as the load is not ­removed, even though the load cannot be increased. This constant stress region is called the yield plateau, or plastic range. At a strain of approximately 12 times the strain at yield, strain hardening begins, and additional load (and stress) is required to cause additional elongation (and strain). A maximum value of stress is reached, after which the specimen begins to “neck down” as the stress decreases with increasing strain, and fracture occurs. Although the cross section is reduced during loading (the Poisson effect), the original cross-sectional area is used to compute all stresses. Stress computed in this way is known as engineering stress. If the original length is used to compute the strain, it is called engineering strain. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 10 Chapter 1: Introduction Steel exhibiting the behavior shown in Figure 1.3b is called ductile because of its ability to undergo large deformations before fracturing. Ductility can be mea- sured by the elongation, defined as Lf 2 L0 e5 3 100(1.1) L0 where e = elongation (expressed as a percent) Lf = length of the specimen at fracture L 0 = original length The elastic limit of the material is a stress that lies between the proportional limit and the upper yield point. Up to this stress, the specimen can be unloaded without permanent deformation; the unloading will be along the linear portion of the diagram, the same path followed during loading. This part of the stress–strain diagram is called the elastic range. Beyond the elastic limit, unloading will be along a straight line parallel to the initial linear part of the loading path, and there will be a permanent strain. For example, if the load is removed at point A in Figure 1.3b, the unloading will be along line AB, resulting in the permanent strain OB. Figure 1.4 shows an idealized version of this stress–strain curve. The propor- tional limit, elastic limit, and the upper and lower yield points are all very close to one another and are treated as a single point called the yield point, defined by the stress Fy. The other point of interest to the structural engineer is the maximum value of stress that can be ­attained, called the ultimate tensile strength, Fu. The shape of this curve is typical of mild structural steels, which are different from one another primarily in the values of Fy and Fu. The ratio of stress to strain within the elastic range, denoted E and called Young’s modulus, or modulus of elasticity, is the same for all structural steels and has a value of 29,000,000 psi (pounds per square inch) or 29,000 ksi (kips per square inch). Figure 1.5 shows a typical stress–strain curve for high-strength steels, which are less ductile than the mild steels discussed thus far. Although there is a linear elastic FIGURE 1.4 f Fu Fy E 1 e Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  1.5: Structural Steel 11 FIGURE 1.5 portion and a distinct tensile strength, there is no well-defined yield point or yield plateau. To use these higher-strength steels in a manner consistent with the use of ductile steels, some value of stress must be chosen as a value for F y so that the same procedures and formulas can be used with all structural steels. Although there is no yield point, one needs to be defined. As previously shown, when a steel is stressed beyond its elastic limit and then unloaded, the path followed to zero stress will not be the original path from zero stress; it will be along a line having the slope of the linear portion of the path followed during loading—that is, a slope equal to E, the modulus of elasticity. Thus there will be a residual strain, or permanent set, after unloading. The yield stress for steel with a stress–strain curve of the type shown in Figure 1.5 is called the yield strength and is ­defined as the stress at the point of unloading that corresponds to a permanent strain of some arbitrarily defined amount. A strain of 0.002 is usually selected, and this method of determining the yield strength is called the 0.2% offset method. As previously mentioned, the two properties usually needed in structural steel design are Fu and Fy, ­regardless of the shape of the stress–strain curve and r­ egardless of how Fy was obtained. For this reason, the generic term yield stress is used, and it can mean either yield point or yield strength. The various properties of structural steel, including strength and ductility, are ­determined by its chemical composition. Steel is an alloy, its principal component being iron. Another component of all structural steels, although in much smaller amounts, is carbon, which contributes to strength but reduces ductility. Other components of some grades of steel include copper, manganese, nickel, chromium, molybdenum, and ­silicon. Structural steels can be grouped according to their composition as follows. 1. Plain carbon steels: mostly iron and carbon, with less than 1% carbon. 2. Low-alloy steels: iron and carbon plus other components (usually less than 5%). The additional components are primarily for increasing strength, which is accomplished at the expense of a reduction in ductility. 3. High-alloy or specialty steels: similar in composition to the low-alloy steels but with a higher percentage of the components added to iron and carbon. These steels are higher in strength than the plain carbon steels and also have some special quality, such as resistance to corrosion. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 12 Chapter 1: Introduction TABLE 1.1 Property A36 A572 Gr. 50 A992 Yield point, min. 36 ksi 50 ksi 50 ksi Tensile strength, min. 58 to 80 ksi 65 ksi 65 ksi Yield to tensile ratio, max. — — 0.85 Elongation in 8 in., min. 20% 18% 18% Different grades of structural steel are identified by the designation assigned to them by the American Society for Testing and Materials (ASTM). This orga- nization develops standards for defining materials in terms of their composition, properties, and performance, and it prescribes specific tests for measuring these attributes (ASTM, 2016a). One of the most commonly used structural steels is a mild steel designated as ASTM A36, or A36 for short. It has a stress–strain curve of the type shown in Figures 1.3b and 1.4 and has the following tensile properties. Yield stress: Fy = 36,000 psi (36 ksi) Tensile strength: Fu = 58,000 psi to 80,000 psi (58 ksi to 80 ksi) A36 steel is classified as a plain carbon steel, and it has the following components (other than iron). Carbon: 0.26% (maximum) Phosphorous: 0.04% (maximum) Sulfur: 0.05% (maximum) These percentages are approximate, the exact values depending on the form of the finished steel product. A36 is a ductile steel, with an elongation as defined by Equation 1.1 of 20% based on an undeformed original length of 8 inches. Steel producers who provide A36 steel must certify that it meets the ASTM standard. The values for yield stress and tensile strength shown are minimum requirements; they may be exceeded and usually are to a certain extent. The tensile strength is given as a range of values because for A36 steel, this property cannot be achieved to the same degree of precision as the yield stress. Other commonly used structural steels are ASTM A572 Grade 50 and ASTM A992. These two steels are very similar in both tensile properties and chemical composition, with a maximum carbon content of 0.23%. A comparison of the ten- sile properties of A36, A572 Grade 50, and A992 is given in Table 1.1. 1.6 S ta n da r d Cross -Sec ti o n al Sh a pe s In the design process outlined earlier, one of the objectives—and the primary e­ mphasis of this book—is the selection of the appropriate cross sections for the individual mem- bers of the structure being designed. Most often, this selection will entail c­ hoosing a standard cross-sectional shape that is widely available rather than requiring the fabrica- tion of a shape with unique dimensions and properties. The s­election of an “off-the- shelf” item will almost always be the most economical choice, even if it means using slightly more material. The largest category of standard shapes i­ncludes those produced Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  1.6: Standard Cross-Sectional Shapes 13 by hot-rolling. In this manufacturing process, which takes place in a mill, molten steel is taken from an electric arc furnace and poured into a continuous casting system where the steel solidifies but is never allowed to cool completely. The hot steel passes through a series of rollers that squeeze the material into the desired cross-sectional shape. Rolling the steel while it is still hot allows it to be deformed with no resulting loss in ductility, as would be the case with cold-working. During the rolling process, the member increases in length and is cut to standard lengths, usually a maximum of 65 to 75 feet, which are subsequently cut (in a fabricating shop) to the lengths required for a particular structure. Cross sections of some of the more commonly used hot-rolled shapes are shown in Figure 1.6. The dimensions and designations of the standard available shapes are defined in the ASTM standards (ASTM, 2010b). The W-shape, also called a wide- flange shape, consists of two parallel flanges separated by a single web. The orien- tation of these elements is such that the cross section has two axes of symmetry. A typical designation would be “W18 3 50,” where W indicates the type of shape, 18 is the nominal depth parallel to the web, and 50 is the weight in pounds per foot of length. The nominal depth is the approximate depth expressed in whole inches. For some of the lighter shapes, it is equal to the depth to the nearest inch, but this is not a general rule for the W-shapes. All of the W-shapes of a given nominal size can be grouped into families that have the same depth from inside-of-flange to inside-of- flange but with different flange thicknesses. FIGURE 1.6 Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 14 Chapter 1: Introduction The American Standard, or S-shape, is similar to the W-shape in having two parallel flanges, a single web, and two axes of symmetry. The difference is in the pro- portions: The flanges of the W are wider in relation to the web than are the flanges of the S. In addition, the outside and inside faces of the flanges of the W-shape are parallel, whereas the inside faces of the flanges of the S-shape slope with respect to the outside faces. An example of the designation of an S-shape is “S18 3 70,” with the S indicating the type of shape, and the two numbers giving the depth in inches and the weight in pounds per foot. This shape was formerly called an I-beam. The angle shapes are available in either equal-leg or unequal-leg versions. A typi- cal designation would be “L6 3 6 3 3 ⁄4” or “L6 3 4 3 5 ⁄ 8.” The three numbers are the lengths of each of the two legs as measured from the corner, or heel, to the toe at the other end of the leg, and the thickness, which is the same for both legs. In the case of the unequal-leg angle, the longer leg dimension is always given first. Although this designation provides all of the dimensions, it does not provide the weight per foot. The American Standard Channel, or C-shape, has two flanges and a web, with only one axis of symmetry; it carries a designation such as “C9 3 20.” This notation is similar to that for W- and S-shapes, with the first number giving the total depth in inches parallel to the web and the second number the weight in pounds per linear foot. For the channel, however, the depth is exact rather than nominal. The inside faces of the flanges are sloping, just as with the American Standard shape. Miscellaneous Channels—for example, the MC10 3 25—are similar to American Standard Channels. The Structural Tee is produced by splitting an I-shaped member at middepth. This shape is sometimes referred to as a split-tee. The prefix of the designation is either WT, ST, or MT, depending on which shape is the “parent.” For example, a WT18 3 105 has a nominal depth of 18 inches and a weight of 105 pounds per foot, and is cut from a W36 3 210. Similarly, an ST10 3 33 is cut from an S20 3 66, and an MT5 3 4 is cut from an M10 3 8. The “M” is for “miscellaneous.” The M-shape has two parallel flanges and a web, but it does not fit exactly into either the W or S cat- egories. The HP shape, used for bearing piles, has parallel flange surfaces, approxi- mately the same width and depth, and equal flange and web thicknesses. HP-shapes are designated in the same manner as the W-shape; for example, HP14 3 117. Other frequently used cross-sectional shapes are shown in Figure 1.7. Bars can have circular, square, or rectangular cross sections. If the width of a rectangular shape FIGURE 1.7 Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203