Steel design
Steel design, also known as structural steel design, is the engineering discipline that involves the analysis, proportioning, and detailing of steel components—such as beams, columns, trusses, and connections—to create frameworks capable of safely supporting specified loads while ensuring stability, serviceability, and durability in buildings, bridges, and other structures.[1] This process relies on established standards to address limit states like yielding, buckling, fracture, and excessive deformation, integrating structural analysis with material properties to optimize performance under axial, flexural, shear, and combined forces.[2] The foundational principles of steel design emphasize strength, stability, and serviceability, guided by consensus standards such as the American Institute of Steel Construction's (AISC) Specification for Structural Steel Buildings (ANSI/AISC 360-22).[2] Two primary methods are employed: Load and Resistance Factor Design (LRFD), which uses resistance factors (φ) to ensure design strength exceeds required strength for probabilistic load and resistance variability, and Allowable Strength Design (ASD), which applies safety factors (Ω) to compare allowable strength against required strength, calibrated for typical load ratios.[2] These methods account for second-order effects, such as P-Δ and P-δ amplification in frames, through direct analysis or effective length approaches, ensuring structures remain stable under gravity, wind, seismic, and other loads.[2] Materials in steel design predominantly include carbon steels conforming to ASTM specifications, such as A36 (yield strength F_y = 36 ksi), A572 Grade 50 (F_y = 50 ksi), and A992 (F_y = 50 ksi for wide-flange shapes), selected for their ductility, weldability, yield strengths up to 50 ksi or more, and high strength-to-weight ratio.[2] Connections, critical to load transfer, utilize high-strength bolts (e.g., ASTM F3125 Groups A and B with minimum tensile strengths of 120 ksi and 150 ksi, respectively), welds per AWS D1.1, and sometimes composite elements with concrete for enhanced stiffness.[2] Design also incorporates serviceability checks for deflections (e.g., limiting live-load deflection to L/360 for floors) and vibration, alongside special provisions for fatigue under cyclic loading and fire resistance, where steel's properties degrade above 400°F (e.g., yield strength reduced to 66% at 1,000°F).[2] Steel design's prominence in modern construction stems from steel's versatility, with over 92% of structural steel recycled content and full recyclability via electric arc furnaces, promoting sustainability.[3] It enables rapid erection through prefabrication—up to 50% faster than methods from a few years prior—reducing on-site labor; early fabricator involvement can save approximately 70% on the steel package costs via offsite assembly, while providing exceptional resilience to extreme events like earthquakes and hurricanes due to steel's elasticity and ductility.[3] Applications span high-rise buildings, industrial facilities, and infrastructure, where adaptability allows for future renovations without major structural alterations.[3]Fundamentals of Steel Design
Overview of Steel Structures
Steel design is the process of selecting and proportioning the members of steel structures to ensure they safely resist applied loads without exceeding strength or serviceability limits, as outlined in standards like the AISC Specification for Structural Steel Buildings.[4] This involves determining the required strength of components such as beams, columns, and connections, while accounting for factors like stability, ductility, and deformation under service conditions.[5] Steel's inherent ductility, for instance, enables the use of limit state design methods that optimize material efficiency by allowing controlled yielding before failure.[4] Key advantages of steel in structural applications stem from its material properties and fabrication processes. It offers a high strength-to-weight ratio, allowing for lighter structures that reduce foundation demands compared to concrete alternatives.[3] Additionally, steel exhibits excellent ductility, enabling it to deform significantly without fracturing, which enhances seismic resilience.[3] Its recyclability is notable, with structural steel containing an average of 92% recycled content and being 100% recyclable without loss of quality, promoting resource efficiency.[6] Construction speed is another benefit, as prefabricated components enable rapid assembly on-site, often 50% faster than traditional methods.[3] Versatility in forms, such as rolled beams, welded plates, and trusses, allows for customized solutions in complex geometries.[3] Common applications of steel structures leverage these attributes in diverse sectors. In buildings, steel frames support high-rises and warehouses, providing open spans and adaptability for future modifications.[7] Bridges frequently use steel girders and trusses for their load-bearing capacity and ease of transportation.[7] Industrial structures, such as factories and power plants, benefit from steel's durability in harsh environments.[7] Offshore platforms employ protected steel for its strength against dynamic ocean loads, with corrosion protection measures such as coatings or special alloys.[7] The basic workflow in steel design begins with conceptual layout, where architects and engineers define the structural system based on project requirements.[8] This progresses to analysis and modeling, incorporating boundary conditions and load cases to verify member sizing and connections.[8] Detailing follows, generating fabrication drawings and specifications, culminating in off-site manufacturing and on-site erection.[8] Sustainability plays a central role in modern steel design, emphasizing material reuse and reduced environmental impact. Steel's closed-loop recycling system minimizes waste, as decommissioned structures are melted and repurposed indefinitely.[6] Low-carbon production methods, such as electric arc furnaces powered by renewable energy, cut greenhouse gas emissions by up to 75% compared to traditional blast furnaces.[6] Industry initiatives, including environmental product declarations, further support lifecycle assessments to guide low-embodied-carbon choices in projects.[6]Historical Evolution
The use of iron in structural engineering began in the 18th century, with the Iron Bridge over the River Severn in Shropshire, England, completed in 1779 as the world's first major cast iron arch bridge, marking a pioneering shift from timber and stone to metal frameworks for spanning challenging terrains.[9] This structure, cast by Abraham Darby III, utilized 378 tons of cast iron, demonstrating the material's compressive strength while incorporating wrought iron elements for tensile connections, though cast iron's brittleness limited its early applications to non-flexural roles.[10] By the early 19th century, wrought iron emerged as a more ductile alternative for tension members in bridges and roofs, as seen in structures like the 1825 Menai Suspension Bridge, where its malleability allowed for longer spans compared to cast iron.[11] The mid-19th century witnessed a pivotal transition to steel, driven by the Bessemer process in 1856, which enabled mass production of mild steel with superior tensile strength (28-32 tons per square inch) and uniformity over wrought iron.[12] This innovation facilitated the rise of steel-framed buildings, exemplified by the 1885 Home Insurance Building in Chicago, the first skyscraper to employ a metal skeleton frame, allowing heights previously unattainable with masonry.[12] In the early 20th century, advancements like electric arc welding, first applied to all-welded steel buildings in 1924 by the General Boiler Company, reduced reliance on rivets and enhanced joint efficiency, though initial adoption was cautious due to concerns over weld quality.[13] The 1940 collapse of the Tacoma Narrows Bridge under moderate winds (42 mph) highlighted aerodynamic vulnerabilities in slender suspension designs, prompting engineers to incorporate wind tunnel testing and torsional stiffening in subsequent steel bridge specifications.[14] Post-World War II, the development of high-strength low-alloy (HSLA) steels in the 1950s and 1960s, with yield strengths up to 50 ksi, enabled lighter, more efficient structures while tying into evolving material grades like ASTM A242 for corrosion resistance.[15] The American Institute of Steel Construction (AISC), formed in 1921 to standardize fabrication and design amid fragmented practices, issued its first specification in 1923 based on allowable stress design (ASD), evolving through editions that incorporated multiple steel grades by 1963.[16] The 1960s marked the adoption of plastic design methods in the AISC specification, allowing structures to utilize full plastic moment capacity for economy in low-rise frames using A36 steel, shifting from elastic limits to collapse mechanisms informed by limit state analysis.[17] By the 1980s, AISC implemented Load and Resistance Factor Design (LRFD) in 1986, introducing probabilistic factors for loads and resistances to better account for variability, replacing pure ASD for most applications.[16] The late 20th century saw computational tools transform steel design, with finite element analysis (FEA) gaining widespread use from the 1970s onward, enabling complex simulations of stress distribution and stability beyond manual calculations, as commercial software like NASTRAN facilitated nonlinear behavior modeling.[18] Post-2000 events, particularly the 2001 World Trade Center attacks, accelerated focus on resilience and sustainability; the NIST investigation revealed fireproofing dislodgement as a key failure mode, leading to updates in the International Building Code (IBC) by 2009, mandating enhanced fire resistance ratings of up to 3 hours for primary structural frames in high-rises, along with provisions for structural redundancy to prevent progressive collapse.[19] These updates, integrated into the International Building Code by 2006, emphasized recyclable steel's role in sustainable design, promoting high-recycled-content grades to minimize environmental impact while ensuring blast and fire resilience.[19]Design Philosophies
Allowable Stress Design
Allowable Stress Design (ASD) is a traditional method in steel structure engineering that ensures the stresses induced by unfactored service loads do not exceed predefined allowable stress limits, thereby incorporating a factor of safety to prevent yielding or failure under normal operating conditions.[20] This approach relies on elastic analysis to compute stresses from expected working loads, such as dead, live, and environmental loads without amplification factors, and compares them directly to allowable values derived from material properties like yield strength (F_y). For instance, in compact sections, the allowable bending stress F_b is set at $0.66 F_y, reflecting a safety margin against the onset of yielding.[20] Similarly, for tension members, the allowable tensile stress on the gross area is $0.60 F_y, equivalent to F_y / 1.67.[20] Safety factors, denoted as \Omega, typically range from 1.5 to 1.67 for strength limits; for example, \Omega = 1.67 applies to tension yielding on the gross section, while \Omega = 1.50 is used for shear.[21] The method assumes linear elastic material behavior, where stresses are proportional to strains up to the yield point, and does not account for ultimate capacity, plastic deformation, or probabilistic variability in loads and material strengths.[22] In the design procedure, engineers first calculate the service loads using basic combinations (e.g., sum of dead and live loads), then select member sizes such that computed stresses remain below allowable limits, followed by checks for serviceability criteria like deflection limits to ensure functionality under working conditions.[20] This step-by-step process emphasizes straightforward computations based on elastic theory, making it suitable for routine applications. ASD offers advantages in simplicity and familiarity, particularly for smaller projects where quick, deterministic calculations suffice, and it inherently promotes serviceability by keeping stresses moderate.[21] However, its limitations include conservatism due to uniform safety factors that do not differentiate between load types or material variabilities, potentially leading to overdesign, and it provides less insight into ultimate behavior compared to modern methods.[22] Historically, ASD was the predominant philosophy in U.S. steel design from the AISC's inception in 1923 through the 1960s and remained widely used until the 1980s, with the 1989 AISC Specification marking its final standalone edition before integration into unified formats.[16][23]Load and Resistance Factor Design
Load and Resistance Factor Design (LRFD) is a probabilistic method used in steel structure design to ensure that the structure's capacity exceeds the effects of factored loads at ultimate limit states, incorporating uncertainties in loads and material resistance through separate factors. The core principle involves verifying that the design strength, obtained by multiplying the nominal resistance by a resistance factor φ (less than 1.0 to account for material and fabrication uncertainties), is at least equal to the required strength from load effects multiplied by load factors γ (greater than 1.0 to account for load overstrength and variability). This approach, formalized in the general inequality φR_n ≥ ∑ γ_i Q_i—where R_n is the nominal resistance and Q_i are the load effects—provides a rational framework for achieving consistent reliability across different failure modes in steel buildings.[24] Key equations in LRFD for steel design illustrate this principle for specific elements. For flexural members, the design check is φM_n ≥ M_u, where M_n is the nominal moment capacity, M_u is the required moment from factored loads, and φ = 0.90 for bending about the strong axis in compact sections, reflecting the ductility of steel. The general form R_u ≥ ∑ γ_i Q_i applies to all limit states, with load combinations such as 1.2D + 1.6L (dead load D and live load L) or 1.2D + 1.6W + 0.5L (including wind load W) used to compute the required strength R_u. Resistance factors φ vary by failure mode, typically ranging from 0.75 (e.g., for tension rupture on the effective net area) to 1.0 (e.g., for tension yielding on the gross area), with values such as 0.90 for axial compression buckling and flexural yielding of compact sections, calibrated to balance economy and safety.[25][26] LRFD's factors are derived from reliability theory, using first-order second-moment methods to target a reliability index β of 3.0 for principal members under gravity loads, corresponding to a limit state exceedance probability of approximately 1 in 740, and β = 4.5 for connections to ensure higher redundancy. Calibration involved statistical analysis of load and resistance distributions, with coefficients of variation for dead loads around 0.10, live loads 0.25, and resistance 0.10–0.15 for steel yielding, adjusting φ and γ to minimize the overlap between load and resistance probability curves while maintaining equivalence to historical designs. This probabilistic basis ensures uniform safety levels, particularly beneficial for steel's ductile behavior under variable loading.[27][26] The design procedure under LRFD begins with selecting trial sections based on service loads, then applying load factors to compute required strengths for relevant combinations, followed by calculating nominal resistances per AISC provisions and applying φ to verify inequalities at all limit states, including strength, serviceability, and stability. Iterations may be needed for optimization, often yielding more efficient sections than traditional methods due to higher utilization of material strength near ultimate capacity. Adopted by the American Institute of Steel Construction (AISC) in 1986 following extensive research initiated in the 1970s, LRFD offers advantages such as 10–20% material savings for buildings dominated by variable loads like live or wind, and better suitability for ductile materials like steel compared to allowable stress methods. While equivalent to allowable stress design (ASD) for typical gravity-loaded structures when calibrated similarly, LRFD permits higher utilization (e.g., up to 20% more in live-load dominant cases) by explicitly addressing load variability, leading to more economical and reliable designs.[25][24]Load Considerations
Types of Structural Loads
Structural loads on steel structures are forces or effects that the structure must resist to ensure safety and performance, categorized primarily into dead loads, live loads, environmental loads, and other specialized loads as defined in standards such as ASCE/SEI 7-22. These loads vary in magnitude, duration, and distribution, influencing the design of steel members to prevent failure under strength or serviceability criteria. Dead and live loads represent gravity-induced forces from permanent and variable sources, while environmental loads arise from natural phenomena like wind, snow, and earthquakes, often requiring site-specific determination. Dead loads consist of the constant weights of the structure itself and fixed components, including the self-weight of steel members calculated from material density and geometry. The density of structural steel is approximately 490 pounds per cubic foot (pcf), allowing engineers to estimate dead loads for beams, columns, and framing by multiplying cross-sectional area, length, and this density value. For example, partitions, mechanical systems, and finishes contribute additional dead loads, typically ranging from 10 to 20 pounds per square foot (psf) depending on building type. Live loads are transient forces resulting from occupancy, use, or movable equipment, varying by building function and reducible over large areas per code provisions. In office buildings, uniform live loads are specified at 50 psf for general floor areas, while concentrated loads of 2,000 pounds may apply over a 2.5-foot by 2.5-foot area to account for furniture or equipment. These loads ensure structures accommodate variable human activity without excessive deflection or vibration. Environmental loads encompass forces from atmospheric and geological events, critical for lateral stability in steel frames. Wind loads are determined using velocity pressure at height q_z = 0.00256 K_z K_t K_d V^2 (in pounds per square foot, where V is basic wind speed in miles per hour, and K_z, K_t, K_d are exposure, topographic, and directionality factors), applied as external and internal pressures on building surfaces. Snow loads derive from ground snow load P_g, mapped by location and adjusted for roof slope, exposure, and thermal factors to yield flat-roof snow load p_f. Note that ASCE 7-22 updates ground snow loads P_g to strength-level values, often increasing them compared to prior editions, with combination factors adjusted accordingly (e.g., 1.0S in LRFD leading cases) to target consistent reliability.[28] Seismic loads are characterized by design spectral response acceleration S_{DS} in the short-period range, derived from mapped maximum considered earthquake values and site soil class, dictating base shear and dynamic response for steel bracing systems. Other loads include temperature-induced effects, impact, and construction-phase forces. Temperature changes cause thermal expansion or contraction, with steel's coefficient \alpha approximately $6.5 \times 10^{-6} per degree Fahrenheit, leading to dimensional changes \Delta L = \alpha L \Delta T that may induce stresses in restrained members. Impact loads account for dynamic effects from moving machinery or vehicles, often amplifying static loads by 20% to 100% depending on equipment type. Construction loads, such as worker and material weights during erection, are typically 20 psf uniform plus concentrated loads up to 300 pounds, ensuring temporary stability of steel assemblies. Loads can be uniformly distributed (e.g., floor live loads), concentrated (e.g., equipment points), or dynamic (e.g., seismic accelerations), with importance factors applied based on occupancy categories to adjust magnitudes for risk. Risk Category I and II structures use an importance factor I_e of 1.0 for seismic loads, Category III uses 1.25, and Category IV uses 1.5, reflecting higher reliability needs.[29] These factors scale loads to prioritize public safety in hospitals versus agricultural buildings. For serviceability, certain loads like live or snow are checked against deflection limits to prevent occupant discomfort or damage to nonstructural elements, independent of strength requirements. Common limits include span length L/360 under live load for floor beams, ensuring vibrations remain below perceptible thresholds, and L/240 for total load including dead weight. These criteria maintain functionality under normal use, contrasting with ultimate strength checks for overload protection.Load Combination Methods
In steel design, load combination methods systematically aggregate various load effects to determine the governing design scenarios that ensure structural safety and reliability. These methods, primarily governed by ASCE/SEI 7-22, account for the simultaneous occurrence of multiple loads while considering their variability and probability of exceedance. The combinations differ based on the design philosophy, with Load and Resistance Factor Design (LRFD) applying load factors greater than unity to nominal loads for strength limit states, and Allowable Strength Design (ASD) using unfactored or partially reduced loads.[30] For LRFD, ASCE/SEI 7-22 Section 2.3 specifies basic combinations for strength design, where load factors amplify dead (D), live (L), roof live (Lr), snow (S), rain (R), wind (W), earthquake (E), flood (Fa), and self-straining (T) loads to reflect their uncertainties. The following table summarizes the primary equations:| Combination | Equation |
|---|---|
| 1 | $1.4(D + F) |
| 2 | $$1.2(D + F + T) + 1.6(L + H) + 0.5(L_r \text{ or } S \text{ or } R)$$ |
| 3 | $$1.2D + 1.0(L_r \text{ or } S \text{ or } R) + (L \text{ or } 0.8W)$$ |
| 4 | $$1.2D + 1.6W + L + 0.5(L_r \text{ or } S \text{ or } R)$$ |
| 5 | $1.2D + 1.0E + L + 0.2S |
| 6 | $0.9D + 1.6W + 1.6H |
| 7 | $0.9D + 1.0E + 1.6H |
| Combination | Equation |
|---|---|
| 1 | D + F |
| 2 | D + H + F + L + T |
| 3 | D + H + F + 0.7(L_r \text{ or } S \text{ or } R) |
| 4 | D + H + F + 0.75(L + T) + 0.525(L_r \text{ or } S \text{ or } R) |
| 5 | D + H + F + (W \text{ or } 0.7E) |
| 6 | D + H + F + 0.75(W \text{ or } 0.7E) + 0.75L + 0.525(L_r \text{ or } S \text{ or } R) |
| 7 | $0.6D + W + H |
| 8 | $0.6D + 0.7E + H |
Material Properties
Steel Grades and Specifications
Steel grades for structural design are classified primarily through standards developed by the American Society for Testing and Materials (ASTM), which define the chemical composition, mechanical requirements, and intended applications to ensure consistency and performance in construction.[32] These specifications cover a range of steels from general-purpose carbon grades to high-strength low-alloy (HSLA) and weathering types, selected based on factors like yield strength, weldability, and environmental exposure.[33] Common ASTM specifications include A36, a versatile carbon structural steel with a minimum yield strength (Fy) of 36 ksi, widely used for buildings, bridges, and general fabrication due to its ductility and ease of welding.[33] ASTM A992, the preferred grade for wide-flange (W) shapes, offers a higher Fy of 50 ksi and is standard for most building columns and beams, providing improved strength-to-weight ratios.[33] For tubular sections like hollow structural sections (HSS), ASTM A500 specifies Grade B (Fy = 42 ksi for round, 46 ksi for shaped) and Grade C (Fy = 50 ksi), suitable for framing and bracing in architectural and industrial applications.[33] High-performance options include ASTM A913, available in grades up to Fy = 65 ksi, which incorporates microalloying elements for enhanced weldability and toughness without requiring post-weld heat treatment.[33] Weathering steels like ASTM A588 (Fy = 50 ksi), often called Corten, form a protective rust layer for corrosion resistance in exposed environments such as bridges and outdoor structures.[33] The chemical composition of these steels is tightly controlled to balance strength, ductility, and fabricability; carbon content typically ranges from 0.05% to 0.25% to maintain weldability and avoid brittleness, while alloying elements like manganese (0.50–1.50%) and silicon (0.15–0.40%) enhance deoxidation and strength.[34] For ASTM A36, maximum carbon is 0.26%, with manganese at 0.60–1.70%, phosphorus below 0.04%, and sulfur below 0.05%.[35] ASTM A992 limits carbon to 0.23% maximum and includes a carbon equivalent formula (CE = C + Mn/6 + (Cr + Mo + V)/5 + (Ni + Cu)/15 ≤ 0.45%) to ensure low-alloy properties for better weld performance.[33] In contrast, ASTM A588 incorporates chromium (0.40–0.65%) and copper (0.25–0.40%) alongside 0.19% maximum carbon to promote atmospheric corrosion resistance.[33] Advanced grades like A913 use niobium or vanadium microadditions (under 0.05%) for grain refinement and higher strength without increasing carbon levels.[33] Structural steels are available in various shapes and forms as outlined in the AISC Steel Construction Manual, including hot-rolled sections such as wide-flange beams (W), American standard beams (S), channels (C), and angles, primarily produced to ASTM A6/A6M dimensions.[36] Cold-formed shapes and plates (up to 4 inches thick) are common for custom fabrication, while HSS under A500 are stocked in square, rectangular, and round profiles up to 20 inches.[36] Availability varies by producer, with real-time listings accessible through AISC resources to confirm stock for specific grades and sizes.[36] Selection of steel grades depends on project-specific needs, including required yield strength for load-bearing capacity, corrosion resistance in harsh environments, and cost-effectiveness; for instance, higher grades like A992 are favored in tall buildings for material efficiency, while A588 reduces maintenance in coastal areas.[37] Trends show increasing adoption of grades above 50 ksi in modern high-rise and seismic designs to optimize weight and sustainability.[37] Internationally, equivalents facilitate global design; for example, the European S355 grade under EN 10025 (with 0.20% maximum carbon and 1.60% manganese) corresponds closely to ASTM A572 Grade 50 (Fy = 50 ksi) in strength and composition, enabling cross-compatibility in Eurocode projects.[34]Mechanical and Physical Properties
Steel used in structural design exhibits key mechanical properties that define its load-bearing capacity and deformation behavior. The yield strength, denoted as F_y, represents the stress at which steel begins to yield plastically, determined using the 0.2% offset strain method as per ASTM A370 testing standards.[38] For common structural carbon steels, such as ASTM A992, F_y typically ranges from 36 to 65 ksi, with a minimum of 50 ksi for wide-flange shapes.[39] The ultimate tensile strength, F_u, follows yielding and generally falls between 1.5 and 2.0 times F_y, enabling significant post-yield capacity before fracture; for example, in A36 steel, F_u minima are 58 ksi against a 36 ksi F_y. The elastic modulus, E, quantifies steel's stiffness in the linear elastic range and is consistently 29,000 ksi for structural applications, allowing predictable deformation under service loads.[39] Poisson's ratio, approximately 0.3, describes the lateral strain response to axial loading, influencing volumetric changes in members.[40] Ductility, measured by percent elongation in tensile tests, exceeds 20% for most grades, with averages around 27-40% for A992 steel, providing the ability to undergo large deformations without brittle failure.[41] Post-yield behavior includes a yield plateau followed by strain hardening, where steel's stress increases with further strain, promoting plasticity and stress redistribution in indeterminate structures during overload events.[41] This hardening enhances energy absorption, critical for seismic resilience. Physical properties of structural steel include a density of 490 lb/ft³, which informs self-weight calculations in design.[39] Thermal conductivity is approximately 29 Btu/hr-ft-°F at room temperature, facilitating heat dissipation in fire scenarios.[42] The coefficient of thermal expansion is 6.5 × 10^{-6} /°F, affecting dimensional stability under temperature variations.[43] Material variability arises from manufacturing processes, with properties verified through mill certificates that document tensile test results per ASTM standards.[38] Toughness, especially in cold climates, is assessed via Charpy V-notch impact testing, which measures energy absorption to prevent brittle fracture; AISC recommends minimum values like 20 ft-lb at 70°F for certain applications.[44] These properties directly influence design approaches: ductility supports Load and Resistance Factor Design (LRFD) by allowing plastic mechanisms and reserve strength beyond elastic limits, while fatigue considerations limit stress ranges for cyclically loaded elements to avoid crack propagation.[26]Design of Primary Elements
Tension and Compression Members
Tension and compression members are fundamental components in steel structures, designed to carry axial loads efficiently while ensuring safety against failure modes such as yielding, rupture, and buckling. Tension members, such as rods and bracing elements, resist pulling forces, with design focused on preventing excessive deformation or fracture at connections. Compression members, including columns and struts, withstand pushing forces but are prone to instability, requiring consideration of slenderness and end conditions to avoid buckling. These designs follow load and resistance factor design (LRFD) principles, utilizing material yield strength F_y and ultimate strength F_u from established steel grades.[45]Tension Design
The nominal tensile strength of a member is governed by the lower of yielding on the gross section or rupture on the effective net section. For yielding, the nominal strength is P_n = F_y A_g, where A_g is the gross cross-sectional area; the design strength under LRFD is \phi P_n with resistance factor \phi_t = 0.90.[45] Rupture strength is P_n = F_u A_e, where A_e is the effective net area accounting for holes and shear lag effects via the factor U; here, \phi_t = 0.75.[45] Block shear, a combined tension and shear failure at connections, must also be checked, with nominal strength R_n = 0.6 F_u A_{nv} + U_{bs} F_u A_{nt} \leq 0.6 F_y A_{gv} + U_{bs} F_u A_{nt}, using \phi = 0.75 for LRFD. Slenderness is limited to L/r \leq 300 to control deflection, though not a strength criterion. Examples include tie rods in trusses or bracing in frames, where net area reductions from bolt holes necessitate larger gross sections to achieve required capacity. For built-up members, stitch connections prevent individual plate buckling under compression from accidental loads.[45]Compression Design
Compression members are designed against buckling, with nominal strength P_n = F_{cr} A_g, where F_{cr} is the critical stress; the LRFD design strength uses \phi_c = 0.90. The slenderness parameter is defined as \lambda = \frac{KL/r}{\pi \sqrt{E / F_y}}. For slender members where \lambda > 1.5 (corresponding to KL/r > 4.71 \sqrt{E / F_y}), elastic buckling governs with F_{cr} = 0.877 F_e and Euler's elastic buckling stress F_e = \frac{\pi^2 E}{(KL/r)^2}, where E = 29,000 ksi is the modulus of elasticity, K is the effective length factor, and r is the radius of gyration.[45] For stockier members (\lambda \leq 1.5), inelastic buckling applies via F_{cr} = (0.658^{\lambda^2}) F_y. The slenderness ratio is limited to KL/r \leq 200 to ensure practical stiffness and avoid excessive deflections. Effective length factors K depend on end restraints: K = 1.0 for pinned-pinned conditions and K = 0.5 for fixed-fixed, with intermediate values from alignment charts for braced or sway frames.[45] Cross-section classification affects capacity: compact elements (\lambda \leq 0.3 \sqrt{E/F_y}) develop full yielding, while slender elements require reduced effective widths to account for local buckling. Built-up sections, such as laced or battened columns, use modified slenderness for individual components. Examples encompass building columns supporting gravity loads or diagonal bracing in moment frames resisting lateral forces.[45]| End Condition | Effective Length Factor K | Theoretical Basis |
|---|---|---|
| Pinned-Pinned | 1.0 | Ideal hinge supports |
| Fixed-Fixed | 0.5 | Full restraint at ends |
| Fixed-Pinned | 0.7 | Partial restraint |
| Fixed-Free | 2.0 | Cantilever |