Steel Design

A structured learning path from steel properties through advanced structural design. Master the design of steel structures per AISC 360 with LRFD and ASD methodologies.

Start Learning Full Handbook

Level 1

Beginner — Steel Material Properties and Section Geometry

Start here if you are new to steel design.

Structural Steel Grades and Properties

Structural steel is manufactured to ASTM standards with specified mechanical properties. The most common grades are ASTM A992 (W-shapes, 345 MPa minimum yield strength), ASTM A572 Grade 50 (plates and bars, 345 MPa), and ASTM A36 (angles, channels, and miscellaneous shapes, 250 MPa). The stress-strain curve shows a well-defined yield point for mild steel, with yield strain ε_y = F_y/E ≈ 0.0017 for 345 MPa steel. The elastic modulus E = 200,000 MPa is essentially constant for all structural steel grades.

Ductility is a key advantage of steel — it can undergo large inelastic deformations before fracture, providing warning of failure and enabling force redistribution in indeterminate structures. The elongation at break is typically 18-25% for structural grades. Fracture toughness is temperature-dependent; the ductile-to-brittle transition temperature must be considered for cold-weather applications. Weldability, corrosion resistance (enhanced by weathering steel grades like ASTM A588), and fire resistance are additional material considerations in steel design.

Section Properties and Hot-Rolled Shapes

Hot-rolled steel shapes are manufactured in standardized series. W-shapes (wide-flange) are the most common beam and column sections, designated by nominal depth and weight per foot (e.g., W12×50 is 12 inches deep at 50 lb/ft). S-shapes (standard I-beams) have sloped flanges, C-shapes (channels) have a single web, L-shapes (angles) are available in equal and unequal leg configurations, and HSS (hollow structural sections) are rectangular or circular tubes.

Key geometric properties include cross-sectional area (A), moment of inertia (I_x, I_y), elastic section modulus (S_x = I_x/c), plastic section modulus (Z_x), and radius of gyration (r = √(I/A)). The shape factor (Z_x/S_x) indicates the reserve strength beyond first yield — typically 1.10-1.20 for W-shapes in strong-axis bending. The torsional constant (J) and warping constant (C_w) are important for torsion and lateral-torsional buckling analysis. Use the Steel Beam Section Properties Calculator to compute section properties.

LRFD and ASD Design Philosophies

AISC 360 provides two alternative design methodologies. Load and Resistance Factor Design (LRFD) applies load factors to service loads (e.g., 1.2D + 1.6L for gravity) and resistance factors (φ) to nominal strengths, requiring Σγ_iQ_i ≤ φR_n. Allowable Strength Design (ASD) applies a single safety factor (Ω) to nominal strength, requiring ΣQ_i ≤ R_n/Ω. LRFD provides more uniform reliability across different load combinations and is preferred for most new design.

Load combinations follow ASCE 7-22. Gravity load combinations: 1.4D (LRFD), 1.2D + 1.6L + 0.5L_r (LRFD). Lateral combinations include wind and seismic loads with directionality and importance factors. Serviceability limit states — deflection (typical limits: L/360 for live load on floors, L/240 for total load on roofs), vibration, drift (H/400 for wind, H/200 for seismic), and camber — must also be checked. The choice between LRFD and ASD is often based on office practice or client preference rather than technical necessity.

Level 2

Intermediate — Tension Members, Beams, and Columns

Build on fundamentals with member design.

Design of Tension Members

Tension members are structural elements subjected to axial tensile forces. The design tensile strength is governed by either yielding of the gross section (φ_t P_n = 0.90 F_y A_g for LRFD) or fracture of the net section at the connection (φ_t P_n = 0.75 F_u A_e). The effective net area (A_e = U A_n) accounts for shear lag — the non-uniform stress distribution when not all elements of the cross-section are connected. The shear lag factor U depends on connection geometry per AISC Table D3.1.

Slenderness limitations for tension members (L/r ≤ 300 for main members) ensure adequate stiffness to prevent excessive vibration and sag. Common tension members include bracing elements, truss bottom chords, tie rods, and hangers. Block shear is a limit state combining tension rupture on one plane and shear yielding on the perpendicular plane, checked at bolted connections. Gusset plate design must also be verified for the tension member connection.

Design of Beams for Flexure and Shear

Steel beam design considers three limit states: flexural strength, shear strength, and serviceability (deflection). The nominal flexural strength M_n depends on the unbraced length (L_b) relative to the limiting lengths L_p and L_r. For L_b ≤ L_p (compact, laterally braced), yielding governs: M_n = M_p = F_y Z_x. For L_p < L_b ≤ L_r (inelastic lateral-torsional buckling), M_n varies linearly between M_p and M_r. For L_b > L_r (elastic LTB), M_n = F_cr S_x ≤ M_p.

Shear strength is typically not critical for standard W-shapes (the web is sized to avoid shear failure). The nominal shear strength is V_n = 0.6 F_y A_w C_v, where A_w = d t_w is the web area and C_v is the web shear coefficient (1.0 for compact webs, less for slender webs per AISC G2). Stiffeners are required when the shear demand exceeds capacity. Deflection limits control beam sizing for long-span floors. Camber (pre-fabricated upward curvature) offsets dead load deflection in large beams. Use the Timber Beam Calculator for timber beams; use section property tools for steel.

Design of Compression Members (Columns)

Column design considers flexural buckling as the primary limit state. The nominal compressive strength P_n = F_cr A_g, where the critical stress F_cr depends on the slenderness ratio (KL/r). The AISC Specification uses a single curve for flexural buckling: for KL/r ≤ 4.71√(E/F_y), F_cr = [0.658^(F_y/F_e)] F_y (inelastic buckling); for KL/r > 4.71√(E/F_y), F_cr = 0.877 F_e (elastic buckling), where F_e = π²E/(KL/r)² is the Euler buckling stress.

The effective length factor K depends on end conditions: K = 0.65 for fixed-fixed, 0.80 for fixed-pinned, 1.0 for pinned-pinned, and 2.0 for fixed-free (cantilever) columns. Frame columns require K-factor calculation using alignment charts (AISC Commentar Fig C-A-7.1) accounting for rotational restraint from beams (G factors). Local buckling of flanges and webs must be checked by limiting width-thickness ratios per AISC Table B4.1a. Torsional and flexural-torsional buckling govern for unsymmetric sections and certain HSS shapes.

Level 3

Advanced — Connections, Plate Girders, and Composite Design

For senior students and practicing engineers.

Bolted and Welded Connections

Connection design is critical — many structural failures originate at connections. High-strength bolts (ASTM A325 or A490) are used in bearing-type connections (where bolt shank bears against the plate) or slip-critical connections (where clamping force transfers load through friction). Bearing-type connections are checked for bolt shear, bearing at bolt holes, and net section rupture. Slip-critical connections require additional check of slip resistance under service loads.

Welded connections use fillet welds (most common, triangular cross-section) or groove welds (for full joint penetration). The design strength of fillet welds is φ R_n = 0.75 × 0.60 F_EXX × A_we, where F_EXX is the electrode classification strength (typically 480-620 MPa) and A_we is the effective weld area. Weld size is limited by the thinner part connected. Eccentric connections (bracket connections, moment connections) induce combined shear and torsion in the bolt group or weld group, analyzed using elastic or instantaneous center of rotation methods.

Plate Girders and Built-Up Sections

Plate girders are built-up welded sections used for spans or loads beyond the capacity of standard rolled shapes. A plate girder consists of a deep web plate with flange plates welded top and bottom. The web is typically slender (h/t_w > 5.70√(E/F_y)), and post-buckling strength (tension field action) is utilized per AISC G3. Transverse stiffeners are provided at supports and concentrated loads, with intermediate stiffeners when shear demand exceeds the web buckling capacity.

Design of plate girders involves proportioning the web depth (typically L/10 to L/12 for bridges), web thickness (based on shear and slenderness limits), flange area (from required moment capacity), and stiffener spacing (from shear design). Hybrid girders use higher-strength steel in flanges with lower-strength web for economy. Bearing stiffeners at concentrated loads and supports must be designed as columns. Flange-to-web welds are sized to transfer the horizontal shear between flange and web.

Composite Steel-Concrete Construction

Composite steel-concrete construction uses the concrete slab acting together with the steel beam through shear connectors (studs) to form an efficient structural system. The concrete slab carries compression while the steel beam carries tension, maximizing the structural efficiency of both materials. The effective flange width of the concrete slab is limited by AISC I3.1a: b_e = min(L/4, s, b_f + 16t_s) for interior beams. The nominal moment capacity uses the plastic stress distribution method.

Shear stud design determines the number of connectors required between the point of maximum moment and zero moment. The nominal strength of a single headed stud is Q_n = 0.5 A_sc √(f'c E_c) ≤ R_g R_p A_sc F_u (per AISC I8.2a). The required number of studs on each side of the maximum moment point equals the horizontal shear force divided by Q_n. Construction loads during the unshored phase (before concrete hardens) must also be checked. Composite construction is standard for steel-framed buildings, reducing beam weight by 20-40% compared to non-composite design.

Practice Exercises

Exercise 1: Tension Member Design

A W12×50 tension member (F_y = 345 MPa, F_u = 450 MPa) is connected through its flanges with two rows of 22 mm diameter bolts. The gross area is 9480 mm² and the net area after holes is 8180 mm². Calculate the available tensile strength using LRFD. The shear lag factor U = 0.85.

Exercise 2: Beam Flexure Design

A simply supported steel beam spans 9 m and carries a dead load of 8 kN/m and live load of 12 kN/m. Select the lightest W-shape (F_y = 345 MPa) for strength and deflection (L/360 for live load). The compression flange is braced at the supports and at third points. Use the Steel Beam Section Properties Calculator to check candidate sections.

Exercise 3: Column Capacity

A W10×45 column (A = 8530 mm², r_x = 110 mm, r_y = 55 mm, F_y = 345 MPa) is 6 m tall with pinned ends (K = 1.0). Calculate the available compressive strength using LRFD. Determine whether the column controls for flexural buckling about the weak axis or strong axis. Verify with the Steel Column Calculator.

Exercise 4: Bolt Group Eccentricity

A bracket connection uses 6 bolts (22 mm diameter, A325) arranged in two vertical rows of three, with 75 mm spacing between bolts and rows. The bracket is subjected to a 150 kN load applied 250 mm from the bolt group centroid. Determine the critical bolt force using the elastic method and check adequacy against bolt shear capacity.

References

AISC 360-22. Specification for Structural Steel Buildings. American Institute of Steel Construction, 2022.
AISC. Steel Construction Manual. 15th ed., American Institute of Steel Construction, 2017.
Salmon, C.G., Johnson, J.E., and Malhas, F.A. Steel Structures: Design and Behavior. 5th ed., Pearson, 2009.
Segui, W.T. Steel Design. 6th ed., Cengage Learning, 2018.
McCormac, J.C. and Csernak, S.F. Structural Steel Design. 6th ed., Pearson, 2020.
ASCE 7-22. Minimum Design Loads and Associated Criteria for Buildings and Other Structures.
Civil Engineering Handbook — Steel Structures chapter.
Engineering Formula Library — Steel design formulas.
Engineering Standards Reference — AISC and AASHTO provisions.
Engineering Glossary — Definitions of steel design terms.