CELE Steel & Timber Design — Steel Tension MembersSummary

The full cross-sectional area of the tension member before accounting for holes. For a rectangular plate, Ag = width × thickness; for rolled shapes (angle, channel), Ag is tabulated in steel manuals. This area is used in the yielding limit state. Example: a 200 mm × 12 mm plate has Ag = 2400 mm².

The effective cross-sectional area after subtracting the area of bolt holes. The hole diameter used in calculation is NOT the bolt diameter, but the bolt diameter plus a standard clearance (typically 2–3 mm to account for punching tolerance and clearance hole practice). NSCP 2015 and AISC 360 generally use dh = db + 2 mm or local practices up to +3 mm. Formula: An = Ag − Σ(dh × t), where dh is hole diameter and t is material thickness. Example: Two 20 mm bolts (dh = 22 mm) in a 12 mm plate: subtraction = 2 × 22 × 12 = 528 mm², so An = 2400 − 528 = 1872 mm².

When holes are arranged in multiple lines and staggered (offset longitudinally), the failure path may zigzag through the plate rather than straight across. For each diagonal segment, add the term s²/(4g) to the net width, where s is the longitudinal pitch (spacing along the member axis) and g is the transverse gage (perpendicular spacing between hole lines). The net width becomes: Wnet = Wg − Σdh + Σ[s²/(4g)]. This accounts for the fact that the zig-zag path is longer and the material has more 'effective width' than a straight cut. Example: Two staggered hole lines, pitch s = 50 mm, gage g = 75 mm: s²/(4g) = 2500/(300) = 8.33 mm added per diagonal; a 200 mm plate with 2 holes becomes 200 − 44 + 8.33 = 164.33 mm net.

Not all parts of a cross-section may be equally effective in transmitting the tensile load, especially when only some elements (e.g., one leg of an angle) are connected. The effective net area is Ae = U·An, where U ≤ 1 is the shear-lag reduction factor. U = 1.0 when the entire cross-section is connected (e.g., a plate bolted across its full width, or a rolled shape bolted through the web and both flanges). U < 1.0 applies to angles bolted through one leg only, channels bolted through the web only, or tees bolted through the stem. AISC 360 and NSCP 2015 provide U-factor tables; common values are U = 0.85 for an angle connected by one leg, U = 0.80 for a channel connected by the web.

The member reaches yield when the tensile stress equals Fy across the entire gross section. The nominal strength is Pn = Fy·Ag. This is a ductile failure mode (member deforms visibly before fracture). Under LRFD (NSCP 2015), the design strength is φt·Pn = 0.90·Fy·Ag. Under ASD, the allowable strength is Pn/Ωt = Fy·Ag / 1.67. Yielding produces a lower nominal strength (Fy < Fu) but applies to the full area (Ag > Ae), and the higher safety factor (φ = 0.90 vs. 0.75) reflects the ductile nature.

The member fails by fracture when the tensile stress reaches Fu (ultimate/tensile strength) across the net effective section. The nominal strength is Pn = Fu·Ae. This is a sudden, brittle failure with little warning. Under LRFD, the design strength is φt·Pn = 0.75·Fu·Ae. Under ASD, the allowable strength is Pn/Ωt = Fu·Ae / 2.00. The lower φ-factor (0.75) reflects the sudden nature and stress concentration at holes; the higher stress (Fu) and reduced area (Ae) both increase the nominal value, but the lower φ combines with Ae to create a 'conservative' scenario.

LRFD requires φt·Pn ≥ Pu (factored load). Calculate Pn for both yielding and rupture, apply the appropriate φ-factor to each, and take the minimum. The governing state is the one with the lower design strength. Example: Plate with Fy = 248 MPa, Fu = 400 MPa, Ag = 2400 mm², Ae = 1872 mm². Yield: 0.90 × 248 × 2400 = 535.68 kN. Rupture: 0.75 × 400 × 1872 = 561.6 kN. Governing = 535.68 kN (yield governs because it is lower). Design rule: φt·Pn = min(0.90·Fy·Ag, 0.75·Fu·Ae). ASD uses the same logic with safety factors instead of φ.

LRFD (Load and Resistance Factor Design, used in NSCP 2015) applies a resistance factor φ to reduce nominal strength: Design Strength = φ·Pn. For tension members, φt = 0.90 for yielding (ductile, predictable) and φt = 0.75 for rupture (sudden, stress-concentrated). ASD (Allowable Stress Design) applies a safety factor Ω to divide nominal strength by a factor: Allowable Strength = Pn/Ω. For yielding, Ωt = 1.67; for rupture, Ωt = 2.00. These reflect the confidence and ductility of each failure mode. Higher φ (or lower Ω) = greater confidence; lower φ (or higher Ω) = greater uncertainty.

Although tension members do not fail by buckling (no Euler instability), NSCP 2015 and AISC 360 recommend limiting the slenderness ratio L/r ≤ 300 to avoid excessive vibration, sag, or deflection under dynamic loads. L is the unbraced length and r is the minimum radius of gyration. For a circular rod, r = d/4 (where d is diameter). Example: 4 m rod with r = 25 mm → L/r = 4000/25 = 160 < 300 ✓. This is NOT a strength check; it is a serviceability and practical recommendation. The recommendation is less stringent for short, stiff members.

At a bolted connection, the material around the bolt group can fail in shear along one or more planes before net-section rupture occurs. Block shear involves a combination of shear rupture along one plane and tension rupture (or yielding) along a perpendicular plane. The nominal block-shear strength is Pn = 0.6·Fu·Anv + U_bs·Fy·Agt (or 0.6·Fy·Avg + U_bs·Fu·Ant, whichever is lower), where Anv is the net shear area, Agt is the gross tension area, and U_bs is a factor. Although detailed block-shear analysis is beyond this summary, reviewees must recognize that it is checked in connection design and can govern in some cases.

NSCP 2015 Section 5.3.6 (Bolted Connections) and AISC 360-16 Section J3.2 specify that the hole diameter for design is 1.5 times the bolt diameter for standard holes, or the nominal bolt diameter plus 2 mm for design purposes in common practice. Philippine practice often uses dh = db + 2 to 3 mm. This accounts for punching tolerance (±1–2 mm) and the standard clearance (1–1.5 mm) between bolt and hole. Using the bolt diameter directly is unconservative and violates code.

In roof or floor trusses, the horizontal tie members (bottom chord) carry tensile forces that tie together the truss legs and prevent them from spreading. These are typically bolted at the joints. The engineer must check both yield and rupture on the net area through the bolt group. The design procedure: (1) estimate load from structural analysis, (2) assume a section size, (3) calculate Ag and An (with hole allowance), (4) check φt·Pn = min(0.90 Fy Ag, 0.75 Fu Ae) ≥ Pu. If capacity is insufficient, increase section size or add bolts (which may reduce net area if holes dominate).

Bracing members (diagonals, K-braces, V-braces) and sag rods (which suspend piping or equipment) are tension members. Sag rods are often small-diameter round rods or angles. The design follows the same two-state approach, but slenderness is a concern because a slender rod under cyclic load (vibration) can fail by fatigue or excessive deflection. The L/r ≤ 300 recommendation is particularly important for sag rods in mechanical systems.

Hangers for suspended floors, mezzanines, or equipment racks are tension members. They may be threaded rods, flat bars, or angles. The design is governed by axial tension, but the designer must also consider the stress concentration at the threads (for threaded rods) or at the bolted ends (for bars and angles). The effective area Ae may be significantly less than Ag due to threading or limited connection.

When designing or checking a bolted joint in a tension member, the designer calculates the net area through the bolt group, applies the shear-lag factor U (which depends on connection geometry), and verifies the rupture strength. Block shear is also checked if the bolt pattern is compact. The position and spacing of bolts affect both An and U; staggered bolts can improve the net area if the stagger is sufficient.

Under NSCP 2015 seismic provisions, bracing members in special moment-resisting frames or concentrically braced frames carry large tension forces during earthquakes. These members must be ductile and capable of large inelastic deformations. The tension design strength is checked, and detailing requirements (bolt spacing, edge distance) are applied to ensure ductility. The shear-lag factor is carefully evaluated because incomplete connections reduce effectiveness.

When designing a tension member, the engineer selects from available sections: plates, angles, channels, double angles, or built-up sections. For each, Ag is known (from tables or calculation) and Ae is calculated with the appropriate U-factor. The design strength is min(0.90 Fy Ag, 0.75 Fu Ae). The engineer adjusts the section size until design strength meets the required capacity. This process is iterative and often uses spreadsheets or design software.