CSA S16 Tension Member Design — Gross Yield, Net Rupture & Shear Lag

Quick Reference: Tension capacity is the lesser of gross section yield (Tr = 0.90 _ Ag _ Fy) and net section rupture (Tr = 0.75 _ An _ Fu). Shear lag reduction per Cl. 12.3. Block shear per Cl. 13.11. All design per CSA S16:24.

Limit States for Tension Members (Cl. 13.2)

CSA S16:24 requires tension members be checked against two limit states. Both must be satisfied; the lower capacity governs.

1. Gross Section Yielding (Cl. 13.2(a))

The member cross-section away from connections must resist yielding:

Tr = phi _ Ag _ Fy

where:

• phi = 0.90 (Cl. 13.1)
• Ag = gross cross-sectional area (mm^2)
• Fy = specified minimum yield strength (MPa)

This limit state prevents excessive elongation of the entire member. For common Canadian structural steels:

2. Net Section Rupture (Cl. 13.2(b))

At connections, the reduced cross-section with bolt holes may rupture before gross yield occurs:

Tr = phi*u * An _ Fu

where:

• phi_u = 0.75 (Cl. 13.1 — reduced factor for fracture limit state)
• An = net area accounting for bolt holes and shear lag (mm^2)
• Fu = specified minimum tensile strength (MPa)

For G40.21 350W: Fu = 450 MPa. For 350WT: Fu = 450 MPa. For A572 Gr. 50: Fu = 450 MPa.

The phi_u = 0.75 is lower than the gross yield phi = 0.90 because:

1. Fracture is a sudden, brittle failure mode vs ductile yielding
2. Net section area calculations have practical variability
3. Ultimate tensile strength Fu has higher statistical scatter than yield Fy

Net Area Calculation (Cl. 12.3)

Bolt Hole Deduction

CSA S16:24 Clause 12.3.2 requires hole diameters to be taken as the nominal bolt diameter plus 2 mm (or plus 1/16 inch) for standard bolt holes. The additional allowance accounts for hole clearance and minor drilling damage:

For a single line of bolts transverse to the member axis, the net area is:

An = Ag - nh _ dh _ t

where:

• nh = number of holes in the critical cross-section
• dh = hole diameter (bolt + 2 mm)
• t = thickness of the connected element

Staggered Bolt Holes (Cl. 12.3.2)

When bolts are staggered in adjacent rows, multiple fracture paths must be evaluated. The minimum net width is found by adding s^2/(4g) for each gauge space:

wn = wg - sum(dh) + sum(s^2/(4g))

where:

• wg = gross width
• s = longitudinal centre-to-centre spacing (pitch) of staggered holes
• g = transverse centre-to-centre spacing (gauge)

For a diamond pattern:

  o---s---o
   \     /
    g   g
   /     \
  o---s---o

The critical path may be straight (wn = wg - 2dh) or diagonal (wn = wg - dh + s^2/(4g)).

Shear Lag Reduction (Cl. 12.3.3)

When only part of a cross-section is connected (as with single-leg angle connections), stress must "shear lag" from the connected element to the unconnected portion. This creates non-uniform stress distribution and reduces effective net area.

Ane = An _ U (for welded connections, U from Cl. 12.3.3.1)

For bolted angles (Cl. 12.3.3.2):

The reduction factors are cumulative — a single-angle with one bolt has a dramatically lower effective area (Ae = 0.60 An) than a double-angle with two bolts (Ae = 0.85 An). This is why double-angle connections are preferred for significant tension members in Canadian practice.

Worked Example 1: Single Angle Tension Member

Given: L89x89x9.5 (3-1/2 x 3-1/2 x 3/8) Grade 350W, connected by one leg with two M20 bolts in a single line. Bolt spacing = 75 mm. No staggered holes.

Section properties: Ag = 1,610 mm^2, t = 9.5 mm

Step 1 — Gross Section Yielding: Tr = 0.90 _ 1,610 _ 350 / 1,000 = 507 kN

Step 2 — Net Area: Hole diameter = 20 + 2 = 22 mm An = 1,610 - 2 _ 22 _ 9.5 = 1,610 - 418 = 1,192 mm^2

Step 3 — Shear Lag: Single angle, 2 bolts in line of force: Ae = 0.75 _ An = 0.75 _ 1,192 = 894 mm^2

Step 4 — Net Section Rupture: Tr = 0.75 _ 894 _ 450 / 1,000 = 302 kN

Governing capacity: 302 kN (net rupture controls).

The shear lag reduction reduces capacity by 40% from gross yield. Single-angle tension members are inherently inefficient because only one leg transfers force.

Worked Example 2: Double Angle Tension Member

Given: 2L76x76x6.4 (2-3x3x1/4), Grade 350W, bolted with two rows of M20 bolts. Each angle Ag = 930 mm^2. Total Ag = 1,860 mm^2.

Step 1 — Gross Section Yielding (both angles): Tr = 0.90 _ 1,860 _ 350 / 1,000 = 586 kN

Step 2 — Net Area per angle: Hole diameter = 22 mm An per angle = 930 - 1 _ 22 _ 6.4 = 930 - 141 = 789 mm^2 Total An = 2 _ 789 = 1,578 mm^2

Step 3 — Shear Lag (Cl. 12.3.3.3, staggered connections): Double angle with 2+ bolts: Ae = 0.85 _ 1,578 = 1,341 mm^2

Step 4 — Net Section Rupture: Tr = 0.75 _ 1,341 _ 450 / 1,000 = 453 kN

Governing capacity: 453 kN (net rupture controls, 77% of gross yield).

Compared to the single-angle example, the double-angle connection retains 77% of gross yield capacity vs 60% for the single angle. The improved shear lag factor (0.85 vs 0.75) and reduced hole deduction per leg make double angles the standard Canadian solution for moderate tension loading.

Worked Example 3: W-Shape Tension Member

Given: W150x22 (W6x15), Grade 350W, bolted through both flanges with 4 M20 bolts (2 rows, 2 bolts per flange). Flange thickness tf = 6.6 mm.

Section properties: Ag = 2,850 mm^2

Step 1 — Gross Section Yielding: Tr = 0.90 _ 2,850 _ 350 / 1,000 = 898 kN

Step 2 — Net Area: Holes in each flange: 2 per flange × 22 mm × 6.6 mm = 290 mm^2 per flange Total hole deduction: 2 _ 290 = 580 mm^2 An = 2,850 - 580 = 2,270 mm^2

Step 3 — Shear Lag: W-shape with both flanges connected: Ae = 0.90 _ An = 0.90 _ 2,270 = 2,043 mm^2

Step 4 — Net Section Rupture: Tr = 0.75 _ 2,043 _ 450 / 1,000 = 689 kN

Governing capacity: 689 kN (net rupture controls, 77% of gross yield).

If only the web were connected (Ae ≈ 0.70 An), the capacity would drop to approximately 537 kN — a 22% penalty. Flange-connected tension members are significantly more efficient for W shapes.

Block Shear (Cl. 13.11)

Block shear checks a potential failure mode where a block of connected material tears out — combining tension rupture on one plane with shear yielding or rupture on perpendicular planes. This is critical for gusset plates, coped beam flanges, and short connection lengths.

Tr + Vr >= Tf

where the resistance has two components:

1. Tension plane: Tr = phi*u * Ut _ An _ Fu (rupture always governs tension plane)
2. Shear plane(s):
   • Shear yield: Vr*y = phi * 0.60 _ Agv _ (Fy+Fy)/2 (combined)
   • Shear rupture: Vr*u = phi_u * 0.60 _ Anv _ Fu

The governing shear component is the lower of Vr_y and Vr_u.

For a typical gusset plate tension connection with two shear planes (one each side):

If Agv _ Fy < Anv _ Fu**: block shear resistance = phi*u * (Ut _ An _ Fu + 0.60 _ Agv _ Fy) **If Agv _ Fy >= Anv _ Fu: block shear resistance = phi*u * (Ut _ An _ Fu + 0.60 _ Anv _ Fu)

where Agv = gross shear area, Anv = net shear area, Ut = 1.0 for uniform tension stress.

Block Shear Worked Example

Given: Gusset plate 10 mm thick × 200 mm wide, connected with 3 M20 bolts at 60 mm pitch. Edge distance = 35 mm, bolt holes = 22 mm diameter.

Gross shear area (2 planes): Agv = 2 _ (60+60+35) _ 10 = 3,100 mm^2 Net shear area: Anv = 2 _ (155 - 2.5 _ 22) _ 10 = 2 _ 100 _ 10 = 2,000 mm^2

Gross tension area: Agt = (200 - 35) _ 10 = 1,650 mm^2 Net tension area: Ant = (165 - 22) _ 10 = 1,430 mm^2

Shear governing mode: Agv _ Fy = 3,100 _ 350 = 1,085 kN, Anv _ Fu = 2,000 _ 450 = 900 kN. Since 900 < 1,085, shear rupture governs.

Block shear resistance = 0.75 _ (1.0 _ 1,430 _ 450 + 0.60 _ 2,000 _ 450) / 1,000 = 0.75 _ (643.5 + 540) / 1,000 = 0.75 _ 1,183.5 / 1,000 = 888 kN

For comparison, gross section yield of the same plate (no holes): Tr = 0.90 _ (200 _ 10) _ 350 / 1,000 = 630 kN. Block shear at 888 kN does not govern in this case — but for shorter connections (fewer bolts, less shear area), block shear frequently controls.

Pin-Connected Tension Members (Cl. 13.2.2)

For eyebars and pin-ended tension rods, additional checks apply beyond gross/net section:

• Pin bearing (Cl. 13.10.3): Bearing stress on the projected area
• Dishing failure (Cl. 13.2.2): Tearout around the pin hole
• Net section at the pin hole: An across the minimum section through the hole

For calculating net area at a pin hole, the hole diameter is taken as the pin diameter plus 0.8 mm (not the 2 mm used for bolted connections). The tighter tolerance reflects the precision fit of pins vs standard bolt holes.

Practical Design Considerations

Connection Efficiency

The ratio of net to gross capacity defines connection efficiency. A well-designed tension member achieves 70-85% efficiency:

Wind Bracing Tension-Only Design

CSA S16 permits tension-only bracing design under Clause 27 (seismic) and general provisions. The brace must have slenderness below 300 (Cl. 10.4.2.1) to prevent excessive vibration and sag. Tension-only braces require end connections capable of developing the full tension capacity, and the compression strut in the opposing direction must be designed independently.

Fatigue Considerations

Tension members in cyclic loading (crane runways, bridges, equipment supports) require fatigue checks per CSA S16 Clause 26. The net section with bolt holes has a lower fatigue category. Pin-connected eyebars are particularly fatigue-sensitive due to stress concentrations around the hole.

CSA S16 vs AISC 360 — Tension Member Comparison

The two codes are nearly identical for tension members — both use the same phi values and similar shear lag factors. The primary differences are:

1. Hole deduction: CSA adds 2 mm, AISC adds 1/16" (1.6 mm) — CSA slightly more conservative for larger bolts
2. Block shear formulation: subtle differences in the interaction of shear yield vs rupture, but results typically within 5%

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Related Pages

• CSA S16 Code Overview — Full CSA S16:24 design code reference
• CSA S16 Bolt Design Guide — Bolt shear, bearing, tension per Cl. 21
• CSA S16 Weld Design Guide — Fillet welds per Cl. 21
• Shear Lag Factor — Comprehensive Guide — AISC and CSA shear lag compared
• Block Shear Design — AISC 360 — Comparison with AISC approach
• Tension Member Design — Fundamentals — General design principles

This page is for educational reference. All formulae per CSA S16:24. For section properties, refer to the current CISC Handbook of Steel Construction. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent PE/SE verification.

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