Tension members look simple, but they still demand a disciplined sequence of checks before a section can be accepted. A single angle used as a bracing member, a hanger, or a tie in a roof truss must be verified against both the gross section yielding limit and the net section failure mode at the bolted connection. This article covers the Eurocode 3 procedure for single angle design in tension, with a worked example for a 60x60x6 angle in grade S275 steel. These member checks run alongside the architectural design and building envelope design process, where section sizes and connection layouts are coordinated with cladding, services, and openings.
Material Properties and Partial Factors
Every EC3 tension check starts with the same two inputs: the characteristic strengths of the steel and the partial factors that convert them into design values. Yield strength fy and ultimate strength fu come from Table 3.1 of EN 1993-1-1, selected by steel grade and plate thickness. γM0 covers yielding of the gross section and γM2 covers fracture of the net section, with defaults of 1.0 and 1.25 that national annexes can change. Material selection follows the same route used across structural steel design: pick the grade first, then read off the thickness-dependent strengths.
| Thickness t (mm) | Yield strength fy (N/mm2) | Ultimate strength fu (N/mm2) |
|---|---|---|
| t ≤ 16 | 275 | 430 |
| 16 < t ≤ 40 | 265 | 410 |
| 40 < t ≤ 63 | 255 | 410 |
| 63 < t ≤ 80 | 245 | 410 |
Reading the strength table
Table 3.1 gives nominal fy and fu values for each grade and thickness range. For S275 steel, the yield strength steps down as plate thickness increases, while the ultimate strength holds steady across the middle ranges.
Thickness governs the strength row
A 60x60x6 angle has a 6 mm leg, so it uses fy = 275 N/mm2 and fu = 430 N/mm2. A plate above 16 mm thickness must drop to the next row, and picking the wrong row is a common error.
Design Tension Resistance of the Gross Section
The first resistance value is the design plastic resistance of the gross section, Npl,Rd, the load at which the full cross section yields:
Npl,Rd = A fy / γM0
The gross area is used because yielding is a section-wide phenomenon; a bolt hole in one leg does not control this limit state. Tension checks on single angles appear constantly in structural retrofit work, including many single-family home renovation projects where trusses are strengthened with new tie members.
Plastic resistance of the gross section
The calculation is a single line: multiply the gross area by the yield strength and divide by γM0, which equals 1.0 under the default values. For the worked example, A = 695 mm2 gives Npl,Rd = 695 x 275 / 1.0 = 191,125 N, or about 191 kN.
Why the gross area is used
Yielding of the gross section is checked in the body of the member, away from the connection. The net section only becomes relevant at the fastener line, where the second resistance value is computed.
Net Section Resistance for Bolted Connections
The second resistance value, Nu,Rd, covers fracture of the net section at the fastener holes. For an angle connected by bolts in one leg, the calculation follows Clause 3.10.3(2) of EN 1993-1-8, referenced from Clause 6.2.3(5), and one of three equations applies depending on the bolt count. The same discipline of comparing resistance with demand appears in the structural design of flexible and rigid pavements, where layer capacities are checked against traffic loading.
Single bolt connection
When the angle is connected with a single bolt, the resistance is controlled by the edge distance e2, the hole diameter d0, and the leg thickness t:
Nu,Rd = 2 (e2 – 0.5 d0) t fu / γM2
The factor of 2 reflects the two strips of material on either side of the bolt hole that must fracture. The term (e2 – 0.5 d0) is the net width of each strip, and a generous edge distance is the cheapest way to raise this resistance.
Hole diameter d0
The hole diameter is the nominal bolt diameter plus clearance. A 12 mm bolt in a standard clearance hole uses d0 = 14 mm. Oversized and slotted holes follow separate rules in EN 1090-2.
Multiple bolt arrangements
When more than one bolt is used, the net area Anet replaces the direct geometry, with reduction factors β2 or β3 from Table 3.8 of EN 1993-1-8. For two bolts, β2 ranges from 0.4 at 2.5d0 spacing to 0.5 at 5d0 or more. For three or more bolts, β3 ranges from 0.5 to 0.7:
Nu,Rd = βn Anet fu / γM2
The table below summarizes the three equations. In every case, the design tensile resistance Nt,Rd is the smaller of Npl,Rd and Nu,Rd.
| Bolts in the line | Equation | Governing variable |
|---|---|---|
| 1 | Nu,Rd = 2 (e2 – 0.5 d0) t fu / γM2 | Edge distance e2 |
| 2 | Nu,Rd = β2 Anet fu / γM2 | β2 = 0.4 to 0.5 |
| 3 or more | Nu,Rd = β3 Anet fu / γM2 | β3 = 0.5 to 0.7 |
Equal and unequal angles
When the angle is equal-legged, Anet is the gross area reduced by the bolt holes. Unequal angles differ: with bolts on the larger leg, Anet is the gross area minus the holes; with bolts on the smaller leg, Anet comes from the equivalent section area. For a 100x75x10 angle bolted on the 75 mm leg, the area of a 75x75x10 angle is used, because load entering the smaller leg cannot spread into the larger leg.
Worked Example: 60x60x6 Angle in Tension
The procedure is best followed with numbers. The example below checks a single angle in tension with a single bolted connection. The spacing, end distance, and edge distance requirements of Clause 3.5 must be satisfied before any resistance value is accepted. The same checklist mindset shows up in accessible kitchen design, where clearances and reach ranges are checked against dimensional standards before a layout is approved.
Design data
The member is a 60x60x6 mm equal angle in grade S275 with a single 12 mm bolt in one leg. The applied force is NEd = 75 kN, with d0 = 14 mm, edge distance e2 = 30 mm, and end distance e1 = 35 mm.
Section properties
The gross area of the 60x60x6 angle is A = 695 mm2, and the 6 mm leg gives fy = 275 N/mm2, fu = 430 N/mm2, with γM0 = 1.0 and γM2 = 1.25.
Calculation steps
- Read the material properties from Table 3.1: fy = 275 N/mm2, fu = 430 N/mm2.
- Take the partial factors from Clause 6.1: γM0 = 1.0, γM2 = 1.25.
- Compute the gross section resistance: Npl,Rd = 695 x 275 / 1.0 = 191,125 N (191.1 kN).
- Compute the net section resistance: Nu,Rd = 2 (30 – 7) x 6 x 430 / 1.25 = 94,944 N (94.9 kN).
- Take the minimum: Nt,Rd = min(191.1, 94.9) = 94.9 kN.
- Verify the utilization: NEd / Nt,Rd = 75 / 94.9 = 0.79, below 1.0. The section is adequate.
Verification summary
The utilization of 0.79 leaves about 21 percent spare capacity. If the applied force exceeded 94.9 kN, the options would be a larger angle, a second bolt, or a larger edge distance. The net section governs, as expected for a single bolt.
| Quantity | Value |
|---|---|
| Gross section resistance Npl,Rd | 191.1 kN |
| Net section resistance Nu,Rd | 94.9 kN |
| Design tensile resistance Nt,Rd | 94.9 kN |
| Applied force NEd | 75 kN |
| Utilization NEd / Nt,Rd | 0.79, OK |
Detailing Requirements for Bolted Angles
A resistance check is only valid if the connection geometry obeys the detailing rules of Clause 3.5 of EN 1993-1-8. Minimum end and edge distances prevent tearing at the fastener, while maximum limits control deformation. Comparable limits appear in highway engineering, where minimum and maximum layer thicknesses keep the response inside the range the design method assumes.
Minimum end and edge distances
For rolled edges, the minimum end distance e1 and edge distance e2 are both 1.2d0, or 16.8 mm with a 14 mm hole; the worked example uses e2 = 30 mm. Sheared or flame-cut edges raise the minimum to 1.5d0, one reason rolled angles are preferred for tension connections.
Practical values for a 12 mm bolt
For a 12 mm bolt with d0 = 14 mm, layout values of 25 to 35 mm are typical on a 60 mm leg. The maximum edge distance is 4t + 40 mm, which equals 64 mm for a 6 mm thick angle.
Maximum spacing limits
The maximum spacing between bolts in the direction of load transfer is the smaller of 14t or 200 mm for tension members, or 84 mm for a 6 mm angle. Spacings above the limit let the plate deform excessively between fasteners. Several rows on the same leg follow the same 14t cap perpendicular to the load.
Spacing and the β factors
The β2 and β3 factors in Table 3.8 are defined at spacings of 2.5d0 and 5.0d0. Spacing bolts at 5d0 or more unlocks the highest factors, a free way to gain net section capacity.
Applying Single Angle Design in Real Projects
Single angles in tension appear in roof bracing, vertical cross bracing, tie members under purlins, and hangers for secondary steel. The sequence here, material properties, gross section check, net section check, and utilization, is short enough to run by hand, which makes it a good candidate for spreadsheet automation and software validation. The angle work sits inside the wider field of steel building design, where beam design and column buckling checks run alongside connection design with the same partial factor philosophy.
Common errors in hand checks
- Using the gross area in the net section check for a single bolt instead of the edge distance geometry.
- Applying the unequal angle rule in reverse when the bolts sit on the larger leg.
- Using the bolt diameter instead of the hole diameter in the net section equation.
- Checking the utilization against Npl,Rd only and missing the lower net section resistance.
- Adopting γM2 = 1.25 without confirming the national annex value for the project.
When to run a software check
Hand checks are fast and transparent, but design software earns its place when many angles share one bracing level. Software handles the iteration and the connection checks, while the hand calculation remains the reference. Both should agree on the utilization before the design is issued.