calcsheetSteelSingle angle in compression
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CSA S16-19 Cl. 13.3 and 13.8, AISC 360-22 Section F10

Single angle in compression

Verified against CSA S16-19, AISC 360-22 and CISC SST 12.1, 2026-10-02

An equal-leg angle brace, concentric or bolted through one leg, to CSA S16 and AISC F10. Check an equal-leg single angle in compression. Concentrically loaded, it takes the equivalent slenderness of CSA S16 Cl. 13.3.2. Bolted through one leg to a gusset, the eccentricity bends it about both principal axes, and it is checked for combined compression and bending: torsional-flexural buckling for the axial resistance, AISC's single angle yielding, leg local buckling and lateral-torsional buckling for bending, and S16's interaction for cross-section, overall member and lateral-torsional buckling strength.

Given

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\(\mathrm{case}\)
\(C_{f}\) \(\mathrm{kN}\) 0-5,000
\(L\) \(\mathrm{mm}\) 100-10,000
\(k\) 0.5-2.5
\(F_{y}\) \(\mathrm{MPa}\) 200-700
\(\mathrm{section}\)
\(t_{p}\) \(\mathrm{mm}\) 3-80
\(e\) \(\mathrm{mm}\) 10-200
t = 6.35 mm b = 76.2 mm
The angle's cross-section to scale, with the gusset and bolt line when bolted through one leg.

Title block

Optional. Printed under the title of the PDF.

This printed copy omits the derivation. The full report, with every step, is the PDF at https://calc.struct.work/calc/single-angle.pdf.

Checks

Check D/C Result
Axial ok\(\htmlClass{sym-C_f}{C_{f}} \leq \htmlClass{sym-C_r}{C_{r}} \quad \Rightarrow \quad \htmlClass{sym-C_f}{20\ \mathrm{kN}} \leq \htmlClass{sym-C_r}{91.79\ \mathrm{kN}}\) 0.22 PASS

Results

Quantity Description Value Unit
\(\htmlClass{sym-C_r}{C_{r}}\) Factored compressive resistance 91.79 \(\mathrm{kN}\)

Derivation

S.1 \[\begin{aligned} \htmlClass{sym-phi}{\phi} &= 0.9 \quad \left(\text{Resistance factor | S16 Cl. 13.1}\right) \end{aligned}\]
S.2 \[\begin{aligned} \htmlClass{sym-E}{E} &= 200\ \mathrm{GPa} \end{aligned}\]
S.3 \[\begin{aligned} \htmlClass{sym-G}{G} &= 77\ \mathrm{GPa} \end{aligned}\]
S.4 \[\begin{aligned} \htmlClass{sym-b}{b} &= 76.2\ \mathrm{mm} \quad \left(\text{Depth of section or height of vertical leg}\right) \end{aligned}\]
S.5 \[\begin{aligned} \htmlClass{sym-t}{t} &= 6.35\ \mathrm{mm} \quad \left(\text{Thickness of flange}\right) \end{aligned}\]
S.6 \[\begin{aligned} \htmlClass{sym-A_0}{A_{0}} &= 927\ \mathrm{mm}^{2} \quad \left(\text{Cross-sectional area}\right) \end{aligned}\]
S.7 \[\begin{aligned} \htmlClass{sym-lambda_l}{\lambda_{l}} &= \frac{\htmlClass{sym-b}{b}}{\htmlClass{sym-t}{t}} \\ &= \frac{\htmlClass{sym-b}{76.2\ \mathrm{mm}}}{\htmlClass{sym-t}{6.35\ \mathrm{mm}}} \\ &= 12 \end{aligned}\]
S.8

S16 Cl. 11, Table 1, legs of angles

\[\begin{aligned} \htmlClass{sym-lambda_3}{\lambda_{3}} &= \frac{250}{\sqrt{\frac{\htmlClass{sym-F_y}{F_{y}}}{1\ \mathrm{MPa}}}} \\ &= \frac{250}{\sqrt{\frac{\htmlClass{sym-F_y}{300\ \mathrm{MPa}}}{1\ \mathrm{MPa}}}} \\ &= 14.43 \end{aligned}\]

Branch: \(\lambda_{l} > \lambda_{3}\) did not hold

S.9 \[\begin{aligned} \htmlClass{sym-A_e}{A_{e}} &= 1 \cdot \htmlClass{sym-A_0}{A_{0}} \\ &= 1 \cdot \htmlClass{sym-A_0}{927\ \mathrm{mm}^{2}} \\ &= 927\ \mathrm{mm}^{2} \end{aligned}\]
S.10 \[\begin{aligned} \htmlClass{sym-r_x}{r_{x}} &= 23.6\ \mathrm{mm} \quad \left(\text{Radius of gyration about axis XX}\right) \end{aligned}\]

Branch: \(\frac{L}{r_{x}} \leq 80\) held

S.11

S16 Cl. 13.3.2.2 a)

\[\begin{aligned} \htmlClass{sym-KL_r}{\mathrm{KL}_{r}} &= 72 + \frac{0.75 \cdot \htmlClass{sym-L}{L}}{\htmlClass{sym-r_x}{r_{x}}} \\ &= 72 + \frac{0.75 \cdot \htmlClass{sym-L}{1500\ \mathrm{mm}}}{\htmlClass{sym-r_x}{23.6\ \mathrm{mm}}} \\ &= 119.7 \end{aligned}\]
S.12 \[\begin{aligned} \htmlClass{sym-lambda_c}{\lambda_{c}} &= \htmlClass{sym-KL_r}{\mathrm{KL}_{r}} \cdot \sqrt{\frac{\htmlClass{sym-F_y}{F_{y}}}{1.974\ \mathrm{TPa}}} \\ &= \htmlClass{sym-KL_r}{119.7} \cdot \sqrt{\frac{\htmlClass{sym-F_y}{300\ \mathrm{MPa}}}{1.974\ \mathrm{TPa}}} \\ &= 1.475 \end{aligned}\]
S.13

S16 Cl. 13.3.1, n = 1.34

\[\begin{aligned} \htmlClass{sym-f_s}{f_{s}} &= \htmlClass{sym-F_y}{F_{y}} \cdot \left(1 + \htmlClass{sym-lambda_c}{\lambda_{c}}^{2 \cdot 1.34}\right)^{\frac{-1}{1.34}} \\ &= \htmlClass{sym-F_y}{300\ \mathrm{MPa}} \cdot \left(1 + \htmlClass{sym-lambda_c}{1.475}^{2 \cdot 1.34}\right)^{\frac{-1}{1.34}} \\ &= 110\ \mathrm{MPa} \end{aligned}\]
S.14 \[\begin{aligned} \htmlClass{sym-C_r}{C_{r}} &= \htmlClass{sym-phi}{\phi} \cdot \htmlClass{sym-A_e}{A_{e}} \cdot \htmlClass{sym-f_s}{f_{s}} \\ &= \htmlClass{sym-phi}{0.9} \cdot \htmlClass{sym-A_e}{927\ \mathrm{mm}^{2}} \cdot \htmlClass{sym-f_s}{110\ \mathrm{MPa}} \\ &= 91.79\ \mathrm{kN} \end{aligned}\]

Questions

When should I use the eccentric case?

When the angle is bolted or welded through one leg and the load reaches it off its centroid, which is almost always. The concentric case is S16's simplified equivalent slenderness for such braces, within its own limits.

Where do the section properties come from?

The CISC Handbook's angle tables: r_x is about the geometric axis, r_x0 and r_y0 about the principal axes, and x_0 is the shear centre's offset from the centroid.

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