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SteelAxial compression of a WT, channel or angle

Axial compression of a WT, channel or angle

CSA S16-19Verified

Sample report sheets

Class 4 effective area and flexural-torsional buckling of a WT, C, MC or single angle. Check a WT, a C or MC channel, or a single angle in concentric compression. Each element is classified, and a class 4 element's excess width comes off the area. The elastic buckling stress is the least root of S16's cubic, which couples twisting with bending about the axes the shear centre is off, and sets the compressive resistance.

Derivation, step by step

SIImperial

First report free, then a free sign-in

PASS Governing: Compressive resistance, D/C 0.49, S16 Cl. 13.1, C_f <= C_r, with C_r by Cl. 13.3.1.1 or, for a Class 4 element, Cl. 13.3.4 a)3 of 3 checks below pass

Given

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Type any value, everything below recomputes. Hover or tap a symbol to trace it.

Loads
CfC_{f} kN\mathrm{kN} 0-20,000
Section
FyF_{y} MPa\mathrm{MPa} 200-700
Buckling about x
LxL_{x} mm\mathrm{mm} 100-20,000
kxk_{x} 0.5-2.5
Buckling about y
LyL_{y} mm\mathrm{mm} 100-20,000
kyk_{y} 0.5-2.5
d = 456 mm b = 304 mm t = 23.9 mm w = 15.9 mm
The cross-section to scale.

Title block

Optional. Printed in the title block of the PDF.

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

Checks

! marks a check that passes with D/C at or above 0.95: close to its limit. The band is a site convention, not a code limit.

Slenderness, x axisS16 Cl. 10.4.2.1, KL/r of a compression member at most 200kx⋅Lxrx≤200⇒1⋅3000 mm143 mm≤200\frac{\htmlClass{sym-k_x}{k_{x}} \cdot \htmlClass{sym-L_x}{L_{x}}}{\htmlClass{sym-r_x}{r_{x}}} \leq 200 \quad \Rightarrow \quad \frac{\htmlClass{sym-k_x}{1} \cdot \htmlClass{sym-L_x}{3000\ \mathrm{mm}}}{\htmlClass{sym-r_x}{143\ \mathrm{mm}}} \leq 200 0.10 PASS
Slenderness, y axisS16 Cl. 10.4.2.1, KL/r of a compression member at most 200ky⋅Lyry≤200⇒1⋅1500 mm62.7 mm≤200\frac{\htmlClass{sym-k_y}{k_{y}} \cdot \htmlClass{sym-L_y}{L_{y}}}{\htmlClass{sym-r_y}{r_{y}}} \leq 200 \quad \Rightarrow \quad \frac{\htmlClass{sym-k_y}{1} \cdot \htmlClass{sym-L_y}{1500\ \mathrm{mm}}}{\htmlClass{sym-r_y}{62.7\ \mathrm{mm}}} \leq 200 0.12 PASS
Compressive resistanceS16 Cl. 13.1, C_f <= C_r, with C_r by Cl. 13.3.1.1 or, for a Class 4 element, Cl. 13.3.4 a)Cf≤Cr⇒1000 kN≤2026 kN\htmlClass{sym-C_f}{C_{f}} \leq \htmlClass{sym-C_r}{C_{r}} \quad \Rightarrow \quad \htmlClass{sym-C_f}{1000\ \mathrm{kN}} \leq \htmlClass{sym-C_r}{2026\ \mathrm{kN}} 0.49 PASS

Results

Cr\htmlClass{sym-C_r}{C_{r}} Factored compressive resistance 2026 kN\mathrm{kN}
Also worth checking
  • Combined axial load and bending, Cl. 13.8 and 13.9: this is concentric compression only
  • A WT, channel or angle loaded eccentrically, as through a connected leg or an end gusset, which puts a moment on the member; for a single angle connected through one leg Cl. 13.3.2.1 to 13.3.2.4 take an equivalent slenderness or the eccentricity, and the resistance can be lower than this concentric one (see the single-angle calculator)
  • Tension, shear and deflection
  • A member whose ends are free to twist: the calc takes K_z = 1.0 and L_z = L_x, which S16 Cl. 13.3.1.2 allows only when both ends are restrained from twisting
  • Local effects at the load points and the connections, including bolts and shear lag
  • Built-up and non-table sections, double angles and back-to-back channels, and any member out of straightness beyond what S16's column curve assumes

Derivation

S.1 Resistance factor

Compared with CSA S16-19 Cl. 13.1 a) (phi = 0.90, structural steel)

ϕ=0.9(Resistance factor | S16 Cl. 13.1)\begin{aligned} \htmlClass{sym-phi}{\phi} &= 0.9 \quad \left(\text{Resistance factor | S16 Cl. 13.1}\right) \end{aligned}
S.2 Steel modulus

Compared with CSA S16-19 Cl. 3 symbols, E = 200 000 MPa assumed

E=200000 MPa\begin{aligned} \htmlClass{sym-E}{E} &= 200000\ \mathrm{MPa} \end{aligned}
S.3 Shear modulus

Compared with CSA S16-19 Cl. 3 symbols, G = 77 000 MPa assumed

G=77000 MPa\begin{aligned} \htmlClass{sym-G}{G} &= 77000\ \mathrm{MPa} \end{aligned}
S.4 Flange width, or short leg of an angle

Accepted by the author: CISC SST 12.1 section table value (sections-data/cisc_12.1/), a given and not a formula; an HSS wall is the table's design thickness Tdes; WT460x111.5 B

b=304 mm(Width of flange or horizontal leg)\begin{aligned} \htmlClass{sym-b}{b} &= 304\ \mathrm{mm} \quad \left(\text{Width of flange or horizontal leg}\right) \end{aligned}
S.5 Flange thickness, or leg thickness of an angle

Accepted by the author: CISC SST 12.1 section table value (sections-data/cisc_12.1/), a given and not a formula; an HSS wall is the table's design thickness Tdes; WT460x111.5 T

t=23.9 mm(Thickness of flange)\begin{aligned} \htmlClass{sym-t}{t} &= 23.9\ \mathrm{mm} \quad \left(\text{Thickness of flange}\right) \end{aligned}
S.6 Depth, or long leg of an angle

Accepted by the author: CISC SST 12.1 section table value (sections-data/cisc_12.1/), a given and not a formula; an HSS wall is the table's design thickness Tdes; WT460x111.5 D

d=456 mm(Depth of section or height of vertical leg)\begin{aligned} \htmlClass{sym-d}{d} &= 456\ \mathrm{mm} \quad \left(\text{Depth of section or height of vertical leg}\right) \end{aligned}
S.7 Web or stem thickness

Accepted by the author: CISC SST 12.1 section table value (sections-data/cisc_12.1/), a given and not a formula; an HSS wall is the table's design thickness Tdes; WT460x111.5 W

w=15.9 mm(Thickness of web)\begin{aligned} \htmlClass{sym-w}{w} &= 15.9\ \mathrm{mm} \quad \left(\text{Thickness of web}\right) \end{aligned}
S.8 Class 3 limit, flanges

Compared with CSA S16-19 Cl. 11.2 Table 1, flanges of I, T and channels 200/sqrt(F_y) (angle legs take 250, lambda_3a in the angle branch)

S16 Cl. 11, Table 1, flanges of tees and channels

λ3=200Fy1 MPa=200350 MPa1 MPa=10.69\begin{aligned} \htmlClass{sym-lambda_3}{\lambda_{3}} &= \frac{200}{\sqrt{\frac{\htmlClass{sym-F_y}{F_{y}}}{1\ \mathrm{MPa}}}} \\ &= \frac{200}{\sqrt{\frac{\htmlClass{sym-F_y}{350\ \mathrm{MPa}}}{1\ \mathrm{MPa}}}} \\ &= 10.69 \end{aligned}
S.9 Shear centre offset, x (principal for an angle)

Accepted by the author: Geometry: x_0 = 0 for a WT, whose shear centre lies on the axis of symmetry (the stem axis); a channel and an angle read Xo and Xop from CISC SST 12.1 (sections-data/cisc_12.1/), table values

x0=0 mm(Shear centre on the stem’s axis, a WT)\begin{aligned} \htmlClass{sym-x_0}{x_{0}} &= 0\ \mathrm{mm} \quad \left(\text{Shear centre on the stem's axis, a WT}\right) \end{aligned}
S.10 Shear centre offset, y (principal for an angle)

Accepted by the author: CISC SST 12.1 section table value (sections-data/cisc_12.1/), a given and not a formula; an HSS wall is the table's design thickness Tdes; WT460x111.5 Yo

y0=110 mm(Distance between centroid and shear centre along geometric axis YY)\begin{aligned} \htmlClass{sym-y_0}{y_{0}} &= 110\ \mathrm{mm} \quad \left(\text{Distance between centroid and shear centre along geometric axis YY}\right) \end{aligned}
S.11 Flange width-to-thickness ratio

Compared with CSA S16-19 Cl. 11.2 Table 1 / Cl. 13.3.4 a), WT flange b_el/t = 0.5 b/t

S16 Cl. 11.3.1 c), half the flange of a tee

λf=0.5⋅bt=0.5⋅304 mm23.9 mm=6.36\begin{aligned} \htmlClass{sym-lambda_f}{\lambda_{f}} &= \frac{0.5 \cdot \htmlClass{sym-b}{b}}{\htmlClass{sym-t}{t}} \\ &= \frac{0.5 \cdot \htmlClass{sym-b}{304\ \mathrm{mm}}}{\htmlClass{sym-t}{23.9\ \mathrm{mm}}} \\ &= 6.36 \end{aligned}

Branch: λf>λ3\lambda_{f} > \lambda_{3} did not hold

S.12 Class 4 excess, flanges

Compared with CSA S16-19 Cl. 13.3.4 a) and Table 1 (area is reduced to A_e only where b_el/t exceeds 200/sqrt(F_y), b_el = b/2 for a T flange per Cl. 11.3.1 c), so A_b = 0 for the WT460x111.5 flange at 6.4 against 10.7)

Ab=0 mm2(Flange not class 4)\begin{aligned} \htmlClass{sym-A_b}{A_{b}} &= 0\ \mathrm{mm}^{2} \quad \left(\text{Flange not class 4}\right) \end{aligned}
S.13 Stem depth-to-thickness ratio

Compared with CSA S16-19 Cl. 11.2 Table 1 / Cl. 13.3.4 a), WT stem b_el/t = d/w

λs=dw=456 mm15.9 mm=28.68\begin{aligned} \htmlClass{sym-lambda_s}{\lambda_{s}} &= \frac{\htmlClass{sym-d}{d}}{\htmlClass{sym-w}{w}} \\ &= \frac{\htmlClass{sym-d}{456\ \mathrm{mm}}}{\htmlClass{sym-w}{15.9\ \mathrm{mm}}} \\ &= 28.68 \end{aligned}
S.14 Class 3 limit, stem

Compared with CSA S16-19 Cl. 11.2 Table 1 (stems of T-sections: 340/sqrt(F_y))

S16 Cl. 11, Table 1, stem of a tee

λ3s=340Fy1 MPa=340350 MPa1 MPa=18.17\begin{aligned} \htmlClass{sym-lambda_3s}{\lambda_{3s}} &= \frac{340}{\sqrt{\frac{\htmlClass{sym-F_y}{F_{y}}}{1\ \mathrm{MPa}}}} \\ &= \frac{340}{\sqrt{\frac{\htmlClass{sym-F_y}{350\ \mathrm{MPa}}}{1\ \mathrm{MPa}}}} \\ &= 18.17 \end{aligned}

Branch: λs>λ3s\lambda_{s} > \lambda_{3s} held

S.15 Class 4 excess, web or stem

Compared with CSA S16-19 Cl. 13.3.4 a), area lost to reduced stem width (lambda_s - lambda_3s) w^2

Ad=(λs−λ3s)⋅w2=(28.68−18.17)⋅(15.9 mm)2=2656 mm2\begin{aligned} \htmlClass{sym-A_d}{A_{d}} &= \left(\htmlClass{sym-lambda_s}{\lambda_{s}} - \htmlClass{sym-lambda_3s}{\lambda_{3s}}\right) \cdot \htmlClass{sym-w}{w}^{2} \\ &= \left(\htmlClass{sym-lambda_s}{28.68} - \htmlClass{sym-lambda_3s}{18.17}\right) \cdot \left(\htmlClass{sym-w}{15.9\ \mathrm{mm}}\right)^{2} \\ &= 2656\ \mathrm{mm}^{2} \end{aligned}
S.16 Gross area

Accepted by the author: CISC SST 12.1 section table value (sections-data/cisc_12.1/), a given and not a formula; an HSS wall is the table's design thickness Tdes; WT460x111.5 A_Th

A0=14300 mm2(Cross-sectional area)\begin{aligned} \htmlClass{sym-A_0}{A_{0}} &= 14300\ \mathrm{mm}^{2} \quad \left(\text{Cross-sectional area}\right) \end{aligned}
S.17 Effective area

Compared with CSA S16-19 Cl. 13.3.4 a), effective area = gross less reduced widths

S16 Cl. 13.3.4 a), A_e from reduced widths meeting Table 1

Ae=A0−Ab−Ad=14300 mm2−0 mm2−2656 mm2=11644 mm2\begin{aligned} \htmlClass{sym-A_e}{A_{e}} &= \htmlClass{sym-A_0}{A_{0}} - \htmlClass{sym-A_b}{A_{b}} - \htmlClass{sym-A_d}{A_{d}} \\ &= \htmlClass{sym-A_0}{14300\ \mathrm{mm}^{2}} - \htmlClass{sym-A_b}{0\ \mathrm{mm}^{2}} - \htmlClass{sym-A_d}{2656\ \mathrm{mm}^{2}} \\ &= 11644\ \mathrm{mm}^{2} \end{aligned}
S.18 Radius of gyration about x (major principal axis for an angle)

Accepted by the author: CISC SST 12.1 section table value (sections-data/cisc_12.1/), a given and not a formula; an HSS wall is the table's design thickness Tdes; WT460x111.5 Rx

rx=143 mm(Radius of gyration about axis XX)\begin{aligned} \htmlClass{sym-r_x}{r_{x}} &= 143\ \mathrm{mm} \quad \left(\text{Radius of gyration about axis XX}\right) \end{aligned}
S.19 Radius of gyration about y (minor principal axis for an angle)

Accepted by the author: CISC SST 12.1 section table value (sections-data/cisc_12.1/), a given and not a formula; an HSS wall is the table's design thickness Tdes; WT460x111.5 Ry

ry=62.7 mm(Radius of gyration about axis YY)\begin{aligned} \htmlClass{sym-r_y}{r_{y}} &= 62.7\ \mathrm{mm} \quad \left(\text{Radius of gyration about axis YY}\right) \end{aligned}
S.20 Torsional constant

Accepted by the author: CISC SST 12.1 section table value (sections-data/cisc_12.1/), a given and not a formula; an HSS wall is the table's design thickness Tdes; WT460x111.5 J

J=2.08×106 mm4(St-Venant torsional constant)\begin{aligned} \htmlClass{sym-J}{J} &= 2.08 \times 10^{6}\ \mathrm{mm}^{4} \quad \left(\text{St-Venant torsional constant}\right) \end{aligned}
S.21 Warping constant

Accepted by the author: CISC SST 12.1 section table value (sections-data/cisc_12.1/), a given and not a formula; an HSS wall is the table's design thickness Tdes; WT460x111.5 Cw

Cw=1.24×1010 mm6(Warping constant)\begin{aligned} \htmlClass{sym-C_w}{C_{w}} &= 1.24 \times 10^{10}\ \mathrm{mm}^{6} \quad \left(\text{Warping constant}\right) \end{aligned}
S.22 Torsional length

Accepted by the author: assumption: the torsional unbraced length L_z is taken as L_x with K_z = 1.0. CSA S16-19 Cl. 13.3.1.2 gives no rule for L_z and allows K_z = 1.0 only when both ends of the member are restrained from twisting; the calc assumes end connections that prevent twist, and its scope list says a member with ends free to twist is not covered

S16 Cl. 13.3.1.2, K_z L_z taken as L_x, K_z = 1.0 with both ends restrained from twisting

Lz=1⋅Lx=1⋅3000 mm=3000 mm\begin{aligned} \htmlClass{sym-L_z}{L_{z}} &= 1 \cdot \htmlClass{sym-L_x}{L_{x}} \\ &= 1 \cdot \htmlClass{sym-L_x}{3000\ \mathrm{mm}} \\ &= 3000\ \mathrm{mm} \end{aligned}
S.23 Polar radius about the shear centre

Compared with CSA S16-19 Cl. 13.3.1.2, r_o^2 = x_o^2 + y_o^2 + r_x^2 + r_y^2

r0=x02+y02+rx2+ry2=(0 mm)2+(110 mm)2+(143 mm)2+(62.7 mm)2=191 mm\begin{aligned} \htmlClass{sym-r_0}{r_{0}} &= \sqrt{\htmlClass{sym-x_0}{x_{0}}^{2} + \htmlClass{sym-y_0}{y_{0}}^{2} + \htmlClass{sym-r_x}{r_{x}}^{2} + \htmlClass{sym-r_y}{r_{y}}^{2}} \\ &= \sqrt{\left(\htmlClass{sym-x_0}{0\ \mathrm{mm}}\right)^{2} + \left(\htmlClass{sym-y_0}{110\ \mathrm{mm}}\right)^{2} + \left(\htmlClass{sym-r_x}{143\ \mathrm{mm}}\right)^{2} + \left(\htmlClass{sym-r_y}{62.7\ \mathrm{mm}}\right)^{2}} \\ &= 191\ \mathrm{mm} \end{aligned}
S.24 Euler stress about x

Compared with CSA S16-19 Cl. 13.3.1.2, F_ex = pi^2 E / (K_x L_x / r_x)^2 (1.974 TPa = pi^2 E)

Fex=1.974×106 MPa(kx⋅Lxrx)2=1.974×106 MPa(1⋅3000 mm143 mm)2=4485 MPa\begin{aligned} \htmlClass{sym-F_ex}{F_{\mathrm{ex}}} &= \frac{1.974 \times 10^{6}\ \mathrm{MPa}}{\left(\frac{\htmlClass{sym-k_x}{k_{x}} \cdot \htmlClass{sym-L_x}{L_{x}}}{\htmlClass{sym-r_x}{r_{x}}}\right)^{2}} \\ &= \frac{1.974 \times 10^{6}\ \mathrm{MPa}}{\left(\frac{\htmlClass{sym-k_x}{1} \cdot \htmlClass{sym-L_x}{3000\ \mathrm{mm}}}{\htmlClass{sym-r_x}{143\ \mathrm{mm}}}\right)^{2}} \\ &= 4485\ \mathrm{MPa} \end{aligned}
S.25 Euler stress about y

Compared with CSA S16-19 Cl. 13.3.1.2, F_ey = pi^2 E / (K_y L_y / r_y)^2

Fey=1.974×106 MPa(ky⋅Lyry)2=1.974×106 MPa(1⋅1500 mm62.7 mm)2=3449 MPa\begin{aligned} \htmlClass{sym-F_ey}{F_{\mathrm{ey}}} &= \frac{1.974 \times 10^{6}\ \mathrm{MPa}}{\left(\frac{\htmlClass{sym-k_y}{k_{y}} \cdot \htmlClass{sym-L_y}{L_{y}}}{\htmlClass{sym-r_y}{r_{y}}}\right)^{2}} \\ &= \frac{1.974 \times 10^{6}\ \mathrm{MPa}}{\left(\frac{\htmlClass{sym-k_y}{1} \cdot \htmlClass{sym-L_y}{1500\ \mathrm{mm}}}{\htmlClass{sym-r_y}{62.7\ \mathrm{mm}}}\right)^{2}} \\ &= 3449\ \mathrm{MPa} \end{aligned}
S.26 Torsional buckling stress

Compared with CSA S16-19 Cl. 13.3.1.2, F_ez = (pi^2 E C_w/(K_z L_z)^2 + G J)/(A r_o^2), K_z L_z taken as L_x, gross A

Fez=1.974×106 MPa⋅CwLz2+G⋅JA0⋅r02=1.974×106 MPa⋅1.24×1010 mm6(3000 mm)2+77000 MPa⋅2.08×106 mm414300 mm2⋅(191 mm)2=312.2 MPa\begin{aligned} \htmlClass{sym-F_ez}{F_{\mathrm{ez}}} &= \frac{\frac{1.974 \times 10^{6}\ \mathrm{MPa} \cdot \htmlClass{sym-C_w}{C_{w}}}{\htmlClass{sym-L_z}{L_{z}}^{2}} + \htmlClass{sym-G}{G} \cdot \htmlClass{sym-J}{J}}{\htmlClass{sym-A_0}{A_{0}} \cdot \htmlClass{sym-r_0}{r_{0}}^{2}} \\ &= \frac{\frac{1.974 \times 10^{6}\ \mathrm{MPa} \cdot \htmlClass{sym-C_w}{1.24 \times 10^{10}\ \mathrm{mm}^{6}}}{\left(\htmlClass{sym-L_z}{3000\ \mathrm{mm}}\right)^{2}} + \htmlClass{sym-G}{77000\ \mathrm{MPa}} \cdot \htmlClass{sym-J}{2.08 \times 10^{6}\ \mathrm{mm}^{4}}}{\htmlClass{sym-A_0}{14300\ \mathrm{mm}^{2}} \cdot \left(\htmlClass{sym-r_0}{191\ \mathrm{mm}}\right)^{2}} \\ &= 312.2\ \mathrm{MPa} \end{aligned}
S.27 Elastic buckling stress

Compared with CSA S16-19 Cl. 13.3.1.1 (c) (smallest root of the cubic in F_ex, F_ey, F_ez, x_o, y_o and r_o^2 = x_o^2 + y_o^2 + r_x^2 + r_y^2; it reduces to (b), the lesser of F_ex and F_eyz, for the WT with x_o = 0); the F_ex, F_ey, F_ez inputs are not covered by this row

S16 Cl. 13.3.1.1 (b) or (c), the cubic

Fe=root⁡min⁡F>0((F−Fex)(F−Fey)(F−Fez)−F2(F−Fey)(x0r0)2−F2(F−Fex)(y0r0)2)=root⁡min⁡F>0((F−4485 MPa)(F−3449 MPa)(F−312.2 MPa)−F2(F−3449 MPa)(0 mm191 mm)2−F2(F−4485 MPa)(110 mm191 mm)2)=302.6 MPa\begin{aligned} \htmlClass{sym-F_e}{F_{e}} &= \operatorname{root}_{\min F > 0}\left((F - \htmlClass{sym-F_ex}{F_{\mathrm{ex}}})(F - \htmlClass{sym-F_ey}{F_{\mathrm{ey}}})(F - \htmlClass{sym-F_ez}{F_{\mathrm{ez}}}) - F^{2}(F - \htmlClass{sym-F_ey}{F_{\mathrm{ey}}})\left(\frac{\htmlClass{sym-x_0}{x_{0}}}{\htmlClass{sym-r_0}{r_{0}}}\right)^{2} - F^{2}(F - \htmlClass{sym-F_ex}{F_{\mathrm{ex}}})\left(\frac{\htmlClass{sym-y_0}{y_{0}}}{\htmlClass{sym-r_0}{r_{0}}}\right)^{2}\right) \\ &= \operatorname{root}_{\min F > 0}\left((F - \htmlClass{sym-F_ex}{4485\ \mathrm{MPa}})(F - \htmlClass{sym-F_ey}{3449\ \mathrm{MPa}})(F - \htmlClass{sym-F_ez}{312.2\ \mathrm{MPa}}) - F^{2}(F - \htmlClass{sym-F_ey}{3449\ \mathrm{MPa}})\left(\frac{\htmlClass{sym-x_0}{0\ \mathrm{mm}}}{\htmlClass{sym-r_0}{191\ \mathrm{mm}}}\right)^{2} - F^{2}(F - \htmlClass{sym-F_ex}{4485\ \mathrm{MPa}})\left(\frac{\htmlClass{sym-y_0}{110\ \mathrm{mm}}}{\htmlClass{sym-r_0}{191\ \mathrm{mm}}}\right)^{2}\right) \\ &= 302.6\ \mathrm{MPa} \end{aligned}
S.28 Slenderness parameter

Compared with CSA S16-19 Cl. 13.3.1.1, lambda = sqrt(F_y/F_e)

λe=FyFe=350 MPa302.6 MPa=1.076\begin{aligned} \htmlClass{sym-lambda_e}{\lambda_{e}} &= \sqrt{\frac{\htmlClass{sym-F_y}{F_{y}}}{\htmlClass{sym-F_e}{F_{e}}}} \\ &= \sqrt{\frac{\htmlClass{sym-F_y}{350\ \mathrm{MPa}}}{\htmlClass{sym-F_e}{302.6\ \mathrm{MPa}}}} \\ &= 1.076 \end{aligned}
S.29 Compressive stress

Compared with CSA S16-19 Cl. 13.3.1.1 (C_r = phi A F_y / (1 + lambda^2n)^(1/n), n = 1.34 hot-rolled, lambda = sqrt(F_y/F_e))

S16 Cl. 13.3.1, n = 1.34

fs=Fy⋅(1+λe2⋅1.34)−11.34=350 MPa⋅(1+1.0762⋅1.34)−11.34=193.3 MPa\begin{aligned} \htmlClass{sym-f_s}{f_{s}} &= \htmlClass{sym-F_y}{F_{y}} \cdot \left(1 + \htmlClass{sym-lambda_e}{\lambda_{e}}^{2 \cdot 1.34}\right)^{\frac{-1}{1.34}} \\ &= \htmlClass{sym-F_y}{350\ \mathrm{MPa}} \cdot \left(1 + \htmlClass{sym-lambda_e}{1.076}^{2 \cdot 1.34}\right)^{\frac{-1}{1.34}} \\ &= 193.3\ \mathrm{MPa} \end{aligned}
S.30 Compressive resistance

Compared with CSA S16-19 Cl. 13.3.4 a) (13.3.1.1 with A_e), C_r = phi A_e F_y/(1+lambda^2n)^(1/n)

Cr=ϕ⋅Ae⋅fs=0.9⋅11644 mm2⋅193.3 MPa=2026 kN\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}{11644\ \mathrm{mm}^{2}} \cdot \htmlClass{sym-f_s}{193.3\ \mathrm{MPa}} \\ &= 2026\ \mathrm{kN} \end{aligned}

Report

Sheet 1 and the first sheet of the working of the PDF report, at the declared values with a sample title block. First report free, then a free sign-in.

Show the two sheets
Sheet 1 of the Axial compression of a WT, channel or angle report: title block, verdict, checks and figures
Sheet 1: title block, verdict, checks, figures · full size
The first sheet of the working in the Axial compression of a WT, channel or angle report: each step with its clause
The working: each step with its clause · full size

Questions

Which axes are r_x and r_y about for an angle?

The principal axes: r_x and r_y are the major and minor principal radii, and x_0 and y_0 the shear centre's offsets along them.

Why is the torsional length L_x?

The member's length between twisting restraints is taken as the x-axis length. Enter L_x as that length.

Revision history

After an independent checker's review: added slenderness checks of KL/r against 200 on each axis (Cl. 10.4.2.1), cited the class 4 effective area (Cl. 13.3.4 a) and the tee half-flange width, and named the single-angle through-one-leg rule (Cl. 13.3.2) as not checked
ValueWasNowUnit
slender_x_ok
slender_y_ok
fix(units,examples): zero keeps its unit, zero cope, shear tab rules
ValueWasNowUnit
x_00 \mathrm{m}0mm\mathrm{mm}
A_b0 \mathrm{m}^{2}0mm2\mathrm{mm}^{2}

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