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This calculator follows the procedures and guidelines of the American Institute of Steel Construction (AISC) Specification of Structural Steel Buildings - Allowable Stress Design and Plastic Design - 9th Edition 1989 (AISC 360).
It calculates actual and allowable stresses in members when subjected to axial load and/or uniaxial or biaxial bending. Therefore it is applicable to both beams and columns. The final result is computed as a Stress Ratio (S.R) of actual stress to allowable stress. A member with S.R ≤ 1 is deemed adequate against strength checks.
❗ This calculation has been written in accordance with AISC 360.
Common steel sections in ASIC


Calculation

Technical Notes

Inputs

Member Properties



Fy, ksi
:50​



d
:15in​



tw
:2in​



bf
:10in​



tf
:0.5in​



Loads



P
:235kips​



Mx, ft-kips
:20​



My, ft-kips
:5​



Design Parameters for Compression Design



Kx
:1​



Ky
:1​



Lx
:10ft​



Ly
:5ft​



Lb
:5ft​



Design Parameters for Flexural Design



Cb
:1​



Cmx
:-1​



Cmy
:-1​



ASIF
:1​


Note on ASIF

'ASIF' is a multiplier of any of the calculated allowable stresses Fa, Fbx and Fby and the Euler column buckling stresses F’ex and F’ey. It appears only when calculating the Stress Ratio (S.R) where a value of 1.0 is typically used.

Output

Member Properties



Cross-sectional area
:38.0​



rt
:2.11453644277324​



J
:40.8333333333333​



Cw, in.^6
:4870.79166666668​



Lc
:8.956685895029583​



Lu
:11.111111111111084​



Lb/rt
:28.375013448011​

X-Axis


Sx
:131.088888888889in3​



Ix
:983.166666666666​



rx
:5.08653192436102​

Y-Axis


Sy
:18.5333333333333in3​



Iy
:92.6666666666667​



ry
:1.56160061834903​


Capacity Checks

Axial (Compression / Tension)



Kx*Lx/rx
:23.5917127395351​



Ky*Ly/ry
:38.4221159334797​



Cc
:106.99879020467306​



fa, ksi
:6.18421052631579​



Fa, ksi
:26.051462689272455​



Pa, kips
:989.955582192355​



fa/Fa
:0.2373843879738212​



:PASS​


Axial tension



Allowable tension stress, Ft (ksi)
:30​



:NA​


Flexure (X-Axis)



fbx, ksi
:1.83081878284455​



Fbx, ksi
:32.4289321881345​



Mrx, ft-kips
:354.25605736630666​



F'ex, ksi
:268.307127907887​



fbx/Fbx
:0.05645633880952863​



fbx<Fbx?
:PASS​


Flexure (Y-Axis)



fby, ksi
:3.23741007194245​



Fby, ksi
:36.0723304703363​



Mry, ft-kips
:55.71171039307483​



F'ey, ksi
:101.15528945027​



fby/Fby
:0.08974773821737689​



fby<Fby?
:PASS​



Combined Check (Stress Ratio)



Stress ratio
:0​



:PASS​



Explanation

The American and British Standards method for design is to compare "allowable stresses" against "actual stresses", where actual stresses are based upon characteristic loads with an overall Factor of Safety (FoS).
The design checks to ACI 360R-22 are based upon ensuring:

actual stress≤allowable stressFoS\text{actual stress}\le\dfrac{\text{allowable stress}}{\text{FoS}}


Compression Check

Column's slenderness ratio (KL/r) is a key parameter in calculating the allowable stress, and is defined as the ratio of its effective length (KL) and radius of gyration (r). These values vary depending on the axis considered (major / minor).
Actual compressive stress is calculated by:

fa=FA\large{f_{a}=\frac{F}{A}}
The formula varies depending on whether the column is buckling elastically or inelastically, and is determined by the factor Cc:

Cc=2π2EFy\large{C_c=\sqrt{\frac{2 \pi^2 E}{F_y}}}
For calculating the allowable axial compressive stress, Fa:

KLr=max(KxLxrx,KyLyry)KLr≤Cc: Fa=[1−(KL/r)22Cc2]Fy53+3(KL/r)8Cc−(KL/r)38Cc3KLr>Cc: Fa=12π2E23(KL/r)2 \normalsize\frac{KL}{r}=\text{max(}\frac{K_xL_x}{r_x},\frac{K_yL_y}{r_y})\\\frac{KL }{r}\le{C_c}:\large \ F_a=\frac{\left[1-\frac{(K L / r)^2}{2 C_c{ }^2}\right] F_y}{\frac{5}{3}+\frac{3(K L / r)}{8 C_c}-\frac{(K L / r)^3}{8 C_c{ }^3}}\\\frac{KL}{r}>C_c:\large\ F_a=\frac{12\pi^2E}{23(KL/r)^2}\

Compression buckling


Flexural Check

Actual bending stress is calculated by:

fb=12MS\large{f_{b}=\frac{12M}{S}}
For calculating the allowable bending stress, Fb:

If  bf2tf≤65Fy : Fby=0.75FyIf  65Fy<bf2tf≤95Fy : Fby=Fy(1.075−0.005bf2tfFy)If  bf2tf>95Fy : Fby=0.6Fy\text{If}\ \ \large\frac{b_f}{2t_f}\le\frac{65}{\sqrt{F_y}}\ :\normalsize\ F_{by}=0.75F_y\\\text{If}\ \ \large\frac{65}{\sqrt{F_y}}<\frac{b_f}{2t_f}\le\frac{95}{\sqrt{F_y}}\ :\normalsize\ F_{by}=F_y(1.075-\frac{0.005b_f}{2t_f}\sqrt{F_y})\\\text{If}\ \ \large\frac{b_f}{2t_f}>\frac{95}{\sqrt{F_y}}\ :\normalsize\ F_{by}=0.6F_y
For calculating allowable resisting moment (Mr) and Euler stress (F'e):

Mr=FbS12Fe′=12Ep223(KL12r)2M_{r}=\frac{F_{b}S}{12}\\F'_{e}=\frac{12Ep^2}{23(KL\frac{12}{r})^2}
Buckling due to bending



Combined Check (Stress Ratio)

The Stress Ratio (S.R.) checks against the combined actions of axial and flexure. A steel section with S.R. ≤ 1 is deemed safe against strength checks.
For axial compression and bending:

faFa+Cmxfbx(1−faFex′)Fbx+Cmyfby(1−faFey′)Fby≤1.0fa0.60Fy+fbxFbx+fbyFby≤1.0\large\frac{f_a}{F_a}+\frac{C_{m x} f_{b x}}{\left(1-\frac{f_a}{F_{e x}^{\prime}}\right) F_{b x}}+\frac{C_{m y} f_{b y}}{\left(1-\frac{f_a}{F_{e y}^{\prime}}\right) F_{b y}} \leq 1.0\\\frac{f_a}{0.60 F_y}+\frac{f_{b x}}{F_{b x}}+\frac{f_{b y}}{F_{b y}} \leq 1.0
For fa/Fa < 0.15 and/or for axial tension and bending, then:

faFa+fbxFbx+fbyFby≤1.0\large\frac{f_a}{F_a}+\frac{f_{b x}}{F_{b x}}+\frac{f_{b y}}{F_{b y}} \leq 1.0

More information about parameters and equations used for column design according to AISC are discussed below:

Formulas for geometric properties

Effective lengths, Lx and Ly (axial compression)

Effective lengths, Lb, Lc and Lu (bending)

Bending coefficients