Steel Beam and Column Designer to AISC 360

Verified by the CalcTree engineering team on June 27, 2024
﻿
This calculator computes 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. 
All calculations are performed in accordance with AISC 360, which is the American Institute of Steel Construction (AISC) Specification of Structural Steel Buildings - Allowable Stress Design and Plastic Design - 9th Edition 1989. 
﻿
Common steel sections in ASIC
CalculationTechnical Notes
This calculator:
requires input for the total depth (﻿d
), web thickness (﻿tw​
), flange thickness (﻿tf​
), design parameters and member loadings. All remaining section properties are calculated
does not check shear, deflection or torsion and does not consider deduction for holes in members subject to tension
assumes the Modulus of Elasticity for steel (﻿E
) is 29,000 ksi
is valid for AISC W, S, M and HP shapes that are not contained in the AISC 9th Edition Manual, as well as for non-hybrid and doubly symmetrical I-shape built-up members which have their flanges continuously welded to the web and which do not qualify as plate girders.
InputsMember Properties
﻿﻿Fy
:{"mathjs":"Unit","value":50,"unit":"ksi","fixPrefix":false}​
﻿
﻿﻿ d
:{"mathjs":"Unit","value":14,"unit":"in","fixPrefix":false}​
﻿
﻿﻿tw
:{"mathjs":"Unit","value":0.44,"unit":"in","fixPrefix":false}​
﻿
﻿﻿bf
:{"mathjs":"Unit","value":14.499999999999998,"unit":"in","fixPrefix":false}​
﻿
﻿﻿tf
:{"mathjs":"Unit","value":0.71,"unit":"in","fixPrefix":false}​
﻿
﻿
Loads
﻿﻿P
:{"mathjs":"Unit","value":8,"unit":"kips","fixPrefix":false}​
﻿
compression (+), tension (-)
﻿﻿Mx
:{"mathjs":"Unit","value":20.000000000000004,"unit":"kips ft","fixPrefix":false}​
﻿
﻿﻿My
:{"mathjs":"Unit","value":0,"unit":"kips ft","fixPrefix":false}​
﻿
Design Parameters for Compression
﻿﻿Kx
:1​
﻿
﻿﻿ Ky
:1​
﻿
﻿﻿Lx
:{"mathjs":"Unit","value":12,"unit":"ft","fixPrefix":false}​
﻿
﻿﻿Ly
:{"mathjs":"Unit","value":12,"unit":"ft","fixPrefix":false}​
﻿
﻿﻿Lb
:{"mathjs":"Unit","value":12,"unit":"ft","fixPrefix":false}​
﻿
﻿
Design Parameters for Flexural
﻿﻿Cb
:1​
﻿
﻿﻿Cmx
:-1​
﻿
﻿﻿Cmy
:-1​
﻿
﻿﻿ASIF
:1​
﻿
👉Note on ASIF
OutputMember Properties
﻿﻿A
:26.1252​
﻿
﻿﻿ rt
:4.010142330665608​
﻿
﻿﻿ J
:3.8573316666666666​
﻿
﻿﻿ Cw, in.^6
:15933.40399021285​
﻿
﻿﻿Lc
:12.987194547792917​
﻿
﻿﻿Lu
:24.51190476190475​
﻿
﻿﻿Lb/rt
:35.908949889092504​
﻿
X-Axis
﻿﻿Sx 
:140.43370120571444in3​
﻿
﻿﻿Ix
:983.0359084400006​
﻿
﻿﻿rx
:6.134156884510232​
﻿
Y-Axis
﻿﻿Sy 
:49.77148407724138in3​
﻿
﻿﻿Iy 
:360.84325956000004​
﻿
﻿﻿ry
:3.7164602037060157​
﻿
Capacity ChecksAxial Compression
﻿﻿Kx*Lx/rx
:23.475108757590473​
﻿
﻿﻿Ky*Ly/ry
:38.74654701169799​
﻿
﻿﻿Cc
:106.99879020467306​
﻿
﻿﻿fa
:0.30621775144305113​
﻿
﻿﻿Fa
:26.00668785181162​
﻿
﻿﻿Pa
:679.4299214661484​
﻿
﻿﻿fa/Fa
:0.011774577108315629​
﻿
﻿﻿ 
:PASS​
﻿
Axial tension
﻿﻿Ft
:30​
﻿
﻿﻿  
:NA​
﻿
Flexure (X-Axis)
﻿﻿fbx
:1.708991488079037​
﻿
﻿﻿Fbx
:32.2795434315458​
﻿
﻿﻿Mrx
:377.7613131102142​
﻿
﻿﻿F'ex
:270.9791819446942​
﻿
﻿﻿fbx/Fbx
:0.05294348390345867​
﻿
﻿﻿fbx<Fbx?
:PASS​
﻿
Flexure (Y-Axis)
﻿﻿fby
:0​
﻿
﻿﻿Fby
:35.69885857886455​
﻿
﻿﻿Mry
:148.06543094447085​
﻿
﻿﻿F'ey
:99.46840237097395​
﻿
﻿﻿fby/Fby
:0​
﻿
﻿﻿fby<Fby?
:PASS​
﻿
﻿
Combined Check (Stress Ratio)
﻿﻿Stress ratio
:0.06​
﻿
﻿﻿     
:PASS​
﻿
﻿
ExplanationThe 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}}actual stress≤FoSallowable stress​
﻿
Compression CheckColumn's slenderness ratio (﻿rKL​
) 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, ﻿fa​
 is calculated by:
﻿
fa=FAf_{a}=\dfrac{F}{A}fa​=AF​
The formula varies depending on whether the column is buckling elastically or inelastically, and is determined by the factor ﻿Cc​
:
﻿
Cc=2π2EFyC_c=\sqrt{\dfrac{2 \pi^2 E}{F_y}}Cc​=Fy​2π2E​​
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 \dfrac{KL}{r}=\text{max(}\dfrac{K_xL_x}{r_x},\dfrac{K_yL_y}{r_y})\\\frac{KL }{r}\le{C_c}: \ F_a=\dfrac{\left[1-\frac{(K L / r)^2}{2 C_c{ }^2}\right] F_y}{\dfrac{5}{3}+\dfrac{3(K L / r)}{8 C_c}-\frac{(K L / r)^3}{8 C_c{ }^3}}\\\dfrac{KL}{r}>C_c:\ F_a=\dfrac{12\pi^2E}{23(KL/r)^2}\ rKL​=max(rx​Kx​Lx​​,ry​Ky​Ly​​)rKL​≤Cc​: Fa​=35​+8Cc​3(KL/r)​−8Cc​3(KL/r)3​[1−2Cc​2(KL/r)2​]Fy​​rKL​>Cc​: Fa​=23(KL/r)212π2E​ 
﻿
Buckling due to compression
Flexural CheckActual bending stress is calculated by:
﻿
fb=12MSf_{b}=\dfrac{12M}{S}fb​=S12M​
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}\ \ \dfrac{b_f}{2t_f}\le\dfrac{65}{\sqrt{F_y}}\ :\ F_{by}=0.75F_y\\\text{If}\ \ \dfrac{65}{\sqrt{F_y}}<\dfrac{b_f}{2t_f}\le\dfrac{95}{\sqrt{F_y}}\ :\ F_{by}=F_y(1.075-\dfrac{0.005b_f}{2t_f}\sqrt{F_y})\\\text{If}\ \ \dfrac{b_f}{2t_f}>\dfrac{95}{\sqrt{F_y}}\ :\ F_{by}=0.6F_yIf  2tf​bf​​≤Fy​​65​ : Fby​=0.75Fy​If  Fy​​65​<2tf​bf​​≤Fy​​95​ : Fby​=Fy​(1.075−2tf​0.005bf​​Fy​​)If  2tf​bf​​>Fy​​95​ : Fby​=0.6Fy​
For calculating allowable resisting moment (Mr) and Euler stress (F'e):
﻿
Mr=FbS12Fe′=12Ep223(KL12r)2M_{r}=\dfrac{F_{b}S}{12}\\F'_{e}=\dfrac{12Ep^2}{23(KL\frac{12}{r})^2}Mr​=12Fb​S​Fe′​=23(KLr12​)212Ep2​
﻿
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\dfrac{f_a}{F_a}+\dfrac{C_{m x} f_{b x}}{\left(1-\dfrac{f_a}{F_{e x}^{\prime}}\right) F_{b x}}+\dfrac{C_{m y} f_{b y}}{\left(1-\frac{f_a}{F_{e y}^{\prime}}\right) F_{b y}} \leq 1.0\\\dfrac{f_a}{0.60 F_y}+\dfrac{f_{b x}}{F_{b x}}+\dfrac{f_{b y}}{F_{b y}} \leq 1.0Fa​fa​​+(1−Fex′​fa​​)Fbx​Cmx​fbx​​+(1−Fey′​fa​​)Fby​Cmy​fby​​≤1.00.60Fy​fa​​+Fbx​fbx​​+Fby​fby​​≤1.0
For ﻿Fa​fa​​≤0.15
 and/or for axial tension and bending, then:
﻿
faFa+fbxFbx+fbyFby≤1.0\dfrac{f_a}{F_a}+\dfrac{f_{b x}}{F_{b x}}+\dfrac{f_{b y}}{F_{b y}} \leq 1.0Fa​fa​​+Fbx​fbx​​+Fby​fby​​≤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
Related ContentSteel Beam and Column Designer to AS4100
Steel Section Designer to EC3

Steel Beam and Column Designer to AISC 360

Calculation

Technical Notes

Inputs

Member Properties

Loads

Design Parameters for Compression

Design Parameters for Flexural

👉Note on ASIF

Output

Member Properties

Capacity Checks

Axial Compression

Axial tension

Flexure (X-Axis)

Flexure (Y-Axis)

Combined Check (Stress Ratio)

Explanation

Compression Check

Flexural Check

Combined Check (Stress Ratio)

Formulas for geometric properties

Effective lengths,

$L_{x}$
and

$L_{y}$
(axial compression)

Effective lengths,

$L_{b}, L_{c}$
and

$L_{u}$
(bending)

Bending coefficients

Related Content

Steel Beam and Column Designer to AISC 360

Calculation

Technical Notes

Inputs

Member Properties

Loads

Design Parameters for Compression

Design Parameters for Flexural

👉Note on ASIF

Output

Member Properties

Capacity Checks

Axial Compression

Axial tension

Flexure (X-Axis)

Flexure (Y-Axis)

Combined Check (Stress Ratio)

Explanation

Compression Check

Flexural Check

Combined Check (Stress Ratio)

Formulas for geometric properties

Effective lengths, ﻿Lx​ and ﻿Ly​ (axial compression)

Effective lengths, ﻿Lb​,Lc​ and ﻿Lu​ (bending)

Bending coefficients

Related Content

Effective lengths,

$L_{x}$
and

$L_{y}$
(axial compression)

Effective lengths,

$L_{b}, L_{c}$
and

$L_{u}$
(bending)