Loading
/custom-emojis/emojis/contour-map.png
Templates
📚
Articles & Resources
📖
Guides & Support
🌵
CalcTree
Bust Common Myths About Java Programming
Loading
/custom-emojis/emojis/calculator.png
Tensile Strength and Capacity Control of the W-Shape Sections According to AISC 360-16
Loading
/custom-emojis/emojis/calculator.png
Concrete Cylinder Strength Vs Cube Strength
Loading
/custom-emojis/emojis/calculator.png
Earthquake Design Action Calculation
EM Wave Propagation Calculator
İKSA YAPILARI PROJELENDİRME HİZMET BEDELİ (2024)
section properties with units
GEOTEKNİK RAPOR (EK-B) ASGARİ HİZMET BEDELİ (2024)
Forward Kinematics of Robotic Arm with 6 Degrees of Freedom
ZEMİN İYİLEŞTİRME/DERİN TEMEL PROJELENDİRME ASGARİ HİZMET BEDELİ (2024)
İKSA YAPILARI PROJELENDİRME HİZMET BEDELİ (2023)
Loading
/custom-emojis/emojis/bending-moment.png
Dezi et. al (2010)
🤾
Projectile motion
Sitemap
Steel Beam and Column Designer to AISC 360's banner
/custom-emojis/emojis/steel-beam.png

Steel Beam and Column Designer to AISC 360

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.
📝This calculation has been written 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


Calculation

Technical Notes

This calculator:
  1. requires input for the total depth (
    
    ), web thickness (
    
    ), flange thickness (
    
    ), design parameters and member loadings. All remaining section properties are calculated
  2. does not check shear, deflection or torsion and does not consider deduction for holes in members subject to tension
  3. assumes the Modulus of Elasticity for steel (
    
    ) is 29,000 ksi
  4. 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.

Inputs

Member 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

Output

Member 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 Checks

Axial 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​



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 (

) is a key parameter in calculating the allowable stress, and is defined as the ratio of its effective length (

) and radius of gyration (

). These values vary depending on the axis considered (major / minor).
Actual compressive stress,

is calculated by:

fa=FAf_{a}=\dfrac{F}{A}
The formula varies depending on whether the column is buckling elastically or inelastically, and is determined by the factor

:

Cc=2π2EFyC_c=\sqrt{\dfrac{2 \pi^2 E}{F_y}}
For calculating the allowable axial compressive stress,

:

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}\
Buckling due to compression


Flexural Check

Actual bending stress is calculated by:

fb=12MSf_{b}=\dfrac{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}\ \ \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_y
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}
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 1.0
For

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 1.0

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

Formulas for geometric properties

Effective lengths,

and

(axial compression)

Effective lengths,

and

(bending)

Bending coefficients

Related Content

  1. Steel Beam and Column Designer to AS4100
  2. Steel Section Designer to EC3