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Steel Beam and Column Designer to AISC 360's banner

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


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

'ASIF' is a multiplier of any of the calculated allowable stresses

,

and

and the Euler column buckling stresses

and

. It appears only when calculating the Stress Ratio (S.R) where a value of 1.0 is typically used.

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


rt=((d−2tf)×tw372+tfbf312)/(bftf+(d−2tf)×tw6)J=(2bftf3+dtw3)3Cw=Iy×(d−tf)24r_t = \sqrt{((d-2t_f)\times \frac{{t_w}^3}{72}+ \frac{t_f{b_f}^3}{12})/(b_ft_f+(d-2t_f)\times \frac{t_w}{6})} \\ J = \frac{(2b_ft_f^3 + dt_w^3)}{3} \\ C_w = \frac{I_y \times (d-t_f)^2}{4}
X-Axis

rx=(IxA)Sx=Ix/(d2)Ix=tw×(d−2tf)312+2×(bftf312+bftf(d2−tf2)2)r_x = \sqrt{(\frac{I_x}{A})} \\ S_x = I_x/(\frac{d}{2})\\I_x = t_w \times \frac{(d-2t_f)^3}{12} + 2\times (\frac{b_ft_f^3}{12} + b_ft_f (\frac{d}{2}-\frac{t_f}{2})^2)
Y-Axis

ry=IyASy=Iy/bf2Iy=(tfbf3)6+(d−2tf)×tw312r_y= \sqrt{\frac{I_y}{A}} \\ S_y = I_y/ \frac{b_f}{2}\\I_y = \frac{(t_fb_f^3)}{6}+(d-2t_f)\times\frac{t_w^3}{12}


Effective lengths,

and

(axial compression)

The effective length of column is the actual unbraced length of the member capable of resisting buckling. This is calculated as a proportion of the actual member length multiplied by Kx and Ky, the effective length factors about the major (x) and minor (y) axis respectively. K is dependent on the restraint conditions at columns ends and can be found in the AISC ASD Manual, as shown below:
Recommended K values - Table C-C2.1 of AISC ASD Manual


Effective lengths,

and

(bending)

The actual unbraced length of the compression flange of the member for X-axis (major) bending is Lb. The "unbraced length" can be more specifically defined as the distance between cross sections braced against twist or lateral displacement of the compression flange.
  1. For most cases, Lb = Ly
  2. For cantilevers braced against twist only at the support, Lb may be taken conservatively as the actual length.
  1. For input values of Lx or Ly or Lb <= 1, the calculator will use Lx or Ly or Lb = 1
Lc is the maximum unbraced length of compression flange at which the allowable X-axis bending stress can be taken as 0.66*Fy or from AISC code Eqn. F1-3 when applicable.
Lu is the maximum unbraced length of compression flange at which the allowable X-axis bending stress can be taken as 0.60Fy when Cb = 1.


Bending coefficients

Cmx and Cmy are the coefficient applied to the X-axis bending term and Y-axis bending term, respectively, in the interaction equation (H1-1) and is dependent upon column curvature caused by applied moments. The Cmx (or Cmy) coefficient value is determined as follows:
  1. Category A - for compression members in frames subject to joint translation (side-sway), Cmx = 0.85.
  2. Category B - for rotationally restrained compression members in frames braced against joint translation (no side-sway) and not subject to transverse loading between their supports in the plane of bending:

Cmx=0.6−0.4×(Mx1Mx2)C_{mx} = 0.6 - 0.4\times (\frac{Mx1}{Mx2})
  1. Category C - for rotationally restrained compression members in frames braced against joint translation (no side-sway) and subject to transverse loading between their supports in the plane of bending, the following Cmx values are permitted:
  1. For members whose ends are restrained against rotation in the plane of bending, Cmx = 0.85
  2. For members whose ends are unrestrained against rotation in the plane of bending, Cmx = 1.0


Related Content

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