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Steel Beam and Column Designer to AS4100's banner

Steel Beam and Column Designer to AS4100

Verified by the CalcTree engineering team on July 20, 2024

This calculator designs a standard steel section by computing the flexural and axial design capacities to Ultimate Limit State (ULS) methods.
All calculations are performed in accordance with AS4100-2020.
Common steel sections


📃 List of symbols used on this page

Calculation

Assumptions

Inputs

Steel Properties



Section
:100 PFC​



fy
:320MPa​



L
:5 m​



Loads

Modification Factors

Output

Section Properties

Member Properties

Capacity checks



Φ
:0.9​


Compression Capacity


Ns=kfAnfyCl 6.2.1Nc=αcNsCl 6.3.3N_{s} = k_fA_nf_y \hspace{1cm}\text{Cl 6.2.1}\\N_{c} = \alpha_cN_s\hspace{1cm}\text{Cl 6.3.3}


Ns
:339kN​

Major axis


αc,x
:0.304​



Nc,x
:103​



φNc,x
:93kN​



N* < φNc,x
:PASS​

Minor axis


αc,y
:0.059​



Nc,y
:20​



φNc,y
:18kN​



N* < φNc,y
:FAIL​



Flexural Capacity


Ms=fyZeCl 5.2.1Mb=αsαmMsCl 5.6.1.1M_{s} = f_y Z_e \hspace{1cm}\text{Cl 5.2.1}\\ M_{b} = \alpha_s \alpha_m M_s \hspace{1cm}\text{Cl 5.6.1.1}
Major axis


Ms,x
:13kN m​

Minor Axis


Ms,y
:4kN m​



αs
:0.31​



αm
:1​



Mb
:3.9885167029982043​



φMb
:4kN m​



M*x < φMb
:FAIL​

👉Note, Mb,x = Mb,y hence a single Mb is reported


Combined Compression and Bending - Section Capacity


Mr=Ms(1−N∗ϕNs)Cl 8.3.2 & Cl 8.3.3\\M_{r}=M_{s}\big(1-\dfrac{N^*}{\phi N_s}\big)\hspace{1cm}\text{Cl 8.3.2 \& Cl 8.3.3}
Major axis


φMr,x
:10kN m​



M*x < φMr,x
:FAIL​

Minor axis


φMr,y
:3kN m​



M*y < φMr,y
:FAIL​



Combined Compression and Bending - In-plane Member Capacity


Mi=Ms(1−N∗ϕNs)Cl 8.4.2.2M_{i}=M_s\big( 1-\dfrac{N^*}{\phi N_{s}}\big)\hspace{1cm}\text{Cl 8.4.2.2}
Major Axis


φMi.x
:6kN m​



M*x < φMi,x
:FAIL​

Minor Axis


φMi,y
:-5kN m​



M*y < φMi,y
:FAIL​



Combined Axial and Bending - Out-of-Plane Member Capacity


Mox=Mbx(1−N∗ϕNcy)Cl 8.4.4.1M_{ox}=M_{bx}\big(1-\dfrac{N^*}{\phi N_{cy}}\big) \hspace{1cm}\text{Cl 8.4.4.1}


φMo.x
:-6kN m​



M*x < φMo,x
:FAIL​



Explanation

Steel is commonly used to construct building frames, including columns, beams and trusses. These elements provide the necessary structural support for the building. Steel's high strength-to-weight ratio, durability and ductility make it an ideal material for various applications.
Ultimate Limit State (ULS) design for steel includes the following checks against failure phenomena.

Compression Check

Section capacity, Ns checks against compressive yielding (squashing) and local buckling.

Ns=kfAnfyCl 6.2.1N_{s} = k_fA_nf_y\hspace{1cm}\text{Cl 6.2.1}
  1. Only 'stocky' compression members fail by yielding, that is, to have a slenderness ratio l/r < 25 approximately.
  2. The form factor is the ratio of the effective to the gross area of the section. If the local buckling form factor, kf = 1.0 then yielding will occur before local buckling, if kf < 1.0 then local buckling will occur before yielding.
Member capacity, Nc checks against flexural buckling (or column buckling or Euler buckling).

Nc=αcNsCl 6.3.3N_{c} = \alpha_cN_s\hspace{1cm}\text{Cl 6.3.3}
  1. Flexural buckling can only occur in slender compression members, that is, when l/r >= 25 approximately.
  2. The theoretical buckling load, Nom, is given by the Euler Equation. The slenderness reduction factor, αc reduces the Euler equation to account for residual stresses and imperfections.
Flexural (Euler) Buckling


Flexural Check

Section capacity, Ms checks against yielding and local buckling of the compression flange or compression part of web.

Ms=fyZeCl 5.2.1M_{s} = f_y Z_e \hspace{1cm}\text{Cl 5.2.1}
  1. Effective section modulus, Ze is based on the slenderness classification of a section as either 'slender', 'compact' or 'non-compact'. The classification is used to understand whether the elastic or plastic material limits should be used. Slender sections should use an elastic approach to prevent buckling, whereas a compact section is allowed to develop full plastic capacity. All standard UB and UC sections have been sized such that they not slender.
Section behaviour based on slenderness classification

Member capacity, Mb checks against flexural-torsional buckling which is where the beam bends in it's minor axis and twists, as this behaviour is the least stiff bending failure.

Mb=αsαmMsCl 5.6.1.1\\ M_{b} = \alpha_s \alpha_m M_s\hspace{1cm}\text{Cl 5.6.1.1}
  1. The elastic flexural-torsional buckling equation, Mo assumes a perfectly elastic and perfectly straight member with a uniform bending moment. The moment modification factor, αm and the slenderness reduction factor, αs reduces the equation to account for non-uniform bending moment and to account for how restraints impact deformations, respectively.
  2. Flexural-torsional buckling won't occur in minor-axis bending as it is already bending in the less stiff axis and it won't occur in CHS or SHS sections since Ix and Iy are equal from symmetry.
Flexural-torsional Buckling


Comparison of Steel and Concrete

Property

Density
Tensile strength
Compressive strength
Failure mechanism
Construction cost
Fire resistance

Durability

Concrete

2,400 kg/m3
2-5MPa


20-50MPa


Brittle
Generally lower
Inherent in cover

Inherent in cover

Steel

7,850 kg/m3
~440MPa


~300MPa


Ductile
Generally higher
Not inherent, needs intumescent paint
Subject to weather and rust

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