Steel Section Designer to EC3

This calculator computes section capacities and utilisation factors of IPE and HE steel sections. It considers axial compression or tension, bending, and shear effects on the section.
All calculations are performed in accordance with EN 1993-1-1:2005 Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings. This code is typically referred to as "EC3" or "Eurocode 3". 
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CalculationList of Inputs that used in this calculator
Technical notes
InputsSection Properties
﻿﻿Section
:IPE 100​
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﻿﻿Production Type
:Rolled​
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Material Properties
﻿﻿Steel Grade
:S355​
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Design Forces
﻿﻿Nt,Ed
:125kN​
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﻿﻿Nc,Ed
:150kN​
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﻿﻿MEd - Major
:50kN m​
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﻿﻿MEd - Minor
:30kN m​
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﻿﻿VEd - Major
:25kN​
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﻿﻿VEd - Minor
:15kN​
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OutputSection Capacities
﻿﻿Nt,Rd
:365.65kN​
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﻿﻿Nc,Rd
:365.65kN​
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﻿﻿Mc,Rd - Major Axis
:13.987kN m​
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﻿﻿Mc,Rd - Minor Axis
:3.266kN m​
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﻿﻿Vc,Rd - Major Axis
:103.744271943278kN​
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﻿﻿Vc,Rd - Minor Axis
:103.744271943278kN​
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Utilization Factors
﻿﻿Nt,Ed/Nt,Rd
:0.34​
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﻿﻿Nc,Ed/Nc,Rd
:0.41​
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﻿﻿MEd/Mc,Rd (Major)
:3.57​
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﻿﻿MEd/Mc,Rd (Minor)
:9.19​
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﻿﻿VEd/Vc,Rd (Major)
:0.24​
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﻿﻿VEd/Vc,Rd (Minor)
:0.14​
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ExplanationSection ClassificationAccording to EC3 Chapter 5.5, sections are classified as Class 1 to 4 depending on how their cross-section behave under compressive load.
Class 1 (Plastic): can form a plastic hinge with the rotation capacity required from plastic analysis without reduction of the resistance.
Class 2 (Compact): can develop their plastic moment resistance, but have limited rotation capacity because of local buckling.
Class 3 (Semi-compact): the stress in the extreme compression fibre of the steel member assuming an elastic distribution of stresses can reach the yield strength, but local buckling is liable to prevent development of the plastic moment resistance.
Class 4 (Slender): local buckling will occur before the attainment of yield stress in one or more parts of the cross-section.
The classification of a section depends on the width to thickness ratio of the parts subject to compression. Detailed table for classification can be found in Table 5.2.
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Stress distribution of a section depending on Class 1 to 4
TensionTension capacity of a section is calculated as per EC3 Chapter 6.2.3 - Equation 6.6.
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Npl,Rd =AfyγM0  A=Area of section fy= Yield strength of steelγM0= partial factor for resistance ofcross sectionsN_{pl,Rd}\ = \frac{Af_y}{\gamma_{M0}}\ \\ \scriptsize\ A= Area\ of\ section\\\ f_y=\ Yield\ strength\ of\ steel\\\gamma_{M0}=\ partial\ factor\ for\ resistance\ of cross\ sectionsNpl,Rd​ =γM0​Afy​​  A=Area of section fy​= Yield strength of steelγM0​= partial factor for resistance ofcross sections
CompressionCompression capacity of a section is calculated as per EC3 Chapter 6.2.4, employing either Equation 6.10 or 6.11 based on the section class.
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Nc,Rd={AfyγM0 if  Class =1, 2 or 3 AefffyγM0 if  Class =4 A = Area of section Aeff= Effective area of section fy= Yield strength of steelγM0 = partial factor for resistance ofcross sectionsN_{c,Rd} = \begin{cases}\\ \frac{Af_y}{\gamma_{M0}}\  \scriptsize{if\ }\ Class\ = 1,\ 2\ or\ 3\ &\\\\ \frac{A_{eff}f_y}{\gamma_{M0}} \ \scriptsize{if\ }\ Class\ = 4\end{cases}\\\scriptsize\ A\ =\ Area\ of\ section\ \\A_{eff}=\ Effective\ area\ of\ section \\\scriptsize\ f_y=\ Yield\ strength\ of\ steel\\\scriptsize\gamma_{M0}\ =\ partial\ factor\ for\ resistance\ of cross\ sections\\ Nc,Rd​=⎩⎨⎧​γM0​Afy​​ if  Class =1, 2 or 3 γM0​Aeff​fy​​ if  Class =4​ A = Area of section Aeff​= Effective area of section fy​= Yield strength of steelγM0​ = partial factor for resistance ofcross sections
Bending MomentBending capacity of a section is calculated as per EC3 Chapter 6.2.5, utilizing Equation 6.13, 6.14, or 6.15 based on the assigned section class.
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Mc,Rd={ Mpl,Rd =WplfyγM0 if Class =1 or 2 Mel,Rd =Wel,minfyγM0 if Class = 3=Weff,minfyγM0 if Class = 4Wpl:Plastic section modulusWel,min:Minimum elastic section modulus Weff,min:Minimum effective section modulus fy: Yield strength of steelγm0: partial factor for resistance ofcross sectionsM_{c,Rd} = \begin{cases}\\\ M_{pl,Rd}\ =\frac{W_{pl}f_y}{\gamma_{M0}}\ \scriptsize{if\ Class\ =1\ or\ 2}\\\ M_{el,Rd}\ =\frac{W_{el,min}f_y}{\gamma_{M0}}\ \scriptsize{if\ Class\ =\ 3}\\\hspace{1.2cm}=\frac{W_{eff,min}f_y}{\gamma_{M0}}\ \scriptsize{if\ Class\ =\ 4}\\\end{cases}\\\scriptsize W_{pl}: Plastic\ section\ modulus\\\\ W_{el,min}: Minimum\ elastic\ section\ modulus\\\ W_{eff,min}: Minimum\ effective\ section\ modulus\\\ f_y:\ Yield\ strength\ of\ steel\\\gamma_{m0}:\ partial\ factor\ for\ resistance\ of cross\ sections\\ Mc,Rd​=⎩⎨⎧​ Mpl,Rd​ =γM0​Wpl​fy​​ if Class =1 or 2 Mel,Rd​ =γM0​Wel,min​fy​​ if Class = 3=γM0​Weff,min​fy​​ if Class = 4​Wpl​:Plastic section modulusWel,min​:Minimum elastic section modulus Weff,min​:Minimum effective section modulus fy​: Yield strength of steelγm0​: partial factor for resistance ofcross sections
Shear Shear capacity of a section is calculated as per EC3 Section 6.2.6 - Equation 6.18.
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Vpl,Rd =Avfy(3)γM0 Av:Shear area fy: Yield strength of steelγm0: partial factor for resistance ofcross sectionsV_{pl,Rd}\ =\frac{A_vf_y\sqrt(3)}{\gamma_{M0}}\\\scriptsize\ A_{v}: Shear\ area\\\ f_y:\ Yield\ strength\ of\ steel\\\gamma_{m0}:\ partial\ factor\ for\ resistance\ of cross\ sectionsVpl,Rd​ =γM0​Av​fy​(​3)​ Av​:Shear area fy​: Yield strength of steelγm0​: partial factor for resistance ofcross sections
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AcknowledgementsThis calculation was built in collaboration with Hakan Keskin. Learn more.
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