Design a Steel Column to EN 1993 (Eurocode 3)

EuropeEN 1993-1-5:2006SCI Publication P360 (2011)

Steel Column

Column loads link from beam reactions above to footing calculations below automatically. Design steel columns and studs to Eurocode 3 with multiple end fixity conditions, checks cover axial compression, bending about both axes, combined bending and axial interaction, lateral torsional buckling, and three deflection limits.

Worked example

Example 1: single-span column with lateral loads

A steel column is 7200 mm high, pinned at the base and on a roller at the top. It carries an axial load at the top and two lateral point loads, and it is braced against lateral movement at the lateral loads. The steps below use the conditions in the image. The design criteria in step 6 are the example’s own settings, not the calculator’s defaults.

Example Steel Column #1, a single-span column 7200 millimeters high with a pinned support at the base and a roller support at the top. An axial load G of 100 kilonewtons acts down at the top, and two lateral loads G of 43 kilonewtons each act at 2400 millimeters and 4800 millimeters from the base, with dimension lines of 2400 millimeters between them. Conditions listed: single-span steel column, 7200 mm high, pinned at the base and on a roller at the top; axial load at the top G of 100 kN (permanent); two lateral loads G of 43 kN each (permanent) at 2400 mm and 4800 mm from the base; axial load eccentricity Capped; buckling lengths of 7200 mm (major axis) and 2400 mm (minor axis and lateral torsional buckling); gamma M2 of 1.1; deflection limits of 5 mm absolute and L over 300; steel S275 to EN 10025-3, interaction method Annex A, self-weight included; find the lightest UC section that passes all checks.

The conditions are:

Single-span steel column, 7200 mm high, pinned at the base and on a roller at the top
Axial load at the top: G of 100 kN (permanent)
Two lateral loads: G of 43 kN each (permanent) at 2400 mm and 4800 mm from the base
Axial load eccentricity: Capped
Buckling lengths: 7200 mm (major axis), 2400 mm (minor axis and lateral torsional buckling)
$\gamma_{M2}$ of 1.1, and deflection limits of 5 mm absolute and L/300
Steel S275 to EN 10025-3, interaction method Annex A, self-weight included
Find the lightest UC section that passes all checks

Add the Steel Column calculator

In your project, choose Add New Calculation, select EU, choose Steel Column under Columns, then choose Interior Single Storey Column.

Add a new calculation window with the EU region selected, Steel Column chosen under Columns, and its presets listed below with Interior Single Storey Column highlighted.

Set the height and the buckling lengths

In Key Properties, enter 7200 mm for the Total Column Height. In Critical Buckling Lengths, enter a Length between restraints of 7200 mm for the flexural major row and 2400 mm for the flexural minor and lateral torsional buckling rows, because the column is braced at the lateral loads. The Effective Length Factor stays at 1, so the Effective Length is 7200 mm, 2400 mm and 2400 mm.

Critical Buckling Lengths table with lengths between restraints of 7200, 2400 and 2400 millimeters, an effective length factor of 1 on each row, and effective lengths of 7200, 2400 and 2400 millimeters for the flexural major, flexural minor and lateral torsional buckling rows.

Place the supports

In Position of Supports from Bottom, set a Pinned support at 0 mm and a Roller support at 7200 mm. Maximum Interior Span shows 7200 mm and Maximum Cantilever shows 0 mm.

Position of Supports from Bottom table with a Pinned support at 0 and a Roller support at 7200 millimeters, a Maximum Interior Span of 7200 millimeters and a Maximum Cantilever of 0 millimeters.

Enter the loads

The preset puts an axial load at the top with a (G) load of 5 kN and a (QI) load of 7 kN. In Axial, Lateral & Moment Loads, select Edit… on the Axial Load row, change the (G) axial load to 100 kN, and delete the (QI) row with the three-dot menu.

Load Magnitudes window with a (G) Permanent Dead Load row of 0 lateral, 100 kilonewtons axial and 0 moment, and the (QI) Imposed Live Load row emptied.

Add two rows, Point Load 1 at 2400 mm and Point Load 2 at 4800 mm. In Load Magnitudes, enter a (G) lateral load of 43 kN on each.

Load Magnitudes window with a (G) Permanent Dead Load row with a lateral load of 43 kilonewtons and no axial load or moment.

Axial, Lateral and Moment Loads table with the Axial Load row at 7200 millimeters with G 100 kilonewtons axial, Point Load 1 at 2400 millimeters and Point Load 2 at 4800 millimeters, each with G 43 kilonewtons, and an axial eccentricity of 103 millimeters on each row.

Set the eccentricity

Set the Default Axial Load Eccentricity to Capped, which takes the face of the member. The list also offers Corner Face, Pure Compression, Custom, Y-axis Face (for example the flange) and Z-axis Face (for example the web). The Axial Eccentricity of each row follows the section, so it changes in step 7.

Default Axial Load Eccentricity list open with the options Corner Face, Capped, Pure Compression, Custom, Y-axis Face and Z-axis Face, and Capped highlighted.

Set the design criteria

In Design Criteria & National Annex Parameters, set

\gamma_{M2}

to 1.1, the Deflection Limit Absolute Criterion to 5 mm, and the three limits in the Horiz. Defl. (Braced Column) row to 300. Annex A (Method 1) stays selected, the simplified check stays No and

\eta

stays 1.

Design Criteria and National Annex Parameters with partial factors of 1, 1 and 1.1, Annex A (Method 1) selected, Add Check according to Simplified Criterion set to No, a deflection limit absolute criterion of 5 millimeters, span limits of 300 for a braced column, and a factor for shear area of 1.

Choose the section

Open the Member Type Select… list. Look for the lightest section whose governing badge is not over 100%. The 356 x 368 x 153 UC shows 100% in red, so it fails, the 356 x 368 x 177 UC shows 85%, and the 356 x 368 x 202 UC shows 73%. The 177 is the lightest UC that passes, so choose it. The governing check is the characteristic deflection.

Member Type list showing the 356 x 368 x 202 UC at 73 percent, the 356 x 368 x 177 UC highlighted at 85 percent, the 356 x 368 x 153 UC at 100 percent in red, and the 356 x 368 x 129 UC at 121 percent in red.

Key Properties section with the section drawing and the Member Type set to 356 x 368 x 177 UC, the Steel Standard and Grade set to EN 10025-3 Simplified EC3, Gr. S275 N/NL, and a Total Column Height of 7200 millimeters.

With the section chosen, the eccentricity fills in as 184 mm about the Y-axis and 186 mm about the Z-axis, the self-weight is 1.74 kN/m, and Y-Axis Lateral Loads Present? reads Yes.

Axial, Lateral and Moment Loads table with an axial eccentricity of 184 millimeters on each row, Default Axial Load Eccentricity set to Capped, and default eccentricities of 184 millimeters about the Y-axis and 186 millimeters about the Z-axis.

Include Self Weight set to Yes, a Self Weight of 1.74 kilonewtons per meter, and Y-Axis Lateral Loads Present set to Yes.

Read the summary

The Summary shows a design compression force of 152 kN, a design moment about the major axis of 131 kN·m and about the minor axis of

-25.2

kN·m, and the capacities and buckling resistances with their badges. Buckling strength in combined bending and axial compression is 0.204, at 20%. The characteristic, frequent and quasi-permanent deflections about the Y-axis are each 4.25 mm, at 85%, which is the governing limit.

Summary with a design compression force of 152 kilonewtons, design moments of 131 and minus 25.2 kilonewton meters, an axial compression capacity of 6215 kilonewtons at 2 percent, bending capacities of 952 and 459 kilonewton meters at 14 and 5 percent, buckling resistances of 5435 and 5931 kilonewtons at 3 percent, a bi-axial criterion of 0.0737, and an interaction value of 0.204 at 20 percent.

Deflection results showing characteristic, frequent and quasi-permanent deflections about the Y-axis of minus 4.25 millimeters, each at 85 percent, and about the Z-axis of 1.44 millimeters, each at 29 percent.

The badges at the top of the sheet show the same checks.

Look at the graphs

In Graphs by Load Case, the Graphed Load Case is Strength: Imposed Leading Variable and the graphs are shown about the Y-axis. The diagram under the moment graph shows the factored loads: 135 kN axial at the top, two lateral loads of 58.1 kN, a moment of 24.9 kN·m, and reactions of 61.5 kN, 54.6 kN and 152 kN. Switch to Service CHAR: Imposed Leading Variable to see the deflection, which peaks at 4.25 mm against the 5 mm limit, and the unfactored loads.

Axial force and shear force graphs for the strength case with the capacities shown as yellow lines.

Bending moment graph for the strength case with the capacities shown as yellow lines, and a load diagram of the factored loads with reactions of 61.5, 54.6 and 152 kilonewtons.

Deflection graph for the service characteristic case, peaking at about 4.25 millimeters with the 5 millimeter limit shown as yellow lines.

Load diagram of the unfactored loads: 100 kilonewtons axial, two lateral loads of 43 kilonewtons, a moment of 18.4 kilonewton meters, and reactions of 45.6, 40.4 and 112 kilonewtons.

See how the combined check is worked out

To see each calculation step, expand Details at the top right of the sheet and select Detailed. In ULS: Buckling Resistance in Combined Bending and Axial Compression (EN 1993-1-1:2005 Cl 6.3.3), the interaction value is the larger of two criteria,

Combined_1

(0.204) and

Combined_2

(0.152). The interaction factors are

k_{yy}

= 1,

k_{yz}

= 0.691,

k_{zy}

= 0.523 and

k_{zz}

= 0.995. Select a label to see its description, reference and equation.

Buckling Strength in Combined Bending and Axial Compression panel with an interaction value of 0.204 at 20 percent and its equation, the interaction value equal to the larger of Combined 1 and Combined 2.

Combined Bending and Axial Compression Criterion 1 panel with a value of 0.204, the reference EN 1993-1-1:2005 Cl 6.3.3 (4) Eq 6.61, and its equation with a case for each interaction method and set of loads.

Combined Bending and Axial Compression Criterion 2 panel with a value of 0.152, the reference EN 1993-1-1:2005 Cl 6.3.3 (4) Eq 6.62, and its equation with a case for each interaction method and set of loads.

Inputs, Calcs.com output and a hand check

Inputs

CalculatorSteel Column

PresetInterior Single Storey

Section356 x 368 x 177 UC

GradeS275, EN 10025-3

Total height

L

7200 mm

Base supportPinned at 0 mm

Top supportRoller at 7200 mm

l_e

, flexural major7200 mm

l_e

, flexural minor2400 mm

l_e

, LT buckling2400 mm

k_e

, all three rows1

Axial load (G)100 kN

Point Load 1 (G)43 kN at 2400 mm

Point Load 2 (G)43 kN at 4800 mm

Eccentricity, Capped,

e_y

184 mm

Eccentricity, Capped,

e_z

186 mm

Self-weight

SW

(included)1.74 kN/m

\gamma_{M2}

1.1

\Delta_{max}

5 mm

Span limits (all three)L/300

Calcs.com output

Design compression

N_{c,Ed}

152 kN

Design moment

M_{y,Ed}

131 kN·m

Design moment

M_{z,Ed}

−25.2 kN·m

Compression capacity

\mathbb{N}_{c,Rd}

6215 kN (2%)

Bending capacity

M_{N,y,Rd}

952 kN·m (14%)

Bending capacity

M_{N,z,Rd}

459 kN·m (5%)

Buckling

N_{b,y,Rd}

5435 kN (3%)

Buckling

N_{b,z,Rd}

5931 kN (3%)

Combined buckling

Interact

0.204 (20%)

Deflection

\delta_{char,y}

−4.25 mm (85%)

Governing checkDeflection, 85%

Lateral reaction at 7200 mm61.5 kN

Lateral reaction at 0 mm54.6 kN

Axial reaction at 0 mm152 kN

Hand check

✓Axial load at the base:

100 + 1.74 \times 7.2 = 112.5

kN, so the factored load is

1.35 \times 112.5 =

152 kN

✓End moment from the eccentric axial load:

100 \times 0.184 = 18.4

kN·m. Lateral reactions:

43 \pm 18.4 / 7.2 = 43 \pm 2.56

, so 45.6 kN and 40.4 kN, and

1.35 \times 40.44 =

54.6 kN factored at the base

✓

M_{y,Ed} = 54.6 \times 2.4 =

131 kN·m, at the first lateral load

✓Deflection with

E = 210\,000

MPa and

I_y = 571 \times 10^6

mm⁴:

23PL^3 / 648EI = 4.75

mm for the two lateral loads, less

ML^2 / 16EI = 0.50

mm from the end moment, gives 4.25 mm

The loads, reactions, major-axis design moment and deflection match the closed-form solution. The capacities, buckling and combined buckling checks, and the minor-axis moment are advanced results from the calculator, with no hand check. This is a sanity check only. Steel Column version 46, Interior Single Storey Column preset.

Method & scope

Property	Detail
Design standards	EN 1993-1-1:2005 (Eurocode 3), EN 1993-1-5:2006, SCI Publication P360 (2011), JRC (2007) Commentary and Worked Examples to EN 1993-1-5
Regions	Europe
Presets	Generic Concentrically-Loaded Column, Outdoor Cantilever Column, Interior Cantilever Column, Interior Single Storey Column, Interior Multi-Storey Column, Perimeter Multi-Storey Column, Corner Multi-Storey Column
What it checks	Structural model and load combinations, Cross-section classification (EN 1993-1-1:2005 Cl 5.5.2), Axial compression and tension resistance (Cl 6.2.3 and 6.2.4), Shear resistance (Cl 6.2.6), Reduced moment resistance incorporating axial and shear forces (Cl 6.2.5), Flexural buckling resistance (EN 1993-1-1:2005 Cl 6.3.1), Lateral torsional buckling (EN 1993-1-1:2005 Cl 6.3.2.1), Combined bending and axial compression, member buckling (EN 1993-1-1:2005 Cl 6.3.3), Shear web buckling (EN 1993-1-5:2006 Cl 5.1-5.5), Deflection checks (EN 1990:2002 Cl 6.5.3)
Key assumptions	As listed in the calculator’s Sheet Details: 1. Column is of uniform cross-section along its full length. 2. Steel profiles are hot-rolled. Hollow Sections are hot-finished. 3. Torsion is not considered. 4. The principles of elastic global analysis (Section 5.4.2) are applied. 5. No plastic redistribution of moments in continuous columns is considered (EN1993-1-1:2005 5.4.1(4)B). 6. No bearing check is conducted. 7. Class 4 sections are not supported. Where a Class 4 section is determined, the calculation will show as failing. 8. Axes Conventions: 9. X axis: parallel to column length. 10. Y axis: column major axis. 11. Z axis: column minor axis. 12. Vocabulary note: ‘Flange’ and ‘Web’ always refer to the major (strong) axis orientation. 13. Hollow sections are analysed as cold-formed (more conservative than hot-finished) for the purposes of buckling checks. 14. Flexural torsional buckling (Cl 6.3.1.4 EN1993.1.1:2005) is not checked as the database hot-rolled sections and hollow sections will always have more critical flexural buckling limits. 15. Supports are equally applied about both axes (i.e. fixed in bending about major and minor axes). 16. Reduction in effective area for penetrations is not calculated. A check is however completed whether penetrations may be ignored for bending capacity.

Analysis and design capabilities

The EU steel column calculator can be used to calculate both the demands as well as the resistance of a straight column.
The analysis capabilities include:

Point Axial and lateral forces
Point moments in the major and minor axis (excluding torsion)
Line Loads (including linearly varying)
Distributed Loads (including varying tributary width). For details on tributary widths, refer article Understand Tributary Width

The design capabilities include:

Cross-section classification (Class 4 section design not available)
ULS: Axial compression and tension resistance (EN 1993-1-1:2005 Cl 6.2.3 & 4)
ULS: Reduced bi-axial moment resistance taking into account axial and shear forces (EN 1993-1-1:2005 Cl 6.2.5)
ULS: Shear resistance (EN 1993-1-1:2005 Cl 6.2.6)
ULS: Lateral torsional buckling resistance of uniform member in bending (EN 1993-1-1:2005 Cl 6.3.2)
ULS: Buckling resistance in combined bending and axial compression (EN 1993-1-1:2005 Cl 6.3.3)
ULS: Flexural buckling resistance in axial compression (EN 1993-1-1:2005 Cl 6.3.1)
ULS: Shear web buckling resistance of uniform member (EN 1993-1-5:2006 Cl 5.1-5.5) including transverse stiffeners.
SLS: Deflection analysis
Penetrations or fastener holes (checks if they may be ignored)

Coordinate system: Within Calcs.com, the X axis is parallel to the column length, the Y axis is the column major axis and the Z axis is the column minor axis. In the Eurocode suite the longitudinal axis is the x-x axis and the y-y and z-z axes are the respective major and minor axes.

Informational and National Annexes

Eurocode allows location-specific factors and/or calculation methods to be utilized. These are usually stipulated within National Annexes to EN1993-1-1:2005. The following customizations are provided within Calcs.com:

Partial Factors for cross-section resistance - The recommended values within EN1993-1-1:2005 Cl 6.1(1) are provided by default, however, modified values should be used specifically to the relevant National Annex.
Interaction Factors for compression and bending buckling resistance - 2 methods are provided within the informational annexes. The engineer should consider both the national annex requirements as well as the validity of each method for the type of sections they are designing. The UK National Annex limits the scope of Annex A to bi-symmetrical sections; unless noted otherwise by your national annex, it is not recommended to use Annex A for PFC sections.
Deflection Limits - These vary based on the type of the structure, whether it is a column or beam, as well as national annex preferences. Extension limits are not provided, however where differential deflections of multiple columns may induce secondary impacts, a separate check should be conducted. These may be adjusted within Project Defaults, which apply to all designs within the project, or amended for this column only.

Assumptions and Limitations

Calcs.com fully exposes all code calculations to see every step of the process employed to design the column. Therefore, the engineer should have confidence that they can look at every calculation and conditional statement that is used to derive the final result. A summary of assumptions is provided below:

Columns are computed by a chosen limit state and load combination. It is up to the user to choose limit states to determine the worst loading case combination. These may be viewed and/or modified in Project Defaults.
Hollow sections are analyzed as cold-formed (more conservative than hot-finished) for the purposes of buckling checks
Flexural torsional buckling (Cl 6.3.1.4 EN1993.1.1:2005) is not checked as the database hot-rolled sections and hollow sections will always have more critical flexural buckling limits.
Supports are equally applied about both axes (i.e. fixed in bending about major and minor axes)

References

The worked example above is based on Example 6.9, Gardner and Nethercot (2011), Designers’ Guide to EN 1993-1-1 (Eurocode 3).

See the exact clause

Every check in this calculator links back to its governing clause in EN 1993. Open the Formula Reference panel on any result and select the clause reference to read it. See Viewing Clauses from Inside a Calculator.

Symbols

These are the labels the calculator shows in its inputs, Summary and tables.

Symbol	Meaning
$L$	Total Column Height
$l_e$	Length between restraints, in the Critical Buckling Lengths table
$k_e$	Effective Length Factor, in the Critical Buckling Lengths table
$l_{cr}$	Effective Length, in the Critical Buckling Lengths table
$k_{LT,max}$	Max Effective Length Factor for Selected Support Arrangement
$L_{maxspan}$	Maximum Interior Span
$L_{maxcant}$	Maximum Cantilever
$z$	Location, in the load tables
$P_y$	Y-Direction (Lateral) Load, in the Load Magnitudes window
$N_x$	X-Direction (Axial) Load, in the Load Magnitudes window
$M$	Moment Load, in the Load Magnitudes window
$e_y$ , $e_z$	Default Eccentricity for Bending about the Y-axis and the Z-axis
$SW$	Self Weight
$\gamma_{M0}$ , $\gamma_{M1}$ , $\gamma_{M2}$	Partial Factor for Cross-Section Resistance
$\Delta_{max}$	Deflection Limit Absolute Criterion
$D_{lim}$	Deflection Limit Span Criterion
$\Delta_{c,lim}$ , $\Delta_{f,lim}$ , $\Delta_{l,lim}$	Characteristic, Frequent and Quasi-Permanent Service limits, as span ratios
$\eta$	Factor for Shear Area
$d_{h,f}$ , $d_{h,w}$	Combined Diameters of Penetrations and Fastener Holes in the Top or Bottom Flange, and in a Single Web
$N_{c,Ed}$	ULS Design Compression Force
$N_{t,Ed}$	ULS Design Tension Force
$\mathbb{N}_{c,Rd}$	Axial Compression Capacity
$\mathbb{N}_{t,Rd}$	Axial Tension Capacity
$N_{b,y,Rd}$	Minimum Design Buckling Resistance of a Compression Member about the Major Axis
$N_{b,z,Rd}$	Minimum Design Buckling Resistance of a Compression Member about the Minor Axis

Calculation method

Structural model and load combinations

The calculator models the steel column as a member under combined axial force and biaxial bending. Loads are entered by type: permanent

(G)

, imposed

(QI)

, snow

(S)

, wind

(W)

, temperature

(T)

and earthquake

(AE)

. EN 1990:2002 governing ULS combinations are generated automatically. Bending moments can be entered directly or linked from beam calculations above. Three serviceability combinations generate deflection checks.

Cross-section classification (EN 1993-1-1:2005 Cl 5.5.2)

Cross-section class (Class 1 through 4) is determined independently for major-axis bending, minor-axis bending, and axial compression based on element slenderness and

\varepsilon = \sqrt{235/f_y}

. The governing class controls which section moduli (plastic, elastic, or effective) are used in the resistance calculations.

Cross-section resistance

Axial compression (Cl 6.2.4):

N_{c,Rd} = A \times f_y / \gamma_{M0}

for Class 1-3, or

A_{eff} \times f_y / \gamma_{M0}

for Class 4. Bending (Cl 6.2.5):

M_{c,Rd}

uses

W_{pl}

for Class 1-2,

W_{el}

for Class 3, and

W_{eff}

for Class 4, independently for both axes. Shear (Cl 6.2.6):

V_{Rd}

is computed from the shear area

A_v

and yield strength

f_y

for each axis. Biaxial bending criterion: For combined major and minor axis bending without axial force, the biaxial criterion limits the sum of moment utilization ratios. Simplified criterion (Cl 6.2.1 (7) Eq 6.2): As a conservative approximation, a linear summation of the utilization ratios for each stress resultant can be requested with Add Check according to Simplified Criterion. This may be applied for Classes 1 to 3.

Flexural buckling resistance (EN 1993-1-1:2005 Cl 6.3.1)

Flexural buckling resistance

N_{b,Rd}

is computed for each axis using the reduction factor

\chi

, derived from the relative slenderness

\lambda = \sqrt{A \times f_y / N_{cr}}

N_{cr}

is the Euler critical load based on the effective buckling length. The imperfection factor

\alpha

depends on the section type and axis (buckling curves

a_0

a

b

c

d

per Table 6.2). buckling utilization

= N_{Ed} / N_{b,Rd} \leq 1.0

Lateral torsional buckling (EN 1993-1-1:2005 Cl 6.3.2.1)

When the compression flange is not fully laterally restrained, LTB resistance

M_{b,Rd}

is computed using

\chi_{LT}

from the relative slenderness

\lambda_{LT}

derived from

M_{cr}

. The critical moment

M_{cr}

accounts for unbraced length, end conditions, and section warping and torsional properties.

Combined bending and axial compression, member buckling (EN 1993-1-1:2005 Cl 6.3.3)

The combined buckling interaction is checked through two criteria,

Combined_1

(EN 1993-1-1:2005 Cl 6.3.3 (4) Eq 6.61) and

Combined_2

(Eq 6.62), using the interaction factors

k_{yy}

k_{yz}

k_{zy}

k_{zz}

\begin{aligned}Combined_1 &= \frac{N_{c,Ed}}{\chi_{y,b} N_{Rk}/\gamma_{M1}} \\ &+ k_{yy}\,\frac{\lvert M_{y,Ed}\rvert}{\chi_{LT} M_{y,Rk}/\gamma_{M1}} \\ &+ k_{yz}\,\frac{\lvert M_{z,Ed}\rvert}{M_{z,Rk}/\gamma_{M1}}\end{aligned}

\begin{aligned}Combined_2 &= \frac{N_{c,Ed}}{\chi_{z,b} N_{Rk}/\gamma_{M1}} \\ &+ k_{zy}\,\frac{\lvert M_{y,Ed}\rvert}{\chi_{LT} M_{y,Rk}/\gamma_{M1}} \\ &+ k_{zz}\,\frac{\lvert M_{z,Ed}\rvert}{M_{z,Rk}/\gamma_{M1}}\end{aligned}

The sheet reports

Interact = \max(Combined_1, Combined_2)

. It picks the terms by interaction method (Annex A or B) and by which axes carry loads, and makes the check only when uni-axial or bi-axial bending is present. Axial compression alone is covered by the

N_{b,Rd}

checks. Interaction factors are derived from the moment distribution (

C_m

factors) and relative slendernesses.

Deflection checks (EN 1990:2002 Cl 6.5.3)

Characteristic, frequent, and quasi-permanent deflections are checked against user-defined span-ratio limits and optional absolute limits in mm.

Load linking

The column’s base reaction is exported as a linked output to connected footing calculations. Axial load at the column top can be linked from beam reactions above, completing the full load path from beam to column to footing automatically. When reactions are linked into a column, the reactions in both axes are shown, identified by X and Y next to the support number.

How to use it

The sheet has Key Properties, Loads, Design Criteria and National Annex Parameters, and Penetrations or Fastener Holes, then the Summary and the graphs. The screenshots show a 203 x 203 x 52 UC column, 5000 mm high, fixed at the bottom and on a roller at the top.

Add the Steel Column calculator

In your project, choose Add New Calculation, select EU, choose Steel Column under Columns, then choose a preset. The presets are Generic Concentrically-Loaded Column, Outdoor Cantilever Column, Interior Cantilever Column, Interior Single Storey Column, Interior Multi-Storey Column, Perimeter Multi-Storey Column and Corner Multi-Storey Column.

Add a new calculation window with the EU region selected, Steel Column chosen under Columns, and its seven presets listed below, starting with Generic Concentrically-Loaded Column.

Choose the member and the steel grade

In Key Properties, Member Type and Steel Standard and Grade each have a Select… button, and Member Type also has Autosize. Select opens a list. Each row shows the section’s or grade’s properties and five badges: axial compression, bending about each axis, characteristic deflection and the governing limit. See Quickly finding the best section with the member selector.

Key Properties section with the section drawing and the Member Type set to 203 x 203 x 52 UC, the Steel Standard and Grade set to EN 10025-3 Simplified EC3, Gr. S275 N/NL, and the Total Column Height, Max Effective Length Factor and Critical Buckling Lengths below.

Member Type list with a filter box, Member Shape, Member Type and Max Depth filters, and columns for designation, mass per metre, second moment of area, elastic section modulus and five utilization badges; the 203 x 203 x 52 UC row is highlighted.

Steel Standard and Grade list with filters for Common Usages, Grade or Type, Country, Standard and thickness, and columns for yield strength, ultimate strength, elastic modulus and five utilization badges; the EN 10025-3 S275 N/NL row is highlighted.

Set the column height and the buckling lengths

Total Column Height is the length from the start to the end of the column. Max Effective Length Factor for Selected Support Arrangement is shown by the sheet. In Critical Buckling Lengths, each of the three rows, flexural major, flexural minor and lateral torsional buckling, has a Length between restraints

l_e

and an Effective Length Factor

k_e

, and the last column gives the Effective Length

l_{cr} = l_e \times k_e

. Take into account any intermediate restraints for buckling in either direction. In the screenshot each row has 5000 mm and a factor of 1.

Place the supports

In Position of Supports from Bottom, choose a Support Type for each support and enter its Position in millimeters, measured from the bottom of the column. The types are Pinned, Fixed and Roller. A cantilever is created at either end by moving the support away from 0 or from the Total Column Height. Maximum Interior Span and Maximum Cantilever are shown below the table.

Position of Supports from Bottom table with a Fixed support at 0 and a Roller support at 5000 millimeters, and Maximum Interior Span of 5000 millimeters and Maximum Cantilever of 0 millimeters below.

Support Type list open with the options Pinned, Fixed and Roller.

Enter the loads

The Loads (EN 1991) section opens with a diagram of the loads. Height of Loads Application is Top Flange or Shear Centre: choose Top Flange if any load is applied at the top flange, and Shear Centre only if all loads are applied at or below the shear centre.

Loads diagram of the column showing an axial load at 5000 millimeters with G 5 kilonewtons, QI 7 kilonewtons, G 4 kilonewtons and QI 6 kilonewtons, and the self-weight of 0.51 kilonewtons per meter; Height of Loads Application is set to Shear Centre.

In Axial, Lateral & Moment Loads, each row has a label, a Location

z

in millimeters, an Axial Eccentricity and Load Magnitudes. Select Edit… on Load Magnitudes to choose a load type and enter the lateral load

P_y

, the axial load

N_x

and the moment

M

. In the screenshots the row is at 5000 mm with (G) Permanent Dead Load 5 kN and (QI) Imposed Live Load 7 kN, both axial.

Axial, Lateral and Moment Loads table with one row labeled Axial Load at a location of 5000 millimeters and an axial eccentricity of 0, with load magnitudes G 0 kN, 5 kN, 0 kN m and QI 0 kN, 7 kN.

Load Magnitudes window with a Load Type column and columns for the Y-direction lateral load, the X-direction axial load and the moment load; the (G) Permanent Dead Load row has 0, 5 and 0, and the (QI) Imposed Live Load row has 0, 7 and 0.

Select Link from Calculator to take a load from another calculation in the project. The Link to reaction window asks you to choose the calculation to link from, and changes in the linked calculation are reflected here automatically.

Link to reaction window, step 1 of 2, with a list to choose another calculator in the project to link from.

Lateral Distributed Loads has a label, a start and end Location, a start and end Load Width and Load Magnitudes. A different load width at the start and the end gives a triangular load.

Lateral Distributed Loads table with columns for label, start location, end location, start load width, end load width and load magnitudes, and no rows entered.

The Default Axial Load Eccentricity is used for every axial load in the table. Pure Compression assumes zero eccentricity. The list also offers Corner Face, Capped, Custom, Y-axis Face (for example the flange) and Z-axis Face (for example the web). The default eccentricities for bending about the Y-axis and the Z-axis are shown below.

Default Axial Load Eccentricity set to Pure Compression, with the default eccentricity for bending about the Y-axis of 0 millimeters and about the Z-axis of 0 millimeters.

A second set of load tables for the other axis is in the Z-axis Lateral Design Loads section below. Axial loads entered in either set are added together.

Choose the building category and the self-weight

Building Category for Imposed Load sets the combination factors for imposed loads from EN 1990:2002 Table A1.1. The categories are A Domestic, Residential Areas; B Office Areas; C Congregation Areas; D Shopping Areas; E Storage Areas; F Traffic Area, Vehicle Weight up to 30 kN; G Traffic Area, 30 kN to 160 kN; and H Roofs. The factors for snow, wind and temperature loads come from Project Defaults. Include Self Weight is Yes or No, and Self Weight shows the member’s weight per meter. Y-Axis Lateral Loads Present? is shown by the sheet and is No when no Y-axis lateral loads are entered.

Building Category for Imposed Load set to A: Domestic, Residential Areas, Include Self Weight set to Yes, the Self Weight shown as 0.51 kilonewtons per meter, and Y-Axis Lateral Loads Present set to No.

Building Category for Imposed Load list open showing categories A to H, from A: Domestic, Residential Areas to H: Roofs.

Set the design criteria

In Design Criteria and National Annex Parameters, the three Partial Factor for Cross-Section Resistance rows are

\gamma_{M0}

\gamma_{M1}

and

\gamma_{M2}

. They default to 1, 1 and 1.25; use the values from your National Annex. Compression and Bending Buckling Interaction is Annex A (Method 1) or Annex B (Method 2). Add Check according to Simplified Criterion is Yes or No. Deflection Limit Absolute Criterion

\Delta_{max}

is a limit in millimeters, and Deflection Limit Span Criterion sets the characteristic, frequent and quasi-permanent limits as span ratios for each span type. Factor for Shear Area

\eta

has a default of 1.

Design Criteria and National Annex Parameters with partial factors of 1, 1 and 1.25, Annex A (Method 1) selected, Add Check according to Simplified Criterion set to No, a deflection limit absolute criterion of 20 millimeters, span limits of 360 for a braced column, and a factor for shear area of 1.

Add penetrations or fastener holes (optional)

Enter the combined diameters of holes in the top or bottom flange,

d_{h,f}

, and in a single web,

d_{h,w}

. Check for Reduction in Section Properties due to Penetrations shows whether the holes can be ignored: it reads Not Required when both are 0 mm.

Penetrations or Fastener Holes section with both combined hole diameters set to 0 millimeters and the check for reduction in section properties shown as Not Required.

Read the results

The Summary shows the design compression and tension forces, the axial compression and tension capacities, and the minimum design buckling resistance about the major and minor axes, each with a utilization badge. The badges at the top of the sheet show the same checks.

In Graphs by Load Case, choose the Graphed Load Case, choose to show the graphs about the Y-axis or the Z-axis, and choose whether to show the capacities on the graphs. The Graphed Load Case list has the strength cases (Imposed, Snow, Wind and Temperature Leading Variable, Earthquake and No Leading Variable) and the service cases, characteristic (Service CHAR) and frequent (Service FREQ).

Summary with a design compression force of 35.1 kilonewtons, a design tension force of 0, an axial compression capacity of 1823 kilonewtons at 2 percent, an axial tension capacity of 1823 kilonewtons at 0 percent, and buckling resistances of 1482 kilonewtons about the major axis at 2 percent and 871 kilonewtons about the minor axis at 4 percent.

Graphed Load Case list open showing the strength cases Imposed Leading Variable, Snow Leading Variable, Wind Leading Variable, Temperature Leading Variable, Earthquake and No Leading Variable, followed by the Service CHAR and Service FREQ cases.

Graphs by Load Case with the strength case Imposed Leading Variable selected, graphs shown about the Y-axis, capacities shown, an axial force graph with the capacities as yellow lines, and a load diagram with a 35.1 kilonewton reaction at the bottom and a 31.7 kilonewton axial load at the top.

See how each check is worked out

To see each calculation step, expand Details at the top right of the sheet and select Detailed. Each check has its own panel, for example ULS: Flexural Buckling Resistance in Axial Compression (EN 1993-1-1:2005 Cl 6.3.1), which lists every step from the buckling curve to the reduction factor. Select a label to see its description, reference and equation. For example, the value to determine the reduction factor for buckling about the major axis,

\phi_{y,b}

= 0.785, has the reference EN 1993-1-1:2005 Cl 6.3.1.2 (1). See View All Detailed Calculation Steps.

Flexural buckling panel in Detailed mode listing the buckling curves b and c, the imperfection factors 0.34 and 0.49, the non-dimensional slenderness ratios 0.646 and 1.11, and the reduction factor value 0.785 with its Formula Reference open, showing the reference EN 1993-1-1:2005 Cl 6.3.1.2 (1) and its equation.

Available presets

Each preset opens the calculator with a typical setup already entered.

Preset	Open in Calcs.com
Generic Concentrically-Loaded Column	Run with preset
Outdoor Cantilever Column	Run with preset
Interior Cantilever Column	Run with preset
Interior Single Storey Column	Run with preset
Interior Multi-Storey Column	Run with preset
Perimeter Multi-Storey Column	Run with preset
Corner Multi-Storey Column	Run with preset

Common questions

What design standard does this calculator use?

The calculator designs steel columns to EN 1993-1-1:2005 (Eurocode 3), with shear buckling per EN 1993-1-5:2006 where applicable. Load combinations follow EN 1990:2002. Partial factors can be adjusted per the relevant National Annex. Cross-section classes are determined for both axes, and buckling curves are selected based on section type and axis of buckling.

What are the key inputs?

Key inputs include the steel section (from the built-in European section database), steel grade, column height, effective length factors for both major and minor axes, loads by type (permanent

G

, imposed

QI

, snow

S

, wind

W

, temperature

T

, earthquake

AE

), bending moments about both axes, and deflection limit ratios. Support conditions (pinned, fixed, roller) are applied equally about both axes, as stated in the calculator’s assumptions.

What checks and outputs does it produce?

The calculator checks cross-section axial compression, axial tension, section bending capacity about both axes (EN 1993-1-1:2005 Cl 6.2.5), shear resistance about both axes (Cl 6.2.6), biaxial bending and the simplified biaxial bending-plus-axial criterion, longitudinal stress (Cl 6.2.9.2), buckling resistance about both axes, lateral torsional buckling (Cl 6.3.2.1), combined bending-and-axial-compression buckling (Cl 6.3.3), shear buckling, and three EN 1990:2002 deflection limits.

How are flexural buckling and LTB checks combined with axial compression?

The combined buckling check follows EN 1993-1-1:2005 Cl 6.3.3 using interaction factors

k_{yy}

k_{zy}

k_{yz}

k_{zz}

from Annex A or B (method 1 or 2). These factors account for the ratio of end moments, moment gradient correction

C_m

, and the relative slendernesses about each axis. The calculator applies both interaction equations and reports the governing utilization ratio.

How is the cross-section class determined for biaxial bending?

Cross-section class is determined independently for major-axis bending, minor-axis bending, and axial compression. The most onerous classification governs for each check. For Class 1 and 2 sections, plastic resistances are used; Class 3 uses elastic section moduli; Class 4 uses effective cross-section properties accounting for local buckling of slender elements.

Does this calculator support load linking with beam and footing calculations?

Yes, axial load at the column top can be linked from beam reactions above, and the column’s base reaction links to connected footing calculations. The full load path, beam to column to footing, updates automatically whenever any upstream input changes.

Next steps

Design a Steel Beam to EN1993

Design steel beams to EN 1993-1-1:2005 (Eurocode 3) with unlimited spans and loads. Checks bending, LTB, shear, web buckling and deflection.

Design a Wood Column to EN1995

Design timber columns and studs to EN 1995-1-1:2004 (Eurocode 5), with load linking and a database of European and UK timber sections.

Design a Wood Beam to EN1995

Design simple and continuous timber beams to EN 1995-1-1:2004+A1:2008 (Eurocode 5) with unlimited supports and loads.

Eurocode 3: Steel Building Sample Project

A Eurocode sample project in Calcs.com, following SCI P387: project defaults, two floor joists, an interior column and a roof truss, with results.

​Worked example

​Example 1: single-span column with lateral loads

​Method & scope

​Analysis and design capabilities

​Informational and National Annexes

​Assumptions and Limitations

​References

​See the exact clause

​Symbols

​Calculation method

​Structural model and load combinations

​Cross-section classification (EN 1993-1-1:2005 Cl 5.5.2)

​Cross-section resistance

​Flexural buckling resistance (EN 1993-1-1:2005 Cl 6.3.1)

​Lateral torsional buckling (EN 1993-1-1:2005 Cl 6.3.2.1)

​Combined bending and axial compression, member buckling (EN 1993-1-1:2005 Cl 6.3.3)

​Deflection checks (EN 1990:2002 Cl 6.5.3)

​Load linking

​How to use it

​Available presets

​Common questions

​Next steps

Design a Steel Beam to EN1993

Design a Wood Column to EN1995

Design a Wood Beam to EN1995

Eurocode 3: Steel Building Sample Project

Worked example

Example 1: single-span column with lateral loads

Method & scope

Analysis and design capabilities

Informational and National Annexes

Assumptions and Limitations

References

See the exact clause

Symbols

Calculation method

Structural model and load combinations

Cross-section classification (EN 1993-1-1:2005 Cl 5.5.2)

Cross-section resistance

Flexural buckling resistance (EN 1993-1-1:2005 Cl 6.3.1)

Lateral torsional buckling (EN 1993-1-1:2005 Cl 6.3.2.1)

Combined bending and axial compression, member buckling (EN 1993-1-1:2005 Cl 6.3.3)

Deflection checks (EN 1990:2002 Cl 6.5.3)

Load linking

How to use it

Available presets

Common questions

Next steps