V. EC3 French NA - Column with Axial Load
Calculate the axial and bending capacities and interaction ratios of a column using the French NA to EC3.
Details
The 5 m tall column as a fixed base and is free to translate and rotate at the top. The column is subject to a 25 kN compressive load and moments of 5 kN·m about the X axis and 10 kN·m about the Z axis. The section is an HD320X127, grade S275 steel.
Calculations
Validation
Bending Capacity
Moment capacity:
The critical moment is given by:
where
- C1
- 2.578
- C2
- 1.554
- 7,477,200
- 22,394
- 23,740
- C2Zg
- 1.554×160 = 248.6
Therefore, Mcr = 1,540.6 kN·m
From the French NA, λLT, 0 = 0.2 + 0.1×b / h = 0.2 + 0.1× 300 / 327 = 0.292, β = 1.0
So,
H/b = 320/300 = 1.067 < 2. So, from Table 6.5 of Eurocode 3, .
From Cl. 6.3.2.3 of Eurocode3:
So,
So, kc = 0.9 and thus modification factor, f = 1 - 0.5(1 - 0.9)×[1 -2(0.619 - 0.8)2] = 0.953
Compression Capacity
Critical compressive values:
Determine χy
h/b = 1.067 < 1.2 and tf = 20.5 mm < 100 mm
So, for y-y axis, use curve “c”. Hence, α = 0.49 [Table 6.2, EC3]
So, ф = 0.5[1+α (λ - 0.2) +λ2)] = 0.936
(governs)
Determine χz
h/b = 1.067 < 1.2 and tf = 20.5 mm < 100 mm
So, for z-z axis, use curve “b”. Hence, α = 0.34 [Table 6.2, EC3]
So, ф = 0.5[1+α (λ - 0.2) +λ2)] = 0.627
(does not govern)
Compression capacity:
Compression ratio: 25 kN / 3,020.2 kN = 0.008
Critical Axial Loads for Flexure and Flexural Torsional Buckling
From NCCI document SN001a-EN-FU:
where
-
; here y0 = z0 =
0
iy = 75.68 mm and iz = 138.23 mm
= 24,835 mm2
Interaction Check
From Annex A, Table A.1 of EC3, we get the auxiliary terms:
The beam has uniform loading and fixed end supports and ψ=1.0.
Determine λ0: C1 = 1, C2 = 0, Mcr = 1,606 kN·m
So, CmLT = 1.0, λmax = max.(λz,λy) = λy = 0.770
Wely/Wply = 0.656 < Cyy . So, Cyy = 0.980
Interaction factors:
Check for Clause 6.3.3-661:
Check for Clause 6.3.3-662:
Results
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| Moment capacity, Mckd (kN·m) | 591.0 | 591.0 | none | |
| Critical moment, Mcr (kN·m) | 1,540.6 | 1,536.7 | negligible | |
| Bending capacity, MB (kN·m) | 533.7 | 534.4 | none | |
| Critical load for torsional buckling, Ncr,T (kN) | 13,889 | 13,898.0 | negligible | |
| Critical load for torsional-flexural buckling, Ncr,TF | 13,889 | 13,898.0 | negligible | |
| Compression interaction, Cl. 6.3.1.1 | 0.008 | 0.008 | none | |
| Bending and compression interaction, Cl 6.3.3-661 | 0.038 | 0.038 | none | |
| Bending and compression interaction, Cl. 6.3.3-662 | 0.038 | 0.037 | 3% | Rounding difference in small numbers. |
Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2026\Samples \Verification Models\09 Steel Design\Europe\EC3 French NA - Column with Axial Load.std is typically installed with the program.
The following design parametersdesign parameters are used:
- The French NA is
specified using
NA 4 - Fixed support:
CMM 2.0 - Fixed base and free
at other end:
CMN 0.7 - The value of
C2 1.554is specified - Program calculated kc per Table
6.6 of EN 1993-1-1:2005:
KC 0
STAAD
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 12-June-20
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 5 0;
MEMBER INCIDENCES
1 1 2;
MEMBER PROPERTY EUROPEAN
1 TABLE ST HD320X127
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
END DEFINE MATERIAL
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
JOINT LOAD
2 FY -25 MX 5 MZ 10
PERFORM ANALYSIS
PARAMETER 1
CODE EN 1993-1-1:2005
NA 4
CMM 2 ALL
C2 1.554 ALL
FU 295000 ALL
PY 275000 ALL
KC 0 ALL
CMN 0.7 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
Output
STAAD.PRO CODE CHECKING - NF EN 1993-1-1:2005
********************************************
NATIONAL ANNEX - NF EN 1993-1-1/NA
PROGRAM CODE REVISION V1.14 BS_EC3_2005/1
STAAD SPACE -- PAGE NO. 3
ALL UNITS ARE - KN METE (UNLESS OTHERWISE Noted)
MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/
FX MY MZ LOCATION
=======================================================================
1 ST HD320X127 (EUROPEAN SECTIONS)
PASS EC-6.3.3-661 0.038 1
25.00 C 5.00 -10.00 0.00
=======================================================================
MATERIAL DATA
Grade of steel = USER
Modulus of elasticity = 205 kN/mm2
Design Strength (py) = 275 N/mm2
SECTION PROPERTIES (units - cm)
Member Length = 500.00
Gross Area = 161.30 Net Area = 161.30
z-axis y-axis
Moment of inertia : 30820.004 9239.001
Plastic modulus : 2149.000 939.100
Elastic modulus : 1926.250 615.933
Shear Area : 109.573 51.728
Radius of gyration : 13.823 7.568
Effective Length : 500.000 500.000
DESIGN DATA (units - kN,m) EUROCODE NO.3 /2005
Section Class : CLASS 1
Squash Load : 4435.75
Axial force/Squash load : 0.006
GM0 : 1.00 GM1 : 1.00 GM2 : 1.25
z-axis y-axis
Slenderness ratio (KL/r) : 36.2 66.1
Compression Capacity : 4078.2 3045.5
Tension Capacity : 3426.0 3426.0
Moment Capacity : 591.0 258.3
Reduced Moment Capacity : 591.0 258.3
Shear Capacity : 1739.7 821.3
BUCKLING CALCULATIONS (units - kN,m)
Lateral Torsional Buckling Moment MB = 534.4
co-efficients C1 & K : C1 =2.570 K =1.0, Effective Length= 5.000
Lateral Torsional Buckling Curve :
Elastic Critical Moment for LTB, Mcr = 1536.7
Compression buckling curves: z-z: Curve b y-y: Curve c
Critical Load For Torsional Buckling, NcrT = 13898.0
Critical Load For Torsional-Flexural Buckling, NcrTF = 13898.0
STAAD SPACE -- PAGE NO. 4
CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m):
CLAUSE RATIO LOAD FX VY VZ MZ MY
EC-6.3.1.1 0.008 1 25.0 0.0 0.0 -10.0 5.0
EC-6.2.9.1 0.020 1 25.0 0.0 0.0 -10.0 5.0
EC-6.3.3-661 0.038 1 25.0 0.0 0.0 -10.0 5.0
EC-6.3.3-662 0.037 1 25.0 0.0 0.0 -10.0 5.0
EC-6.2.5 0.019 1 25.0 0.0 0.0 -10.0 5.0
EC-6.3.2 LTB 0.019 1 25.0 0.0 0.0 -10.0 5.0
Torsion has not been considered in the design.
_________________________
************** END OF TABULATED RESULT OF DESIGN **************