V. EC3 Belgian NA - I Section with UDL

Calculate the bending capacity of a beam using an I section subject to a uniformly distributed load per the Belgian NA to EC3.

Details

The section is a HD320X127, Grade S275 steel. The member is a 5 m, fixed-fixed span subject to a 10 kN/m uniform load.

Calculations

Validation

Moment capacity:

The critical moment is given by:

where

C₁: 2.578
C₂: 1.554
k: 0.5
: 29,909,000
: 5,599
: 5,934
C₂Z_g: 1.554×160 = 248.6

Therefore, M_cr = 1,712 kN·m

From the Belgian NA, λ_{LT, 0} = 0.2, β = 1.0

So,

H/b = 320/300 = 1.067 < 2. So, from Table 6.5 of Eurocode 3, α_LT = 0.34.

From Cl. 6.3.2.3 of Eurocode3:

Ф_LT = 0.5[1+α_LT (λ_LT- λ_{LT, 0}) + β× λ_LT ²] = 0.5[1 + 0.34×(0.589 - 0.2) +1 × 0.588²] = 0.739

So,

From Table 6.6 of the Eurocode 3, k_c = 0.9

Modification factor:

, OK

If Cl. 6.3.2.2 is used to determine χ_LT :

H/b = 320/300 = 1.067 < 2. So, from Table 6.3 of Eurocode 3, α_LT = 0.21.

Ф_LT = 0.5[1+α_LT (λ_LT- 0.2) + λ_LT ²] = 0.5[1+0.21×(0.588 - 0.2) +1×0.588²] = 0.713

Results

Table 1. Comparison of results for EC3 Belgian NA - I Section with UDL
Result Type	Reference	STAAD.Pro	Difference
Moment capacity, M_ckd (kN·m)	591.0	591.0	none
Critical moment, M_cr (kN·m)	1,712	1,712.9	negligible
Bending capacity, M_B (kN·m)	521.8	522.1	negligible
Bending capacity, M_B (kN·m)	528.9	528.8	negligible

Input

The file C:\Users\Public\Public Documents\STAAD.Pro 2026\Samples \Verification Models\09 Steel Design\Europe\EC3 Belgian NA - I Section with UDL.std is typically installed with the program.

The following design parametersdesign parameters are used:

The Belgian NA is specified using NA 8
Fully fixed span: CMN 0.5
Uniformly distributed load w/ fixed-fixed supports: CMM 2
The value of C2 1.554 is specified
The parameter KC instructs the program to calculate the value of k_c
A second design parameter set is used with MTH 1 to use Cl 6.3.2.2 to determine Ф_LT
Note: The previously set parameters are still used as they are not specified again with a different value, which is the default behavior in STAAD.Pro batch design.

STAAD

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 14-Apr-20
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 5 0 0;
MEMBER INCIDENCES
1 1 2;
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
MEMBER PROPERTY EUROPEAN
1 TABLE ST HD320X127
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 2 FIXED
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
MEMBER LOAD
1 UNI GY -10
PERFORM ANALYSIS
PARAMETER 1
CODE EN 1993-1-1:2005
NA 8
C2 1.554 ALL
CMM 2 ALL
CMN 0.5 ALL
PY 275000 ALL
KC 0 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE EN 1993-1-1:2005
NA 8
MTH 1 ALL
CHECK CODE ALL
FINISH

Output

                         STAAD.PRO CODE CHECKING - NBN EN 1993-1-1:2005
                         ********************************************
                         NATIONAL ANNEX - NBN EN 1993-1-1 ANB : 2018
 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-6.3.2 LTB       0.040         1
                        0.00            0.00          20.83        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  :     0.000
      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         :       4180.9         4180.9
      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 =  522.1 
      co-efficients C1 &amp; K : C1 =2.578 K =0.5, Effective Length= 5.000
      Lateral Torsional Buckling Curve : Curve b
      Elastic Critical Moment for LTB,               Mcr   =  1712.9 
      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-6.2.5       0.035     1     0.0     25.0     0.0    20.8     0.0
   EC-6.2.6-(Y)   0.030     1     0.0     25.0     0.0    20.8     0.0
   EC-6.3.2 LTB   0.040     1     0.0     25.0     0.0    20.8     0.0
    Torsion has not been considered in the design.
                        _________________________
   ************** END OF TABULATED RESULT OF DESIGN **************
    39. PARAMETER 2
    40. CODE EN 1993-1-1:2005
    41. NA 8
    42. MTH 1 ALL
    43. CHECK CODE ALL
 STEEL DESIGN    
                         STAAD.PRO CODE CHECKING - NBN EN 1993-1-1:2005
                         ********************************************
                         NATIONAL ANNEX - NBN EN 1993-1-1 ANB : 2018
 PROGRAM CODE REVISION V1.14 BS_EC3_2005/1
      STAAD SPACE                                              -- PAGE NO.    5 
 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-6.3.2 LTB       0.039         1
                        0.00            0.00          20.83        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  :     0.000
      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         :       4180.9         4180.9
      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 =  528.8 
      co-efficients C1 &amp; K : C1 =2.578 K =0.5, Effective Length= 5.000
      Lateral Torsional Buckling Curve : Curve a
      Elastic Critical Moment for LTB,               Mcr   =  1712.9
      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.    6 
   CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m):
    CLAUSE        RATIO  LOAD     FX       VY      VZ      MZ      MY   
   EC-6.2.5       0.035     1     0.0     25.0     0.0    20.8     0.0
   EC-6.2.6-(Y)   0.030     1     0.0     25.0     0.0    20.8     0.0
   EC-6.3.2 LTB   0.039     1     0.0     25.0     0.0    20.8     0.0
    Torsion has not been considered in the design.
                        _________________________
   ************** END OF TABULATED RESULT OF DESIGN **************