V. EC3 Polish NA - I Section with UDL

Calculate the bending capacity of a beam using an I section subject to a uniformly distributed load per the Polish 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
=
7,477,200
=
22,394
=
23,737
C2Zg
=
1.554×160 = 248.6

Therefore, Mcr = 1,539 kN·m

From the Polish NA, λLT, 0 = 0.4, β = 0.75

So,

H/b = 320/300 = 1.067 < 2

So, from Table 6.5 of Eurocode 3, αLT = 0.34 (buckling curve “b”)

From Cl. 6.3.2.3 of Eurocode3:

Ф ɑ

So, Ф Ф

For the Polish NA, the value of kc is evaluated as:

where

ɑs
=
Ms / Mh = -10.42 / 20.83 = -0.5 for -1 ≤ ɑs ≤ 1; per Table B.3 of Annex B of EC3.
ψ
=
1 for 0 ≤ ψ ≤ 1
CmLT
=
0.1 - 0.8×ɑs = 0.5 > 0.4, thus use CmLT = 0.5

So,

Modification factor:

, thus use

Results

Table 1. Comparison of results for EC3 French NA - I Section with UDL
Result Type Reference STAAD.Pro Difference Comments
Moment capacity, Mckd (kN·m) 591.0 591.0 none
Critical moment, Mcr (kN·m) 1,539 1,541.5 negligible
Bending capacity, MB (kN·m) 591.0 591.0 none

Input

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

The following design parametersdesign parameters are used:

  • The Polish NA is specified using NA 6
  • Uniformly distributed load w/ fixed-fixed supports: CMM 2
  • The value of C2 1.554 is specified
  • The yield strength is directly specified by PY 275000.

STAAD

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 1-Feb-21
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 6
C2 1.554 ALL
CMM 2 ALL
PY 275000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH

Output

 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-6.2.5           0.035         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 :  1.10
                                      z-axis          y-axis
      Slenderness ratio (KL/r) :         36.2           66.1
      Compression Capacity     :       4078.2         3045.5
      Tension Capacity         :       4435.8         4435.8
      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 =  591.0 
      co-efficients C1 &amp; K : C1 =2.578 K =1.0, Effective Length= 5.000
      Lateral Torsional Buckling Curve : Curve b
      Elastic Critical Moment for LTB,               Mcr   =  1541.5 
      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   0.035     1     0.0     25.0     0.0    20.8     0.0
   ADDITIONAL CHECKS AS PER NATIONAL ANNEX [NA FOR PN-EN 1993-1-1:2006 ] (units- kN,m):
   EC CLAUSE           NA-CLAUSE        RATIO   LOAD      FX       VY       VZ     MZ       MY
    Torsion has not been considered in the design.
                        _________________________
   ************** END OF TABULATED RESULT OF DESIGN **************