# 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.

## Validation

Moment capacity:

The critical moment is given by:

$M c r = C 1 π 2 E I ( k L ) 2 { ( k k w ) 2 I w I + ( k L ) 2 G I t π 2 E I + ( C 2 Z g ) 2 − C 2 Z g }$
where
 C1 = 2.578 C2 = 1.554 k = 0.5 $π 2 E I y k L 2$ = 29,909,000 $k k w 2 I w I y$ = 5,599 $k L 2 G I t π 2 E I y$ = 5,934 C2Zg = 1.554×160 = 248.6

Therefore, Mcr = 1,712 kN·m

From the Belgian NA, λLT, 0 = 0.2, β = 1.0

So, $λ L T = w y f y M c r = 2,149 × ( 10 ) 3 × 275 1,712 × ( 10 ) 6 = 0.588$

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

From Cl. 6.3.2.3 of Eurocode3:

ФLT = 0.5[1+αLTLT- λLT, 0) + β× λLT2] = 0.5[1 + 0.34×(0.589 - 0.2) +1 × 0.5882] = 0.739

So, $χ L T = Ф L T + Ф L T 2 - β λ L T 2 - 1 = 0.843$

From Table 6.6 of the Eurocode 3, kc = 0.9

Modification factor: $f = 1 - 0.5 1 - k c 1 - 2 λ L T - 0.8 2 = 1 - 0.5 1 - 0.9 1 - 2 0.588 - 0.8 2 = 0.955$

$χ L T , m o d = χ L T f = 0.883 < 1 λ L T 2 = 2.897$, OK

If Cl. 6.3.2.2 is used to determine χLT:

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

ФLT = 0.5[1+αLTLT- 0.2) + λLT2] = 0.5[1+0.21×(0.588 - 0.2) +1×0.5882] = 0.713

$χ L T = Ф L T + Ф L T 2 - λ L T 2 - 1 = 0.895$

## Results

Table 1. Comparison of results for EC3 Belgian NA - I Section with UDL
Moment capacity, Mckd (kN·m) 591.0 591.0 none
Critical moment, Mcr (kN·m) 1,712 1,712.9 negligible
Bending capacity, MB (kN·m) 521.8 522.1 negligible
Bending capacity, MB (kN·m) 528.9 528.8 negligible

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

The following design 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 kc
• A second design parameter set is used with MTH 1 to use Cl 6.3.2.2 to determine ФLT
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 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
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


                         STAAD.PRO CODE CHECKING - NBN EN 1993-1-1:2005
********************************************
NATIONAL ANNEX - NBN EN 1993-1-1 ANB : 2018
PROGRAM CODE REVISION V1.13 BS_EC3_2005/1
STAAD SPACE                                              -- PAGE NO.    3
ALL UNITS ARE - KN   METE (UNLESS OTHERWISE Noted)
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
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               :       81.998          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
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           :       1301.9          821.3
BUCKLING CALCULATIONS (units - kN,m)
Lateral Torsional Buckling Moment       MB =  522.1
co-efficients C1 & 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
ALL UNITS ARE - KN   METE (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
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 and deflections have 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 V1.13 BS_EC3_2005/1
STAAD SPACE                                              -- PAGE NO.    5
ALL UNITS ARE - KN   METE (UNLESS OTHERWISE Noted)
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
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               :       81.998          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
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           :       1301.9          821.3
BUCKLING CALCULATIONS (units - kN,m)
Lateral Torsional Buckling Moment       MB =  528.8
co-efficients C1 & 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
ALL UNITS ARE - KN   METE (UNLESS OTHERWISE Noted)