# V. EC3 German NA - I Section with UDL

Calculate the bending capacity of a beam using an I section subject to a uniformly distributed load per the German 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 = 0.712 C2 = 0.652 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 = 0.652×160 = 104.3

Therefore, Mcr = 966.7 kN·m

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

So, $λ L T = w y f y M c r = 2,149 × ( 10 ) 3 × 275 966.7 × ( 10 ) 6 = 0.782$

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×(0.782 - 0.2) +1 × 0.7822] = 0.794

So, $χ L T = Ф L T + Ф L T 2 - β λ L T 2 - 1 = 0.827$

So, $k c ⁢ = 1 / C 1 = 1 / 0.712 = 1.182 > 1$ but this value cannot be used, so from Table 6.6 of the Eurocode 3, kc = 0.9

Modification factor: $f = 1 - 0.5 1 - k c 1 - 2 λ L T - 0.8 2 = 1 - 0.5 1 - 0.9 1 - 2 0.782 - 0.8 2 = 0.950$

$χ L T , m o d = χ L T f = 0.871 < 1 λ L T 2 = 1.635$, OK

## Results

Table 1. Comparison of results for EC3 German NA - I Section with UDL
Moment capacity, Mckd (kN·m) 591.0 591.0 none
Critical moment, Mcr (kN·m) 966.7 967.3 negligible
Bending capacity, MB (kN·m) 467.7 467.8 negligible

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

The following design parameters are used:

• The German NA is specified using NA 10
• Fully fixed span: CMN 0.5
• Uniformly distributed load w/ fixed-fixed supports: CMM 2
• The value of C2 0.652 is specified
• The parameter KC 0 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 1-Aug-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
1 UNI GY -10
PERFORM ANALYSIS
PARAMETER 1
CODE EN 1993-1-1:2005
NA 10
C2 0.652 ALL
CMM 2 ALL
CMN 0.5 ALL
FU 300000 ALL
KC 0 ALL
*MTH 1 ALL
PY 275000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH


                         STAAD.PRO CODE CHECKING - DIN EN 1993-1-1:2010-12
********************************************
NATIONAL ANNEX - DIN EN 1993-1-1/NA:2010-12
PROGRAM CODE REVISION V1.14 BS_EC3_2005/1
STAAD SPACE                                              -- PAGE NO.    3
ALL UNITS ARE - KN   METE (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
*** WARNING:CMN PARAM INVALID FOR NATIONAL ANNEX
NATIONAL ANNEX ONLY DEALS WITH END RESTRAINT FACTORS OF K = KW = 1.
HENCE WILL USE ANNEX F FROM DD ENV 1993-1-1:1992
1 ST   HD320X127   (EUROPEAN SECTIONS)
PASS     EC-6.3.2 LTB       0.045         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 :  1.10          GM2 :  1.25
z-axis          y-axis
Slenderness ratio (KL/r) :         36.2           66.1
Compression Capacity     :       3707.4         2768.6
Tension Capacity         :       3484.1         3484.1
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 =  467.8
co-efficients C1 & K : C1 =0.712 K =0.5, Effective Length= 5.000
Lateral Torsional Buckling Curve : Curve b
Elastic Critical Moment for LTB,               Mcr   =   967.3
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   0.045     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 **************