# V. EC3 German NA - Built up Section with UDL

Calculate the bending capacity of a beam using a built-up I section subject to a uniformly distributed load per the German NA to EC3.

## Details

The section built up from 300 mm × 20.5 mm flange plates and a 279 mm × 11.5 mm web. Grade S275 steel. The member is a 5 m, fixed-fixed span subject to a 10 kN/m uniform load.

## Validation

Section Properties

• Moment of inertia about major axis,
• Moment of inertia about minor axis,
• Elastic section modulus about major axis,
• Elastic section modulus about minor axis,
• Plastic section modulus about major axis,
• Torsional constant,
• Warping constant,

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, $λ L T = w y f y M c r = 2,066 × ( 10 ) 3 × 275 966.7 × ( 10 ) 6 = 0.767$

H/b = 320/300 = 1.067 < 2. So, use buckling curve "c". From Table 6.5 of Eurocode 3, αLT = 0.49.

From Cl. 6.3.2.3 of Eurocode3:

ФLT = 0.5[1+αLTLT- λLT, 0) + β× λLT2] = 0.5[1 + 0.49×(0.767 - 0.2) +1 × 0.7672] = 0.810

So, $χ L T = Ф L T + Ф L T 2 - β λ L T 2 - 1 = 0.785$

Calculate kc: $k c = 1 C 1 = 1 0.712 = 1.185 > 1.0$ ; use the value from Table 6.6 of EC3: kc = 0.9.

Modification factor: $f = 1 - 0.5 1 - k c 1 - 2 λ L T - 0.8 2 = 1 - 0.5 1 - 0.9 1 - 2 0.767 - 0.8 2 = 0.950$

$χ L T , m o d = χ L T f = 0.883 < 1 λ L T 2 = 1.702$, OK

## Results

Table 1. Comparison of results for EC3 German NA - I Section with UDL
Moment capacity, Mckd (kN·m) 568.1 568.1 none
Critical moment, Mcr (kN·m) 966.7 967.3 negligible
Bending capacity, MB (kN·m) 426.5 426.5 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Europe\EC3 German NA - Built up 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 SBLT 1 indicates a built-up section
• The parameter KC 0 instructs the program to calculate the value of kc
• The parameter PY 275000 indicates an fy of 275 MPa
STAAD SPACE
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 5 0 0;
MEMBER INCIDENCES
1 1 2;
START USER TABLE
TABLE 1
UNIT METER KN
WIDE FLANGE
BUILTUP1
0.01613 0.32 0.0115 0.3 0.0205 0.0003082 9.239e-005 2.251e-006 0.00368 0.0082
END
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+008
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-005
DAMP 0.03
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 UPTABLE 1 BUILTUP1
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 2 FIXED
1 UNI GY -10
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PARAMETER 1
CODE EN 1993-1-1:2005
NA 10
C2 0.652 ALL
CMM 2 ALL
CMN 0.5 ALL
SBLT 1 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.    4
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   BUILTUP1    (UPT)
PASS     EC-6.2.6-(Y)       0.049         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        :    30820.002        9239.001
Plastic modulus          :     2065.718         931.725
Elastic modulus          :     1926.250         615.933
Shear Area               :       82.000          32.085
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         :       4180.9         4180.9
Moment Capacity          :        568.1          256.2
Reduced Moment Capacity  :        568.1          256.2
Shear Capacity           :       1301.9          509.4
BUCKLING CALCULATIONS (units - kN,m)
Lateral Torsional Buckling Moment       MB =  426.5
co-efficients C1 & K : C1 =0.712 K =0.5, Effective Length= 5.000
Lateral Torsional Buckling Curve : Curve c
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.    5
CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m):
CLAUSE        RATIO  LOAD     FX       VY      VZ      MZ      MY
EC-6.2.5       0.037     1     0.0     25.0     0.0    20.8     0.0
EC-6.2.6-(Y)   0.049     1     0.0     25.0     0.0    20.8     0.0
EC-6.3.2 LTB   0.049     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 **************