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.
Calculations
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:
where
- C1
- 0.712
- C2
- 0.652
- k
- 0.5
- 29,909,000
- 5,599
- 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,
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:
So,
Calculate kc : ; use the value from Table 6.6 of EC3: kc = 0.9.
Modification factor:
, OK
Results
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| 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 |
Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2026\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 parametersdesign 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 0.652is specified - The parameter
SBLT 1indicates a built-up section - The parameter
KC 0instructs the program to calculate the value of kc - The parameter
PY 275000indicates an fy of 275 MPa
STAAD
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
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
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
Output
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)
MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/
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-6.3.2 LTB 0.049 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 : 30820.002 9239.001
Plastic modulus : 2065.718 931.725
Elastic modulus : 1926.250 615.933
Shear Area : 82.000 36.800
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 : 1.10 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 : 1301.9 584.3
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) 0.043 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 **************