# V. EC3 Belgian NA - Tee Section

Calculate the bending capacity of a beam using an Tee section subject to a uniformly distributed load and varying end moments per the Belgian NA to EC3.

## Details

The section is an Indian INST150 with fy = 300 MPa. The member is a 5 m, simply-supported span under a 2 kN/m uniform load. The left support has a -5.0 kN·m moment applied and the right support has a 2.5 kN·m moment applied.

## Validation

Moment capacity:

The critical moment is given by:

$M c r = C 1 π 2 E I ( k z L ) 2 [ ( k z k w ) 2 I w I z + ( k z L ) 2 G I T π 2 E I z + ( C 2 Z g - C 3 Z j ) 2 − ( C 2 Z g - C 3 Z j ) ]$
where
 C1 = 1.0 C2 = 1.0 C3 = 1.0 $π 2 E I y k L 2$ = 215,300 $k k w 2 I w I y$ = $1 1 2 1.08 × ( 10 ) 8 266 × ( 10 ) 4 = 40.60$ $k L 2 G I T π 2 E I y$ = $( 1 × 5,000 ) 2 × 205,000 × 10.9 × ( 10 ) 4 2.6 × π 2 × 205,000 × 266 × ( 10 ) 4 = 39,922$ C2Zg = 1.0×10 / 2 =5 Ψf = 1 (Ift = 0, as there is no tension flange present in the Tee section) zj = 0.8×Ψf×hs/2 = 0.8×1×145 / 2 = 58 mm C3Zj = 1.0×58 =58

Therefore,

## Results

Table 1.
Moment capacity, Mckd (kN·m) 17.56 17.6 negligible
Critical moment, Mcr (kN·m) 55.9 55.9 none

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 - Tee Section.std is typically installed with the program.

The following design parameters are used:

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 20-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+008
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-005
DAMP 0.03
END DEFINE MATERIAL
MEMBER PROPERTY INDIAN
1 TABLE ST ISNT150
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 2 PINNED
2 MZ 2.5
1 MZ -5
1 UNI GY -2
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PARAMETER 1
CODE EN 1993-1-1:2005
NA 8
CMM 7 ALL
*MU 1.25 ALL
C1 1 ALL
C2 1 ALL
C3 1 ALL
CMN 1 ALL
PY 300000 ALL
*KC 1 ALL
TRACK 2 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.    4
ALL UNITS ARE - KN   METE (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
1 ST   ISNT150     (INDIAN SECTIONS)
PASS     EC-6.3.2 LTB       0.775         1
0.00            0.00         -10.03        2.08
=======================================================================
MATERIAL DATA
Modulus of elasticity    =  205 kN/mm2
Design Strength  (py)    =  300  N/mm2
SECTION PROPERTIES (units - cm)
Member Length =    500.00
Gross Area =   29.20          Net Area =   29.20
z-axis          y-axis
Moment of inertia        :      638.000         266.000
Plastic modulus          :      106.000          57.800
Elastic modulus          :       58.532          35.467
Shear Area               :       20.000          15.900
Radius of gyration       :        4.674           3.018
Effective Length         :      500.000         500.000
DESIGN DATA (units - kN,m)   EUROCODE NO.3 /2005
Section Class            :   CLASS 3
GM0 :  1.00          GM1 :  1.00          GM2 :  1.25
z-axis          y-axis
Slenderness ratio (KL/r) :        107.0          165.7
Compression Capacity     :        345.4          169.3
Tension Capacity         :        756.9          756.9
Moment Capacity          :         17.6           10.6
Reduced Moment Capacity  :         17.6           10.6
Shear Capacity           :        346.4          275.4
BUCKLING CALCULATIONS (units - kN,m)
Lateral Torsional Buckling Moment       MB =   12.9
co-efficients C1 & K : C1 =1.000 K =1.0, Effective Length= 5.000
Lateral Torsional Buckling Curve : Curve d
Elastic Critical Moment for LTB,               Mcr   =    55.9
Compression buckling curves:     z-z:  Curve c   y-y:  Curve c
Critical Load For Torsional Buckling,          NcrT  =  2778.8
Critical Load For Torsional-Flexural Buckling, NcrTF =   215.3
STAAD SPACE                                              -- PAGE NO.    5
ALL UNITS ARE - KN   METE (UNLESS OTHERWISE Noted)