# V. EC3 Singapore 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 Singaporean NA to EC3.

## Details

The section is an Indian INST100 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 $π 2 E I y k L 2$ = 64,421 $k k w 2 I w I y$ = $1 1 2 30.76 79.6 = 0.386$ $k L 2 G I T π 2 E I y$ = $( 1 × 5,000 ) 2 × 205,000 × 7.33 × ( 10 ) 4 2.6 × π 2 × 205,000 × 79.6 × ( 10 ) 4 = 89,714$ C2Zg = 1.0×10 / 2 =5 Ψf = 1 (Ift = 0, as there is no tension flange present in the Tee section) hs = D - 0.5×tf = 100 - 0.5 × 10 = 95 mm zj = 0.8×Ψf×hs/2 = 0.8×1×95 / 2 = 38 mm C3Zj = 1.0×38 =38

Therefore,

## Results

Table 1.
Moment capacity, Mckd (kN·m) 13.7 13.7 none
Critical moment, Mcr (kN·m) 21.5 21.5 none

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

The following design parameters are used:

STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 10-Jul-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 ISNT100
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 7
CMM 7 ALL
C1 1 ALL
C2 1 ALL
C3 1 ALL
CMN 1 ALL
PY 300000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH


                         STAAD.PRO CODE CHECKING - SS EN 1993-1-1:2010
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NATIONAL ANNEX - NA to SS EN 1993-1-1:2010
PROGRAM CODE REVISION V1.14 BS_EC3_2005/1
STAAD PLANE                                              -- PAGE NO.    4
ALL UNITS ARE - KN   METE (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
*     1 ST   ISNT100     (INDIAN SECTIONS)
FAIL     EC-6.3.2 LTB       1.064         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 =   19.20          Net Area =   19.20
z-axis          y-axis
Moment of inertia        :      180.000          79.600
Plastic modulus          :       45.500          26.600
Elastic modulus          :       25.210          15.920
Shear Area               :       13.333          10.900
Radius of gyration       :        3.062           2.036
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 :  1.10
z-axis          y-axis
Slenderness ratio (KL/r) :        163.3          245.6
Compression Capacity     :        116.5           55.1
Tension Capacity         :        565.5          565.5
Moment Capacity          :         13.7            8.0
Reduced Moment Capacity  :         13.7            8.0
Shear Capacity           :        230.9          188.8
BUCKLING CALCULATIONS (units - kN,m)
Lateral Torsional Buckling Moment       MB =    9.4
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   =    21.5
Compression buckling curves:     z-z:  Curve c   y-y:  Curve c
Critical Load For Torsional Buckling,          NcrT  =  4275.7
Critical Load For Torsional-Flexural Buckling, NcrTF =    64.4
STAAD PLANE                                              -- PAGE NO.    5
CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m):
CLAUSE        RATIO  LOAD     FX       VY      VZ      MZ      MY
EC-6.2.5       0.735     1     0.0      0.3     0.0   -10.0     0.0
EC-6.2.6-(Y)   0.029     1     0.0      5.5     0.0     2.5     0.0
EC-6.3.2 LTB   1.064     1     0.0      0.3     0.0   -10.0     0.0
Torsion has not been considered in the design.
_________________________
************** END OF TABULATED RESULT OF DESIGN **************
44. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= OCT 19,2021   TIME= 18: 4:48 ****
STAAD PLANE                                              -- PAGE NO.    6
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