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 f_y = 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:

M_{ckd} = \frac{W_{ply} f_{y}}{γ_{M 0}} = \frac{45.5 \times {(10)}^{3} \times 300}{1.0 \times {(10)}^{6}} = 13.7 kN·m

The critical moment is given by:

M_{c r} = C_{1} \frac{π^{2} E I}{{(k_{z} L)}^{2}} [\sqrt{{(\frac{k_{z}}{k_{w}})}^{2} \frac{I_{w}}{I_{z}} + \frac{{(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
$\frac{π^{2} E I_{y}}{{(k L)}^{2}}$	=	64,421
${(\frac{k}{k_{w}})}^{2} \frac{I_{w}}{I_{y}}$	=	${(\frac{1}{1})}^{2} \frac{30.76}{79.6} = 0.386$
$\frac{{(k L)}^{2} G I_{T}}{π^{2} E I_{y}}$	=	$\frac{{(1 \times 5,000)}^{2} \times 205,000 \times 7.33 \times {(10)}^{4}}{2.6 \times π^{2} \times 205,000 \times 79.6 \times {(10)}^{4}} = 89,714$
C₂Z_g	=	1.0×10 / 2 =5
Ψ_f	=	1 (I_ft = 0, as there is no tension flange present in the Tee section)
h_s	=	D - 0.5×t_f = 100 - 0.5 × 10 = 95 mm
z_j	=	0.8×Ψ_f×h_s/2 = 0.8×1×95 / 2 = 38 mm
C₃Z_j	=	1.0×38 =38

Therefore, $M_{cr} = 1.0 \times 64,421 [\sqrt{0.386 + 89,714 + {(5 - 38)}^{2}} - (5 - 38)] = 21.5 kN·m$

Results

Table 1.
Result Type	Reference	STAAD.Pro	Difference	Comments
Moment capacity, M_ckd (kN·m)	13.7	13.7	none
Critical moment, M_cr (kN·m)	21.5	21.5	none

STAAD.Pro Input

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:

The Singaporean NA is specified using NA 7
Simply-supported span: CMN 1.0
Varying end moments and a uniformly distributed load: CMM 7
The values of C1 1.0, C2 1.0, and C3 1.0 are specified
Note: Since these parameters are specified, MU is not specified as it would be ignored in favor of the direct coefficient specifications. Refer to D5.D.10.2 Clause 6.3.2.2 –Elastic critical moment and imperfection factors for LTB checks for additional details.

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
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
JOINT LOAD
2 MZ 2.5
1 MZ -5
MEMBER LOAD
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 Output

                         STAAD.PRO CODE CHECKING - SS EN 1993-1-1:2010
                         ********************************************
                         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)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          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                
      Grade of steel           =  USER          
      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     
      Squash Load              :    576.00
      Axial force/Squash load  :     0.000
      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
      STAAD PLANE                                              -- PAGE NO.    6
             *********** END OF THE STAAD.Pro RUN ***********         
               **** DATE= OCT 27,2022   TIME= 15:23:14 ****
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