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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:

M ckd = W ply f y γ M 0 = 58.53 × ( 10 ) 3 × 300 1.0 × ( 10 ) 6 = 17.56  kN·m

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, M cr = 1.0 × 215,300 [ 40.60 + 39,922 + 5 - 58 2 - 5 - 58 ] = 55.9  kN·m

Results

Table 1.
Result Type Reference STAAD.Pro Difference Comments
Moment capacity, Mckd (kN·m) 17.56 17.6 negligible  
Critical moment, Mcr (kN·m) 55.9 55.9 none  

STAAD.Pro Input

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
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 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 Output

                         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)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          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                
      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 =   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     
      Squash Load              :    876.00
      Axial force/Squash load  :     0.000
      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)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
   CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m):
    CLAUSE        RATIO  LOAD     FX       VY      VZ      MZ      MY   
   EC-6.2.5       0.571     1     0.0      0.3     0.0   -10.0     0.0
   EC-6.2.6-(Y)   0.020     1     0.0      5.5     0.0     2.5     0.0
   EC-6.3.2 LTB   0.775     1     0.0      0.3     0.0   -10.0     0.0
    Torsion and deflections have not been considered in the design.
                        _________________________