V. EC3 Singapore NA - Varying End Mom CMM8

Calculate the bending capacity of a beam using an I section subject to a concentrated load and varying end moments per the Singaporean NA to EC3.

Details

The section is a HD320X127, Grade S275 steel. The member is a 5 m, simply-supported span subject to a 10 kN/m uniform load. The left support has a -10.0 kN·m moment applied and the right support has a 8.0 kN·m moment applied.

Validation

Moment capacity:

M_{c k d} = \frac{W_{p l y} f_{y}}{γ_{M 0}} = \frac{2,149 \times {(10)}^{3} \times 275}{1.0 \times {(10)}^{6}} = 591.0 kN·m

The critical moment is given by:

M_{c r} = C_{1} \frac{π^{2} E I}{{(k L)}^{2}} {\sqrt{{(\frac{k}{k_{w}})}^{2} \frac{I_{w}}{I} + \frac{{(k L)}^{2} G I_{t}}{π^{2} E I} + {(C_{2} Z_{g})}^{2}} - C_{2} Z_{g}}

where

k_w	=	k = 1
$\frac{π^{2} E I_{y}}{{(k L)}^{2}}$	=	7,477,200
${(\frac{k}{k_{w}})}^{2} \frac{I_{w}}{I_{y}}$	=	22,394
$\frac{{(k L)}^{2} G I_{t}}{π^{2} E I_{y}}$	=	23,737
C₂Z_g	=	0.17×160 = 27.2

μ = \frac{F L}{4 M} = \frac{4 \times 5}{4 \times 10} = 0.5 > 0

From the graph, C₁ = 1.184, C₂ = 0.17

C₂z_g = 0.17×160 = 27.2

Therefore, M_cr = 1,676 kN·m

Results

Table 1.
Result Type	Reference	STAAD.Pro	Difference	Comments
Moment capacity, M_ckd (kN·m)	591.0	591.0	none
Critical moment, M_cr (kN·m)	1,676	1,676.5	negligible

STAAD.Pro Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Europe\EC3 Singapore NA - Varying End Mom CMM8.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
Concentrated load with varying end moments: CMM 8
The value of C2 0.17 is specified

STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 03-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 EUROPEAN
1 TABLE ST HD320X127
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 2 PINNED
*2 FIXED BUT FX FZ MZ
LOAD 1 LOADTYPE Dead  TITLE DL
MEMBER LOAD
1 CON GY -4
JOINT LOAD
2 MZ 8
1 MZ -10
PERFORM ANALYSIS
PARAMETER 1
CODE EN 1993-1-1:2005
NA 7
CMM 8 ALL
C1 1.184 ALL
C2 0.17 ALL
C3 1 ALL
CMN 1 ALL
PY 275000 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.    3
 ALL UNITS ARE - KN   METE (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
       1 ST   HD320X127   (EUROPEAN SECTIONS)
                           PASS     EC-6.3.2 LTB       0.025         1
                        0.00            0.00         -14.00        2.50
 =======================================================================
   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        :    30820.004        9239.001
      Plastic modulus          :     2149.000         939.100
      Elastic modulus          :     1926.250         615.933
      Shear Area               :       81.998          51.728
      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 :  1.00          GM2 :  1.10
                                      z-axis          y-axis
      Slenderness ratio (KL/r) :         36.2           66.1
      Compression Capacity     :       4078.2         3045.5
      Tension Capacity         :       4435.8         4435.8
      Moment Capacity          :        591.0          258.3
      Reduced Moment Capacity  :        591.0          258.3
      Shear Capacity           :       1301.9          821.3
   BUCKLING CALCULATIONS (units - kN,m)
      Lateral Torsional Buckling Moment       MB =  564.6
      co-efficients C1 & K : C1 =1.184 K =1.0, Effective Length= 5.000
      Lateral Torsional Buckling Curve : Curve b
      Elastic Critical Moment for LTB,               Mcr   =  1676.5
      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 PLANE                                              -- PAGE NO.    4
   CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m):
    CLAUSE        RATIO  LOAD     FX       VY      VZ      MZ      MY   
   EC-6.2.5       0.024     1     0.0      1.6     0.0   -14.0     0.0
   EC-6.2.6-(Y)   0.003     1     0.0     -2.4     0.0   -13.0     0.0
   EC-6.3.2 LTB   0.025     1     0.0      1.6     0.0   -14.0     0.0
    Torsion has not been considered in the design.
                        _________________________
   ************** END OF TABULATED RESULT OF DESIGN **************