# V. EC3 Singapore NA - Channel Section with Conc Load

Calculate the bending capacity of a channel section beam under subject to a pair of concentrated load per the Singaporean NA to EC3

## Details

The section is a C15X50, grade S275 steel. The member is a 6 m span, simply supported beam is subject to two concentrated loads of 10 kN each at the 1/3 points (2 m from either support).

## 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 = 1.046 C2 = 0.42 C3 = 1.0 $π 2 E I y k L 2$ = 257,320 $k k w 2 I w I y$ = 28,852 $k L 2 G I T π 2 E I y$ = 315,300 C2Zg = 0.42×0.5×381 = 80.01 βf = $bc3+tcbc3+tc+bt3+tt=0.5$ (From SN030a-EN-EU) zj = 0.4×hs(2βf - 1) = 0 for βf ≥ 0.5 C3Zj = 0

Therefore,

## Results

Table 1.
Moment capacity, Mckd (kN·m) 308.7 308.7 none
Critical moment, Mcr (kN·m) 137.8 137.1 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Europe\EC3 Singapore NA-Channel Section with Conc Load.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 and C3 1
• Concentrated loads at 1/3 points supports: CMM 5
• The value of C2 0.42 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 6 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 AMERICAN
1 TABLE ST C15X50
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 2 PINNED
*2 FIXED BUT FX FZ MZ
1 CON GY -10 2
1 CON GY -10 4
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PARAMETER 1
CODE EN 1993-1-1:2005
NA 7
C2 0.42 ALL
C3 1 ALL
CMM 5 ALL
CMN 1 ALL
FU 295000 ALL
PY 275000 ALL
KC 0 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH


 STEEL DESIGN
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)
FX            MY             MZ       LOCATION
=======================================================================
1 ST   C15X50      (AISC SECTIONS)
PASS     EC-6.3.2 LTB       0.191         1
0.00            0.00         -20.00        2.00
=======================================================================
MATERIAL DATA
Modulus of elasticity    =  205 kN/mm2
Design Strength  (py)    =  275  N/mm2
SECTION PROPERTIES (units - cm)
Member Length =    600.00
Gross Area =   94.84          Net Area =   94.84
z-axis          y-axis
Moment of inertia        :    16815.750         457.855
Plastic modulus          :     1122.514         133.391
Elastic modulus          :      882.716          61.711
Shear Area               :       20.800          69.290
Radius of gyration       :       13.316           2.197
Effective Length         :      600.000         600.000
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) :         45.1          273.1
Compression Capacity     :       2170.6          227.2
Tension Capacity         :       2289.1         2289.1
Moment Capacity          :        308.7           36.7
Reduced Moment Capacity  :        308.7           36.7
Shear Capacity           :        330.2         1097.9
BUCKLING CALCULATIONS (units - kN,m)
Lateral Torsional Buckling Moment       MB =  104.5
co-efficients C1 & K : C1 =1.046 K =1.0, Effective Length= 6.000
Lateral Torsional Buckling Curve : Curve d
Elastic Critical Moment for LTB,               Mcr   =   137.1
Compression buckling curves:     z-z:  Curve c   y-y:  Curve c
Critical Load For Torsional Buckling,          NcrT  =  4512.3
Critical Load For Torsional-Flexural Buckling, NcrTF =  4286.4
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       0.065     1     0.0     10.0     0.0   -20.0     0.0
EC-6.2.6-(Y)   0.009     1     0.0     10.0     0.0     0.0     0.0
EC-6.3.2 LTB   0.191     1     0.0     10.0     0.0   -20.0     0.0
Torsion has not been considered in the design.
_________________________
************** END OF TABULATED RESULT OF DESIGN **************