# V. EC3 Singapore NA - I Section with UDL

Calculate the bending capacity of a beam using an I section subject to a uniformly distributed load per the Singaporean NA to EC3.

## Details

The section is a HD320X127, Grade S275 steel. The member is a 5 m, fixed-fixed span subject to a 10 kN/m uniform load.

## Validation

Moment capacity:

The critical moment is given by:

$M c r = C 1 π 2 E I ( k L ) 2 { ( k k w ) 2 I w I + ( k L ) 2 G I t π 2 E I + ( C 2 Z g ) 2 − C 2 Z g }$
where
 C1 = 0.712 C2 = 0.652 k = 0.5 $π 2 E I y k L 2$ = 29,909,000 $k k w 2 I w I y$ = 5,599 $k L 2 G I t π 2 E I y$ = 5,934 C2Zg = 0.652×160 = 104.3

Therefore, Mcr = 966.7 kN·m

From the Singaporean NA, λLT, 0 = 0.4, β = 0.75

So, $λ L T = w y f y M c r = 2,149 × ( 10 ) 3 × 275 966.7 × ( 10 ) 6 = 0.782$

H/b = 320/300 = 1.067 < 2. So, from Table 6.5 of Eurocode 3, αLT = 0.34.

From Cl. 6.3.2.3 of Eurocode3:

ФLT = 0.5[1+αLTLT- λLT, 0) + β× λLT2] = 0.5[1 + 0.34×(0.782 - 0.2) +1 × 0.7822] = 0.794

So, $χ L T = Ф L T + Ф L T 2 - β λ L T 2 - 1 = 0.827$

So, $k c ⁢ = 1 / C 1 = 1 / 0.712 = 1.182 > 1$ but this value cannot be used, so from Table 6.6 of the Eurocode 3, kc = 0.9

Modification factor: $f = 1 - 0.5 1 - k c 1 - 2 λ L T - 0.8 2 = 1 - 0.5 1 - 0.9 1 - 2 0.782 - 0.8 2 = 0.950$

$χ L T , m o d = χ L T f = 0.871 < 1 λ L T 2 = 1.635$, OK

If Cl. 6.3.2.2 is used to determine χLT:

H/b = 320/300 = 1.067 < 2. So, from Table 6.3 of Eurocode 3, αLT = 0.21.

 ФLT = 0.5[1+αLT (λLT- 0.2) + λLT2] = 0.5[1+0.21×(0.782 - 0.2) +1×0.7822] = 0.867$χ L T = Ф L T + Ф L T 2 - λ L T 2 - 1 = 0.806$ (Cl. 6.3.2.2)

## Results

Table 1. Comparison of results for EC3 Singaporean NA - I Section with UDL
Moment capacity, Mckd (kN·m) 591.0 591.0 none
Critical moment, Mcr (kN·m) 966.7 967.3 negligible
Bending capacity, MB (kN·m) 514.4 514.5 negligible
Bending capacity, MB (kN·m) 476.3 476.3 none

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

The following design parameters are used:

• The Singaporean NA is specified using NA 7
• Fully fixed span: CMN 0.5
• Uniformly distributed load w/ fixed-fixed supports: CMM 2
• The parameter KC instructs the program to calculate the value of kc
• A second design parameter set is used with MTH 1 to use Cl 6.3.2.2 to determine ФLT
Note: The previously set parameters are still used as they are not specified again with a different value, which is the default behavior in STAAD.Pro batch design.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 20-June-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 FIXED
1 UNI GY -10
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PARAMETER 1
CODE EN 1993-1-1:2005
NA 7
CMM 2 ALL
CMN 0.5 ALL
KC 0 ALL
PY 275000 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE EN 1993-1-1:2005
NA 7
CMM 2 ALL
CMN 0.5 ALL
KC 0 ALL
MTH 1 ALL
PY 275000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH


                         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 SPACE                                              -- PAGE NO.    4
ALL UNITS ARE - KN   METE (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
*** WARNING:CMN PARAM INVALID FOR NATIONAL ANNEX
NATIONAL ANNEX ONLY DEALS WITH END RESTRAINT FACTORS OF K = KW = 1.
HENCE WILL USE ANNEX F FROM DD ENV 1993-1-1:1992
1 ST   HD320X127   (EUROPEAN SECTIONS)
PASS     EC-6.3.2 LTB       0.040         1
0.00            0.00          20.83        0.00
=======================================================================
MATERIAL DATA
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
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 =  514.5
co-efficients C1 & K : C1 =0.712 K =0.5, Effective Length= 5.000
Lateral Torsional Buckling Curve : Curve b
Elastic Critical Moment for LTB,               Mcr   =   967.3
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 SPACE                                              -- PAGE NO.    5
CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m):
CLAUSE        RATIO  LOAD     FX       VY      VZ      MZ      MY
EC-6.2.5       0.035     1     0.0     25.0     0.0    20.8     0.0
EC-6.2.6-(Y)   0.030     1     0.0     25.0     0.0    20.8     0.0
EC-6.3.2 LTB   0.040     1     0.0     25.0     0.0    20.8     0.0
Torsion has not been considered in the design.
_________________________
************** END OF TABULATED RESULT OF DESIGN **************
39. PARAMETER 2
40. CODE EN 1993-1-1:2005
41. NA 7
42. CMM 2 ALL
43. CMN 0.5 ALL
44. KC 0 ALL
45. MTH 1 ALL
46. PY 275000 ALL
47. TRACK 2 ALL
48. CHECK CODE ALL
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 SPACE                                              -- PAGE NO.    6
ALL UNITS ARE - KN   METE (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
*** WARNING:CMN PARAM INVALID FOR NATIONAL ANNEX
NATIONAL ANNEX ONLY DEALS WITH END RESTRAINT FACTORS OF K = KW = 1.
HENCE WILL USE ANNEX F FROM DD ENV 1993-1-1:1992
1 ST   HD320X127   (EUROPEAN SECTIONS)
PASS     EC-6.3.2 LTB       0.044         1
0.00            0.00          20.83        0.00
=======================================================================
MATERIAL DATA
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
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 =  476.3
co-efficients C1 & K : C1 =0.712 K =0.5, Effective Length= 5.000
Lateral Torsional Buckling Curve : Curve a
Elastic Critical Moment for LTB,               Mcr   =   967.3
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 SPACE                                              -- PAGE NO.    7
CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m):
CLAUSE        RATIO  LOAD     FX       VY      VZ      MZ      MY
EC-6.2.5       0.035     1     0.0     25.0     0.0    20.8     0.0
EC-6.2.6-(Y)   0.030     1     0.0     25.0     0.0    20.8     0.0
EC-6.3.2 LTB   0.044     1     0.0     25.0     0.0    20.8     0.0
Torsion has not been considered in the design.
_________________________
************** END OF TABULATED RESULT OF DESIGN **************