Belgian National Annex Calculation as per EC3

• Introduction:

The following is a validation problem for a detailed calculation of the additional clauses for Belgian National Annex. (Belgian NA document: “NBN EN 1993-1-1:2005”)

The Belgian National Annex implementation is a part of the Eurocode 3 design code (EN 1993-1-1:2005) in the Steel design module of STAAD.Pro.

To invoke and use the Belgian National Annex, the user needs to set the value of the “NA” parameter to ‘8’.

• Validation Problem:

A European I section cantilever beam (HD320X127, S275 grade steel) , 5 m has been subjected to a concentrated point Load of 25 KN (FY) and concentrated moments 5 KN-m (MX) and 10 KN-m (MZ) at the free end.

 Outputs: MA= 10 KN-m, MB= 10 KN-m, SFA= 0 KN, SFB= 0 KN

• Text Input Information:

The following is the text input information of the STAAD model:

STAAD SPACE

START JOB INFORMATION

ENGINEER DATE 21-Feb-14

END JOB INFORMATION

INPUT WIDTH 79

UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 5 0;

MEMBER INCIDENCES
1 1 2;

MEMBER PROPERTY EUROPEAN
1 TABLE ST HD320X127

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
CONSTANTS
MATERIAL STEEL ALL

SUPPORTS
1 FIXED

LOAD 1 LOADTYPE None TITLE LOAD CASE 1
JOINT LOAD
2 FY -25 MX 5 MZ 10
PERFORM ANALYSIS

PARAMETER 1
CODE EN 1993-1-1:2005
NA 8 ALL
CMM 2 ALL
C2 1.554 ALL
FU 295000 ALL
PY 275000 ALL
*SGR 1 ALL
CMN 0.7 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH

• Manual Calculation:

We get: D= 320 mm, B= 300 mm, Tf= 20.5 mm, Tw= 11.5 mm, Iz= 30820 cm⁴, Iy= 9239 cm⁴,

 Zz= 1926.5 cm³, Zy= 615.93 cm³, J= 225.1 cm⁴, H= 2.069*10^12 mm⁶

Moment Capacity, M_ckd = W_ply*f_y/GM0 = 2149*1000*275/ (1*10^6) = 590.975 KN-m

STAAD.Pro value is 591 KN-m[OK]

Here, CMM=2.0, CMN=0.7

So, C1 = 2.578, C2 = 1.554

Π²*E*Iy/ (kL)² = 7477192.555

(k/kw)² * (Iw/Iy) = 22394.19851

(kL) ² *G*It/( Π²*E*Iy) = 23736.5416

C2Zg = 1.554*160 =248.64

So, Mcr = 1540.6 KN-m

STAAD.Pro value is 1541.5 KN-m[OK]

From Belgian NA, λ_{LT, 0} = 0.4, β = 0.75

So, λ_LT = √ (w_y*f_y/M_cr) = √ (2149*10^3*275/1540600000) = 0.619355

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

From Cl. 6.3.2.3 of Eurocode3, we get:

Ф_LT = 0.5[1+α_LT (λ_LT- λ_{LT, 0}) + β* λ_LT²]

        = 0.5*[1+0.34*(0.619355-0.4) +0.75*0.619355²] = 0.681141

So, χ_LT = [Ф_LT+ √ (Ф_LT²- β* λ_LT²)]^-1 = 0.908294

So, M_B = χ_LT*w_y*f_y/GM1 = 0.908294*2149000*275/(1*10^6)

= 536.77 KN-m

STAAD.Pro value is 536.8 KN-m [OK]

N_Ed = 25 KN,                                                                      N_Rk = A*f_y = 4435.75 KN

My­_Ed = 5 KN-m,               Mz_Ed = 10 KN-m,             My_Rk = 258.3 KN-m

Determination of χ_y:

h/b = 1.067 < 2 & t_f = 20.5 mm < 100 mm

So, for y-y axis, we will use curve ‘c’. Hence, α = 0.49 [Table 6.2, EC3]

So, ф = 0.5[1+α (λ-0.2) +λ²)] = 0.9363

Determination of χ_z:

h/b = 1.067 < 2 & t_f = 20.5 mm < 100 mm

So, for z-z axis, we will use curve ‘c’. Hence, α = 0.34 [Table 6.2, EC3]

So, ф = 0.5[1+α (λ-0.2) +λ²)] = 0.6266

Compression Capacity = χ_y*N_Rk = 0.68087*4435.75 =3020.169 KN

Compression Ratio = 25/3020.169 = 0.00828

STAAD.Pro value for compression ratio is 0.008 [OK]

Critical Axial Loads for Flexural and Flexural Torsional Buckling:

From NCCI document SN001a-EN-FU:

Here, y₀ = z₀ = 0

i_y = 75.68 mm, i_z = 138.23 mm

So, i₀² = 75.68² + 138.23² = 24834.995

Interaction Check:

From Annex A, Table A.1 of EC3, we get the auxiliary terms:

χ_LT = 0.908294

 Wz = w_plz/w_elz = 2149/1926 = 1.1158

Wy = w_ply/w_ely = 939/615.933 = 1.525 > 1.5, so, w_y = 1.5

 CMM = 2.0, ψ=1.0

Determination of λ₀:

C1=1, C2=0

Mcr = 1605.96 KN