# V. EC3 - Pinned column using non-slender UKC section

Verify the design of a pinned column per the EC3 2005 design code.

## Details

The column is 8 m with pinned ends. The member is a 305 x 305 x 97 UKC shape with S275 grade steel. The axial load is 2,000 kN and Lcry/L =0.7.

Partial safety factors:

ΓM0 = 1.0

ΓM1 = 1.0

## Validation

Effective Length Calculations

Lcry = 0.7 × 8,000 = 5,600 mm

Lcrz = 1.0 × 8,000 = 8,000 mm

Yield Strength

The maximum thickness = 15.4 mm < 40 mm; therefore fy = 275 N/mm2 [EN 1993-1-1:2005 Table 3.1]

Section Classification

 ε = √(235/fy) = 0.92 [EN 1993-1-1:2005 Table 5.2]

Outstanding flange (flange under uniform compression):

c = (b-tw-2r)/2 = (305.3 – 9.9 – 2 x 15.2)/2 = 132.3 mm

'

c /tf = 132.3 /15.4 = 8.6 < 10 ε

Class 2 element [EN 1993-1-1:2005 Table 5.2 Sheet 2]

Internal compression part (web in bending):

c =h-2tf-2r = 307.9-2 x 15.4 – 2 x 15.2 = 246.7 mm

c / tw = 246.7/ 9.9 = 24.92 < 33 ε

Class 1 element [EN 1993-1-1:2005 Table 5.2 Sheet 1]

Therefore, section is a Class 2 section.

Axial Resistance

Design axial resistance:

 Nc, Rd = A × fy/Γm0 = 123.4 cm2(102)×275 kN/mm2 / 1.0 ×10-3 = 2,283 kN > 2,000 kN [EN 1993-1-1:2005 Cl. 6.2.4]

Lateral Buckling

Determine the elastic critical moment, Mcr:

 [EN 1993-1-1:2005 Cl. 6.3.1.1]

Ncr = (π2×E×Iy)/Ly2 = [π2 x 205,000 x 7,308(104] /(56,002 x 1,000) = 4715 kN

λ = (A × fy /Ncr) 0.5 = (123×102 × 275 / 4,715×103)0.5 = 0.847

h/b = 307.9 /305.3 = 1 < 1.2 & tf < 100 mm

 α = 0.49 [EN 1993-1-1:2005 Table 6.3]

 ϕ = 0.5 [1 + α(λ – 0.2) + λ2] [EN 1993-1-1:2005 Cl. 6.3.2.3]

ϕ = 0.5 [1 + 0.49(0.847 – 0.2) +0.8472] = 1.017

$χ = 1 ∅ + ∅ 2 - λ 2 = 1 1.017 + 1.017 2 - 0.847 2 =0.639<1.0$

Critical Ratio

P / NbRd = 2,000 / 2,161 = 0.925

## Results

Table 1. Comparison of results
Critical Ratio 0.925 0.925 none

Tip: You can copy and paste this content directly into a .std file to run in STAAD.Pro.

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Europe\EC3\EC3 - Pinned column using non-slender UKC section.STD is typically installed with the program.

STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 04-Jan-08
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 8 0;
MEMBER INCIDENCES
1 2 1;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
END DEFINE MATERIAL
MEMBER PROPERTY BRITISH
1 TABLE ST UC305X305X97
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FY MX MY MZ
2 FY -2000
PERFORM ANALYSIS
PARAMETER 1
CODE EN 1993-1-1:2005
SGR 1 ALL
LY 5.6 ALL
GM1 1 ALL
GM0 1 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH


                         STAAD.PRO CODE CHECKING - EN 1993-1-1:2005
********************************************
NATIONAL ANNEX - NOT USED
PROGRAM CODE REVISION V1.13 BS_EC3_2005/1
STAAD PLANE                                              -- PAGE NO.    3
ALL UNITS ARE - KN   METE (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
1 ST  UC305X305X97 (BRITISH SECTIONS)
PASS     EC-6.3.1.1         0.925         1
2000.00 C          0.00           0.00        0.00
=======================================================================
MATERIAL DATA
Grade of steel           =  S 275
Modulus of elasticity    =  205 kN/mm2
Design Strength  (py)    =  275  N/mm2
SECTION PROPERTIES (units - cm)
Member Length =    800.00
Gross Area =  123.00          Net Area =  123.00
z-axis          y-axis
Moment of inertia        :    22200.002        7310.001
Plastic modulus          :     1590.000         726.000
Elastic modulus          :     1442.027         478.873
Shear Area               :       84.627          35.174
Radius of gyration       :       13.435           7.709
Effective Length         :      800.000         560.000
DESIGN DATA (units - kN,m)   EUROCODE NO.3 /2005
Section Class            :   CLASS 2
GM0 :  1.00          GM1 :  1.00          GM2 :  1.25
z-axis          y-axis
Slenderness ratio (KL/r) :         59.5           72.6
Compression Capacity     :       2677.4         2161.6
Tension Capacity         :       3382.5         3382.5
Moment Capacity          :        437.3          199.7
Reduced Moment Capacity  :        202.6          156.4
Shear Capacity           :       1343.6          558.5
BUCKLING CALCULATIONS (units - kN,m)
Lateral Torsional Buckling Moment       MB =  307.5
co-efficients C1 & K : C1 =1.132 K =1.0, Effective Length= 8.000
Lateral Torsional Buckling Curve : CURVE b
Elastic Critical Moment for LTB,               Mcr   =   442.5
Compression buckling curves:     z-z:  Curve b   y-y:  Curve c
Critical Load For Torsional Buckling,          NcrT  =  5058.6
Critical Load For Torsional-Flexural Buckling, NcrTF =  5058.6
STAAD PLANE                                              -- PAGE NO.    4
ALL UNITS ARE - KN   METE (UNLESS OTHERWISE Noted)