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
Steel grade S275
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
Critical Ratio
P / NbRd = 2,000 / 2,161 = 0.925
Results
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| Critical Ratio | 0.925 | 0.925 | none |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Europe\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
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
JOINT LOAD
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 Output
STAAD.PRO CODE CHECKING - EN 1993-1-1:2005 ******************************************** NATIONAL ANNEX - NOT USED 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 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 Squash Load : 3382.50 Axial force/Squash load : 0.591 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 CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m): CLAUSE RATIO LOAD FX VY VZ MZ MY EC-6.3.1.1 0.925 1 2000.0 0.0 0.0 0.0 0.0 Torsion has not been considered in the design. _________________________ ************** END OF TABULATED RESULT OF DESIGN **************