Interactive Buckling of Cold-Formed Steel Sections Applied in Pallet Rack Upright Members D. Dubina, V. Ungureanu, A. Crisan Politehnica University of Timişoara
Peculiarities of cold-formed thin-walled sections Cold forming technologies modify the properties of base material and induces specific residual stresses Thin walled sections (class 4, usually) are : highly sensitive to local and sectional instability modes highly sensitive to geometrical imperfections characterized by interaction of local and overall buckling modes Conclusion : stability analysis of such members would need for a specific treatment, compared with conventional hot-rolled sections!
Simple Instabilities L Local Buckling D Distortional Buckling F Flexural Buckling T Torsional Buckling FT Flexural-Torsional buckling L D F T FT
Coupled Instabilities L Local Buckling D Distortional Buckling F Flexural Buckling T Torsional Buckling FT Flexural-Torsional buckling L + D F + L F+D FT+L FT+D
Erosion Concept N u =N cr y I: Weak interaction (WI), ψ.1 II: Moderate interaction (MI),.1 ψ.3 III: Strong interaction (SI),.3 ψ.5 IV: Very Strong interaction (VSI), ψ>.5 Thin walled members
Coupled Instabilities design methods EUROCODE3 (EN1993-1-1) Buckling curves Ayrton-Perry model a a b c d a.13.21.34.49.76 N b, Rd 1 2 A eff M1 A eff N cr f 2 y f y 1 2 c AISI AS/NZ46 Axial load P n is: P A F n c e n c.85 2 c c n y for 1.5, F.658 f.658 for 1.5, F f 2 c c n y f F y e A e is the effective area at F n F e minimum critical stress (F, T, FT)
Coupled Instabilities ECBL approach N=N/N pl 1 2 y Q a 1-y 1-.2 D Q D Results/numerical simulations Q D ND A f Q D y Sectional instability: N D =Q D M Coupled instability: N(y,Q D ) Q D y N(y,Q D )=Q D -y N EULER =1/ 2.2 QD -.1 QD QD QD +.1 QD = (Q. N pl /N cr ).5 1. Defining the sectional capacity 2. Determining the coupling point (M) 3. Definition of the coupling interval ( ± 1%) 4. Computation of coupling erosion (y D ) 5. Determination of a imperfection factor based on the design value of the erosion factor (y D )
Experimental Program EN 15512:29 Steel static storage systems - Adjustable pallet racking systems - Principles for structural design Annex A (normative) Testing A.1 Materials tests A.1.1 Tensile test A.1.2 Bend tests A.2 Tests on components and connections A.2.1 Stub column compression test A.2.2 Compression tests on uprights - Checks for the effects of distortional buckling A.2.3 Compression tests on uprights - Determination of buckling curves A.2.4 Bending tests on beam end connectors A.2.5 Looseness tests on beam end connectors A.2.6 Shear tests on beam end connectors and connector locks A.2.7 Tests on floor connections A.2.8 Tests for the shear stiffness of upright frames A.2.9 Bending tests on upright sections A.2.1 Bending tests on beams A.2.11 Tests on upright splices
Experimental Program EN15512:29 a. Stub column tests b. Upright buckling tests Additional: c. Distortional buckling tests d. Interactive buckling tests
Experimental Program buckling length Distortional buckling specimens LBA analysis PERFORATED t eq (Davies or experimental)
Experimental Program buckling length Interactive buckling tests ECBL Approach (Distortional + Flexural) N=N/N pl 1 Q D Sectional instability: N D =Q D M N EULER =1/ 2 Q D y N(y,Q D )=Q D -y.2 QD QD A f N cr y L cr, CUPLARE
Experimental Program RS125x3.2mm RS95x2.6mm f y =465.18 N/mm 2 f u =537.4 N/mm 2 E=22941 N/mm 2 f y =461.41 N/mm 2 f u =538.9 N/mm 2 E=27464 N/mm 2 A net /A brut =.86 A net /A brut =.76
STUB column test results RS125 RS95 18 specimens 6 brut section @ 51mm 12 net section @ 51mm 18 specimens 6 brut section @ 41mm 12 net section @ 41mm 437.16kN 39.75kN 336.85kN 273.79kN
UPRIGHT Test Results RS125 RS95 15 specimens 5 brut section @ 12mm 1 net section @ 12mm 15 specimens 5 brut section @ 12mm 1 net section @ 12mm 354.95kN 324.77kN 264.28kN 22.kN
Remark: The test for distortion according with EN15512 is realized for an upright section of a length equal with the length between two subsequent nodes. However, depending on the crosssection dimensions this length can be offend larger than distortional critical length and the obtained test result can be the one corresponding to the interaction distortionalglobal. Suggestion: For the consistency of the testing procedure compression and bending tests for specimens of critical distortional length would be necessary!
Distortional buckling results RS125 RS95 1 specimens 5 brut section @ 67mm 5 net section @ 71mm 6 specimens 3 brut section @ 59mm 3 net section @ 61mm 417,37kN 348,32kN 39,4kN 257,84kN
Interactive buckling results RS125 RS95 16 specimens 18 specimens 7 brut section 3 @ 211mm 3 @ 231mm 3 @ 251mm 9 brut section 3 @ 151mm 3 @ 161mm 3 @ 176mm 9 net section 3 @ 211 mm 3 @ 231 mm 3 @ 251 mm 32,29kN 269,71kN 9 net section @ 151mm @ 161mm @ 176mm 225,73kN 197,36kN
Calibration of a imperfection factor y i N N D D N D A f N y exp, i N D considered sectional strength N exp,i experimental failure force for specimen i N exp, i N exp, i A f y A cross-sectional area f y yield strength y m 1 n i1 y y 2 d d 2 d n y y N a 1 y d 1.2 i D N D y i erosion for specimen i y m mean value of erosion y d design value of erosion standard deviation a imperfection coefficient (calibrated value)
Axial Force [kn] Axial Force [kn] Experimental net sections 5 4 3 RS125N EN15512 ECBL N ECBL B TESTS 2 1 1 2 3 4 5 Length [mm] 3 RS95N EN15512 ECBL B 2 ECBL N TESTS 1 5 1 15 2 25 3 35 4 Length [mm]
Axial load [kn] Axial Load [kn] Axial Load [kn] Experimental net sections 5 4 3 2 RS125N TESTS Brut moment of inertia Net moment of inertia M11 1 1 2 3 4 4 5 Length [mm] 4 3 3 2 2 RS125N RS95N TESTS Brut moment of inertia Net moment of inertia M11 M11 1 1 1 2 3 4 5 1 Length 2 [mm] 3 4 Length [mm]
Axial load [kn] Axial Load [kn] Axial Load [kn] Experimental net sections 5 4 3 2 RS125N TESTS Brut moment of inertia Net moment of inertia M111 1 1 2 3 4 4 5 Length [mm] 4 3 3 2 2 RS125N RS95N TESTS Brut moment of inertia Net moment of inertia M111 M11 1 1 1 2 3 4 5 1 Length 2 [mm] 3 4 Length [mm]
Numerical simulations Sensitivity study Numerical model calibration Software: ABAQUS/CAE 6.7.1 Elements: S4R Mesh: 5x5mm End assemblies: RIGID BODY with PINNED NODES 2 steps analysis: 1. LBA > buckling modes 2. GMNIA > ultimate capable force
Numerical simulations Sensitivity study LBA => Profile N D,cr [kn] N pl [kn] Q D RS125N 37.48 483.16.767 RS95N 34.78 286.69 1.* + N=N/N pl 1 Q D Q D ND A f y Sectional instability: N D =Q D M N EULER =1/ 2 Q D y N(y,Q D )=Q D -y.2 QD
Numerical simulations Sensitivity study D+ distortional buckling mode scaled with ( t) D- distortional buckling mode scaled with (-t) F+ flexural buckling mode scaled with ( L/75) F- flexural buckling mode scaled with (-L/75) Ecc_Y load eccentricity in Y direction Ecc_Z load eccentricity in Z direction
Numerical simulations C PR D+ F+ D+ F+ Ecc_-2 RS125B RS125N RS95B RS95N y.387.395.49.54 a.259.273.587. 639 y.45.422.547.56 a.294.327.824.893 Small increase in y => significant increase in a Considering all imperfections => too conservative Loading eccentricity => great influence when coupled with initial bow imperfection (same sense)
Axial load [kn] Axial load [kn] Numerical simulations RS125 12 1 RS125B Cth (D+F) D FT F 8 Cth (D+FT) Squah Load ND,cr 6 Cpr (ND,CR+F) GMNIA TESTS 4 2 1 2 3 4 5 6 1 1 1 Length [mm] 12 1 RS125N Cth (D+F) D FT F 8 Squash Load ND,cr 6 Cth (D+FT) GMNIA TESTS 4 Cpr (ND,cr+F) 1 2 2 3 4 5 6 1 1 1 Length [mm]
Axial load [kn] Axial load [kn] Numerical simulations RS95 8 D 6 RS95B Cth (D+F) Cth (D+FT) FT F ND,cr Squash Load 4 Cpr (Npl+F) GMNIA TESTS 2 1 2 3 4 5 6 1 1 1 Length [mm] 8 D 6 RS95N Cth (D+F) FT F ND,cr 4 Cth (D+FT) Cpr (Npl+F) Squash Load GMNIA TESTS 2 1 2 3 4 5 6 1 1 1 Length [mm]
Axial Load [kn] Axial Load [kn] Numerical simulations buckling curves 5 4 3 2 RS125N TESTS Brut moment of inertia Net moment of inertia M11 1 1 2 3 4 5 Length [mm] 5 LBA > N cr,d 4 3 2 RS125N GMNIA > N U,D TESTS Brut moment of inertia Net moment of inertia M11 1 1 2 3 4 5 Length [mm]
Axial load [kn] Axial Load [kn] Axial load [kn] Axial Load [kn] Numerical simulations buckling curves 4 5 4 3 3 2 2 RS125N RS95N TESTS Brut moment of inertia Net moment of inertia M11 M11 1 1 1 2 3 4 5 Length [mm] 1 2 3 4 Length [mm] 4 5 LBA > N cr,d 4 3 3 2 2 GMNIA > N U,D RS125N RS95N TESTS Brut moment of inertia Net moment of inertia M11 M11 1 1 1 2 3 4 5 1 Length [mm] 2 3 4 Length [mm]
Concluding remarks The ECBL concept can be used to adapt the European buckling curves for the case of perforated cold formed members It is very important to correctly define: the sectional capacity the global buckling mode (F, T, FT) (the corresponding coupling length) Reduced number of experimental/numerical tests Experimental Short length specimens (sectional capacity) 3 tests Relevant tests for interactive buckling 3 x 3 tests
Concluding remarks The critical combination of imperfections can be determined based on ECBL approach The partial safety coefficient M1 can be properly determined applying Annex D of EN199 EN15512, even if is based on the brut section properties, is to conservative for usual lengths The effect of perforations can not be ignored for global calculations
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