NCCI: Buckling lengths of columns: rigorous approachNCCI: Buckling lengths of columns: rigorous approach SN008a-EN-EU NCCI: Buckling lengths of columns: rigorous approach This NCCI gives information concerning the calculation of the buckling length for columns, to be used for the buckling verification (slenderness approach). Simple aids (e.g. diagrams, tables) are presented. Contents 1. 2. Basis Columns in building frames 2 2 Created on Thursday, January 15, 2009 This material is copyright - all rights reserved. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement Page 1 An equivalent buckling length may also be used to relate the critical load of a non-uniform member to that of a uniform member under similar conditions of loading and restraint.all rights reserved. 2. January 15. Basis The buckling length Lcr of a compression member is the length of an otherwise similar member with “pinned ends” (ends restrained against lateral movement but free to rotate in the plane of buckling) which has the same elastic critical buckling load. Pinned Fixed Fixed Pinned Figure 2. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement Columns in building frames The buckling length Lcr of a column in a non-sway mode may be obtained from Figure 2. Created on Thursday.1. the theoretical buckling length for elastic critical buckling may conservatively be adopted. 2009 This material is copyright .1 Buckling length ratio Lcr / L for a column in a non-sway mode Page 2 . An equivalent buckling length may be used to relate the critical load of a member subject to non-uniform loading to that of an otherwise similar member subject to uniform loading.NCCI: Buckling lengths of columns: rigorous approach NCCI: Buckling lengths of columns: rigorous approach SN008a-EN-EU 1. In the absence of more accurate information. 2: a) non-sway mode (Figure 2.14(η1 + η 2 ) + 0.8(η1 + η 2 ) + 0.1) Lcr 1 − 0. Pinned Created on Thursday.2) (2.2 Buckling length ratio Lcr / L for a column in a sway mode The following empirical expressions may be used as conservative approximations instead of reading values from Figure 2.055(η1 + η 2 ) L b) sway mode (Figure 2.1 and Figure 2.6η1η 2 (2.NCCI: Buckling lengths of columns: rigorous approach NCCI: Buckling lengths of columns: rigorous approach SN008a-EN-EU The buckling length Lcr of a column in a sway mode may be obtained from Figure 2.2) Page 3 .2(η1 + η 2 ) − 0. 2009 This material is copyright .5 + 0.12η1η 2 = L 1 − 0.all rights reserved.1) Lcr 2 = 0. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement Fixed Fixed Pinned Figure 2.2. January 15. 3 the distribution factors η1 and η2 are obtained from: η1 = Kc K c + K 11 + K 12 (2.4 and obtaining the distribution factors η1 and η2 from: η1 = η2 = where K c + K1 K c + K1 + K11 + K 12 Kc + K2 K c + K 2 + K 21 + K 22 (2. 2009 This material is copyright .all rights reserved. Page 4 .3 Distribution factors for columns These models may be adapted to the design of continuous column.5) (2.NCCI: Buckling lengths of columns: rigorous approach NCCI: Buckling lengths of columns: rigorous approach SN008a-EN-EU For the theoretical models shown in Figure 2. In the general case where (N/Ncr) varies. by assuming that each length of column is loaded to the same value ratio (N/Ncr). For each length of a continuous column the assumption made above may be introduced by using the model shown in Figure 2. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement (a) Non-sway mode (b) Sway mode Figure 2. January 15.3) η2 = where and Kc Kc K c + K 21 + K 22 is the column stiffness coefficient I/L is the effective beam stiffness coefficient (2. this leads to a conservative value of Lcr/L for the most critical length of column.4) Kij Created on Thursday.6) K1 and K2 are the stiffness coefficients for the adjacent lengths of column. 4 Distribution factors for continuous column Where the beams are not subject to significant axial forces.NCCI: Buckling lengths of columns: rigorous approach NCCI: Buckling lengths of columns: rigorous approach SN008a-EN-EU Created on Thursday. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement Figure 2.75 1.1.5 I L I L ⎛ θ ⎞I ⎜1 + 0.1 Effective stiffness coefficient for a beam Effective beam stiffness coefficient K (provided that beam remains elastic) Conditions of rotational restraint at far end of beam Fixed at far end 1.5 0. provided that they remain elastic under the design moments. 2009 This material is copyright .0 I L I L Pinned at far end Rotation as at near end (double curvature) Rotation equal and opposite to that at near end (single curvature) General case Rotation θa at near end and θb at far end 0. their effective stiffness coefficients may be determined by reference to Table 2.all rights reserved. January 15. Table 2.5 b ⎟ ⎜ θa ⎟ L ⎝ ⎠ Page 5 . their effective stiffness coefficients should be adjusted accordingly.5 I L I L I L Other beams with direct loads 0.all rights reserved.NCCI: Buckling lengths of columns: rigorous approach NCCI: Buckling lengths of columns: rigorous approach SN008a-EN-EU For building frames with concrete floor slabs. 2009 This material is copyright .0 1. Stability functions may be used. the increased stiffness coefficient due to axial tension may be neglected and the effects of axial compression (when N/NE > 0. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement Where. its effective stiffness coefficient should be reduced accordingly. provided that the frame is of regular layout and the loading is uniform. Page 6 . the design moment in any of the beams exceeds Wel fy/γM0. Table 2.4 ⎜ NE ⎝ Where NE = ⎞ ⎟ ⎟ ⎠ π 2 EI L2 or by using the conservative approximations given in Table 2.0 1.5 Beams with end moments only I L Created on Thursday. as a conservative assumption the beam may be assumed to be pinned at the point or points concerned. Where a beam has semi-rigid joints.3.1) may be allowed for by multiplying the second moment of area of the beams I by the factor ⎛ N ⎜1 − 0. As a simple alternative. it is normally sufficiently accurate to assume that the effective stiffness coefficients of the beams are as shown in Table 2.2.75 0. Where the beams are subject to significant axial forces.0 I L I L 1. January 15. for the same load case.2 Effective stiffness coefficient for a beam in a building frame with concrete floor slabs Non-sway mode Sway mode Loading conditions for the beam Beams directly supporting concrete floor slabs 1. January 15.all rights reserved.NCCI: Buckling lengths of columns: rigorous approach NCCI: Buckling lengths of columns: rigorous approach SN008a-EN-EU Table 2.0 ⎜ L⎝ NE ⎟ ⎠ Rotation as at near end (double curvature) Rotation equal and opposite to that at near end (single curvature) Created on Thursday.75 ⎜1 − 1.0 ⎜1 − 0. 2009 This material is copyright .3 Approximate formulae for reduced beam stiffness coefficients due to axial compression Effective beam stiffness coefficient K (provided that beam remains elastic) Conditions of rotational restraint at far end of beam Fixed I⎛ N 1.5 ⎜1 − 0.5 ⎜1 − 1.2 ⎟ ⎜ L⎝ NE ⎟ ⎠ I⎛ N ⎞ ⎟ 0. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement Page 7 .0 ⎜ L⎝ NE ⎟ ⎠ I⎛ N ⎞ 1.4 ⎜ L⎝ NE ⎞ ⎟ ⎟ ⎠ Pinned I⎛ N ⎞ ⎟ 0. UK 2. 2009 This material is copyright .05 15/7/05 Matthias Oppe Christian Müller D C Iles G W Owens A bureau A Olsson C Müller J Chica G W Owens SCI CTICM SBI RWTH Labein SCI 30/6/05 30/6/05 30/6/05 30/6/05 30/6/05 08/6/06 3. France Created on Thursday. Sweden 4.06. Spain Resource approved by Technical Coordinator TRANSLATED DOCUMENT This Translation made and checked by: Translated resource approved by: Page 8 . Germany 5.all rights reserved. January 15. Use of this document is subject to the terms and conditions of the Access Steel Licence Agreement NCCI: Buckling lengths of columns: rigorous approach EN 1993-1-1 Company RWTH RWTH SCI Date 06.NCCI: Buckling lengths of columns: rigorous approach NCCI: Buckling lengths of columns: rigorous approach SN008a-EN-EU Quality Record RESOURCE TITLE Reference(s) ORIGINAL DOCUMENT Name Created by Technical content checked by Editorial content checked by Technical content endorsed by the following STEEL Partners: 1.05 10.06.
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