Higher Certificate in Civil Engineering
: Structural Analysis I - Laboratory Report
: HKIVE (Tsing Yi), Room CL02
Date & Time
: 15 October 2001, 19:00 to 20:15
Experiment No. 1
: Column Buckling Test
1. To study the effect of support conditions on the load, carrying capacity of a slender column. 2. To compare the experimental buckling loads Pcr of test specimens with those predicted by the Euler equation.
1. SM 105 strut apparatus (Issuing Voucher: 0203141 & Inventory Ledger: CN/s/01/10), 2. Aluminum bar specimen (20 x 3 x 600 mm approximate),
3. Measuring ruler,
4. Venier caliper.
The factors affecting the column’s load – carrying capacity are the connection between the slenderness of the column and its tendency to buckle, the influence of the ‘fixity’ of the ends of the column, and the shape of its section on that slenderness. When the line of action of the resultant load is coincident with the centre of gravity axis of the column (Fig. 1a), the column is said to be axially loaded and the stress produced in the material is said to be a direct compressive stress. This stress is uniform over the cross-section of the column. The term concentric loading is sometimes used instead of axial loading. When the load is not axial, it is said to be eccentric (i.e. off-centre) and bending stress is induced in the column as well as a direct compressive stress (Fig. 1b). It has the effect of increasing the compression on the area to the right and decreasing the compression on the portion to the left. For design factors, the maximum axial load a column can be allowed to support depends on the material of which the column is made and the slenderness of the column. The slenderness involves not only the height of the column, but also the size and shape of its cross-section and the manner in which the two ends of the column are supported or fixed. A very short column will fail due to crushing of the material, but long columns are likely to fail by ‘buckling’, the failing load being much less than that which would cause failure in a short column of identical cross-section dimensions.
A long thin homogeneous column, axially loaded, suffers no deflection as the load is gradually applied until a critical load (the collapsing or buckling load P) is reached. At this load, instability occurs and the column buckles into a curve. The curve of Fig. 2 is not the arc of a circle, and Euler found (with the aid of the calculus) that the buckling load P gets less as the slenderness of the column increases. Euler’s formula is not used for design, since (except for very long columns) it gives a value of the collapsing load which is much higher than the actual collapsing load of practical columns, but it still forms part of modern column formulae. The values of permissible compressive stresses for struts are the product of the grade stress and modification factors appropriate to given conditions of services. It should be noted that the slenderness ratio the length of the column was qualified by the term ‘effective’. For the purpose of calculating the slenderness ratio of columns, an effective length should be assumed. This effective length can be defined as that length of the column, which is subject to buckling. The reason why the effective length of a column may be less or greater than the actual length in a building or structure is as follows. The safe compressive stress for a column depends not only on actual length and cross-sectional dimensions of the column but also on the manner in which the ends of the column are restrained or fixed. The Table A has been derived for one conditions of end fixing (both ends pinned or hinged).
Effective length of column
Type of ‘fixity’
Effective length of column
BS 5950, BS 5268
1) Effectively held in position and restrained in direction at both ends. 0.7L
2) Effectively held in position at...
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