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# lab 8 - Year 2010 Month 11 Day 15 Buckling Column Test of a...

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Year 2010 Month 11 Day 15 Buckling Test of a Column Aerospace Engineering Laboratory II Name : Martin Suhartono Student ID : 20106182

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1. Objective To understand the buckling phenomenon on a simple one dimensional column as well as the factors that influences the structural stability of a column To use a Southwell plot in identifying the eccentricity, initial defects as well as the critical load in buckling 2. Introduction Buckling is one the many failure modes in engineering. It is specifically characterized by the sudden failure of a structure subjected to a high compressive stress, which is usually lower than the ultimate compressive stress of the material. Additionally, buckling is also regarded as a form of elastic instability. Closely related to buckling is the slenderness ratio. It is generally the ratio between the effective length of a column to the radius of gyration of the cross sectional area of the column. It basically determines the classification of a column and its corresponding critical buckling load. In a nutshell, the critical load is inversely proportional with slenderness ratio squared. The critical buckling load, P cr , may be approximated using Euler’s formula which states: Where E is the modulus of elasticity, I is the area moment of inertia, K is the column effective length factor and L is the unsupported length of the column. This formula then suggests several characteristics of buckling phenomenon. Firstly, elasticity is the essential factor in determining the buckling critical load for a particular material instead of the ultimate compressive stress. Moreover, the critical buckling load is directly proportional with the second moment of area of the structure. This means that a structure with its material distributed as far as possible from its principle axes of the cross section will possess higher critical buckling load. Lastly, it is stated that boundary conditions have significant effects in deciding the critical load of a slender column, because it governs the mode of bending and the distance between inflection points on a deflected column. For our experiment, K will be 0.5 as the column is fixed at both ends. In our experiment, we will observe Euler’s buckling (also called bifurcation buckling). This type of buckling does not exhibit the sudden collapse of the structure when it is loaded slightly above the critical load. Instead, the structure will deform to a buckled configuration that shapes like a bow. The column will also be hinged at both ends and thus, the Euler formula may be expressed as: Where (l/r) is the slenderness ratio.
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