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The column is free from initial stress. The weight of the column is neglected. The column is initially straight (no eccentricity of the axial load). Pin joints are friction-less (no moment constraint) and fixed ends are rigid (no rotation deflection). The cross-section of the column is uniform throughout its length.
The effective length is calculated from the actual length of the member considering the rotational and relative translational boundary conditions at the ends. Slenderness captures the influence on buckling of all the geometric aspects of the column, namely its length, area, and second moment of area.
where r = radius of gyration of column cross-section which is equal to the square root of (I/A), K = ratio of the longest half sine wave to the actual column length, E t = tangent modulus at the stress F cr, and KL = effective length (length of an equivalent hinged-hinged column). From Equation (2) it can be noted that the buckling strength of ...
The columns of A span the column space, but they may not form a basis if the column vectors are not linearly independent. Fortunately, elementary row operations do not affect the dependence relations between the column vectors. This makes it possible to use row reduction to find a basis for the column space. For example, consider the matrix
where L is the column length and N the number of theoretical plates. [5] The relation between plate number and peak width at the base is given by
It is the distance between the centre (the heart) of a column and the centre (the heart) of another column. By expressing a distance in c.t.c., one can measure ...
A special type of area density is called column density (also columnar mass density or simply column density), denoted ρ A or σ. It is the mass of substance per unit area integrated along a path; [ 1 ] It is obtained integrating volumetric density ρ {\displaystyle \rho } over a column: [ 2 ] σ = ∫ ρ d s . {\displaystyle \sigma =\int \rho ...
A chemist in the 1950s using column chromatography. The Erlenmeyer receptacles are on the floor. ... where L is the length of the column. [8]