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The slenderness ratio is an indicator of the specimen's resistance to bending and buckling, due to its length and cross section. If the slenderness ratio is less than the critical slenderness ratio, the column is considered to be a short column. In these cases, the Johnson parabola is more applicable than the Euler formula. [5]
Fig. 1: Critical stress vs slenderness ratio for steel, for E = 200 GPa, yield strength = 240 MPa. Euler's critical load or Euler's buckling load is the compressive load at which a slender column will suddenly bend or buckle. It is given by the formula: [1] = where
In architecture, the slenderness ratio, or simply slenderness, is an aspect ratio, the quotient between the height and the width of a building. In structural engineering , slenderness is used to calculate the propensity of a column to buckle .
The Perry–Robertson formula is a mathematical formula which is able to produce a good approximation of buckling loads in long slender columns or struts, and is the basis for the buckling formulation adopted in EN 1993. The formula in question can be expressed in the following form:
A short steel column is one whose slenderness ratio does not exceed 50; an intermediate length steel column has a slenderness ratio ranging from about 50 to 200, and its behavior is dominated by the strength limit of the material, while a long steel column may be assumed to have a slenderness ratio greater than 200 and its behavior is dominated ...
Pencil towers became one of the most typical building types in Hong Kong, beside tong lau and cruciform apartments. [9] Overall, buildings with a slenderness ratio of up to 18:1 have dominated the Mid-Levels residential district, making Hong Kong the "world capital" of pencil-thin towers. In the 21st century Hong Kong pencil tower developments ...
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
For a water-filled glass tube in air at sea level: γ = 0.0728 J/m 2 at 20 °C; θ = 20° (0.35 rad) ρ = 1000 kg/m 3; g = 9.8 m/s 2; and so the height of the water column is given by: . Thus for a 2 mm wide (1 mm radius) tube, the water would rise 14 mm.