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This formula was derived in 1744 by the Swiss mathematician Leonhard Euler. [2] The column will remain straight for loads less than the critical load. The critical load is the greatest load that will not cause lateral deflection (buckling). For loads greater than the critical load, the column will deflect laterally.
Very hard steel (e.g. chisels, quality knife blades): HRC 55–66 (Hardened High Speed Carbon and Tool Steels such as M2, W2, O1, CPM-M4, and D2, as well as many of the newer powder metallurgy Stainless Steels such as CPM-S30V, CPM-154, ZDP-189. There are alloys that hold a HRC upwards 68-70, such as the Hitachi developed HAP72.
ISO 18265: "Metallic materials — Conversion of hardness values" (2013) ASTM E140-12B(2019)e1: "Standard Hardness Conversion Tables for Metals Relationship Among Brinell Hardness, Vickers Hardness, Rockwell Hardness, Superficial Hardness, Knoop Hardness, Scleroscope Hardness, and Leeb Hardness" (2019)
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.
It is also known as the stiffness to weight ratio or specific stiffness. High specific modulus materials find wide application in aerospace applications where minimum structural weight is required. The dimensional analysis yields units of distance squared per time squared.
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It is also known as the strength-to-weight ratio or strength/weight ratio or strength-to-mass ratio. In fiber or textile applications, tenacity is the usual measure of specific strength. The SI unit for specific strength is Pa ⋅ m 3 / kg , or N ⋅m/kg, which is dimensionally equivalent to m 2 /s 2 , though the latter form is rarely used.
The deflection must be considered for the purpose of the structure. When designing a steel frame to hold a glazed panel, one allows only minimal deflection to prevent fracture of the glass. The deflected shape of a beam can be represented by the moment diagram, integrated (twice, rotated and translated to enforce support conditions).