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  2. Euler's critical load - Wikipedia

    en.wikipedia.org/wiki/Euler's_critical_load

    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.

  3. Johnson's parabolic formula - Wikipedia

    en.wikipedia.org/wiki/Johnson's_parabolic_formula

    In structural engineering, Johnson's parabolic formula is an empirically based equation for calculating the critical buckling stress of a column. The formula is based on experimental results by J. B. Johnson from around 1900 as an alternative to Euler's critical load formula under low slenderness ratio (the ratio of radius of gyration to ...

  4. Cylinder stress - Wikipedia

    en.wikipedia.org/wiki/Cylinder_stress

    For the thin-walled assumption to be valid, the vessel must have a wall thickness of no more than about one-tenth (often cited as Diameter / t > 20) of its radius. [4] This allows for treating the wall as a surface, and subsequently using the Young–Laplace equation for estimating the hoop stress created by an internal pressure on a thin-walled cylindrical pressure vessel:

  5. Buckling - Wikipedia

    en.wikipedia.org/wiki/Buckling

    This results in a non-linear behaviour in the load carrying behaviour of these details. The ratio of the actual load to the load at which buckling occurs is known as the buckling ratio of a sheet. [1] High buckling ratios may lead to excessive wrinkling of the sheets which may then fail through yielding of the wrinkles. Although they may buckle ...

  6. Perry–Robertson formula - Wikipedia

    en.wikipedia.org/wiki/Perry–Robertson_formula

    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:

  7. Roark's Formulas for Stress and Strain - Wikipedia

    en.wikipedia.org/wiki/Roark's_Formulas_for_Stress...

    It also features expanded tables and cases, improved notations and figures within the tables, consistent table and equation numbering, and verification of correction factors. The formulas are organized into tables in a hierarchical format: chapter, table, case, subcase, and each case and subcase is accompanied by diagrams.

  8. Bending - Wikipedia

    en.wikipedia.org/wiki/Bending

    The proportions of the beam are such that it would fail by bending rather than by crushing, wrinkling or sideways buckling. Cross-sections of the beam remain plane during bending. Deflection of a beam deflected symmetrically and principle of superposition. Compressive and tensile forces develop in the direction of the beam axis under bending loads.

  9. Permissible stress design - Wikipedia

    en.wikipedia.org/wiki/Permissible_stress_design

    Such loads may include pressure thrusts and the weight of materials. The predicted stresses and deflections are compared with allowable values that have a "factor" against various failure mechanisms such as leakage, yield, ultimate load prior to plastic failure, buckling, brittle fracture, fatigue, and vibration/harmonic effects.