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  2. Theoretical strength of a solid - Wikipedia

    en.wikipedia.org/wiki/Theoretical_strength_of_a...

    The stress-displacement, or vs x, relationship during fracture can be approximated by a sine curve, = (/), up to /4. The initial slope of the σ {\displaystyle \sigma } vs x curve can be related to Young's modulus through the following relationship:

  3. Direct stiffness method - Wikipedia

    en.wikipedia.org/wiki/Direct_stiffness_method

    The structure’s unknown displacements and forces can then be determined by solving this equation. The direct stiffness method forms the basis for most commercial and free source finite element software. The direct stiffness method originated in the field of aerospace. Researchers looked at various approaches for analysis of complex airplane ...

  4. Single displacement reaction - Wikipedia

    en.wikipedia.org/wiki/Single_displacement_reaction

    A single-displacement reaction, also known as single replacement reaction or exchange reaction, is an archaic concept in chemistry. It describes the stoichiometry of some chemical reactions in which one element or ligand is replaced by atom or group. [1] [2] [3] It can be represented generically as: + +

  5. Bending of plates - Wikipedia

    en.wikipedia.org/wiki/Bending_of_plates

    For rectangular plates, Navier in 1820 introduced a simple method for finding the displacement and stress when a plate is simply supported. The idea was to express the applied load in terms of Fourier components, find the solution for a sinusoidal load (a single Fourier component), and then superimpose the Fourier components to get the solution ...

  6. Vibration of plates - Wikipedia

    en.wikipedia.org/wiki/Vibration_of_plates

    The governing equations for the dynamics of a Kirchhoff-Love plate are , = ¨, + (,) = ¨ ¨, where are the in-plane displacements of the mid-surface of the plate, is the transverse (out-of-plane) displacement of the mid-surface of the plate, is an applied transverse load pointing to (upwards), and the resultant forces and moments are defined as

  7. Bending - Wikipedia

    en.wikipedia.org/wiki/Bending

    The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically 1/10 or less, of the other two. [1] When the length is considerably longer than the width and the thickness, the element is called a beam .

  8. Young's modulus - Wikipedia

    en.wikipedia.org/wiki/Young's_modulus

    Young's modulus is the slope of the linear part of the stress–strain curve for a material under tension or compression.. Young's modulus (or Young modulus) is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise.

  9. Substitution reaction - Wikipedia

    en.wikipedia.org/wiki/Substitution_reaction

    The two reactions are named according tho their rate law, with S N 1 having a first-order rate law, and S N 2 having a second-order. [2] S N 1 reaction mechanism occurring through two steps. The S N 1 mechanism has two steps. In the first step, the leaving group departs, forming a carbocation (C +). In the second step, the nucleophilic reagent ...