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  2. Exponential integral - Wikipedia

    en.wikipedia.org/wiki/Exponential_integral

    In mathematics, the exponential integral Ei is a special function on the complex plane. ... This page was last edited on 24 September 2024, at 07:42 (UTC).

  3. Euler's identity - Wikipedia

    en.wikipedia.org/wiki/Euler's_identity

    In mathematics, Euler's identity [note 1] (also known as Euler's equation) is the equality + = where . is Euler's number, the base of natural logarithms, is the imaginary unit, which by definition satisfies =, and

  4. Moment-area theorem - Wikipedia

    en.wikipedia.org/wiki/Moment-Area_Theorem

    If there are mixed with distributed loads and concentrated, the moment diagram (M/EI) will results parabolic curves, cubic, etc. Then, assume and draw the deflection shape of the structure by looking at M/EI diagram. Find the rotations, change of slopes and deflections of the structure by using the geometric mathematics.

  5. Conjugate beam method - Wikipedia

    en.wikipedia.org/wiki/Conjugate_beam_method

    A M/EI diagram is a moment diagram divided by the beam's Young's modulus and moment of inertia. To make use of this comparison we will now consider a beam having the same length as the real beam, but referred here as the "conjugate beam." The conjugate beam is "loaded" with the M/EI diagram derived from the load on the real beam.

  6. Nondimensionalization - Wikipedia

    en.wikipedia.org/wiki/Nondimensionalization

    Nondimensionalization is the partial or full removal of physical dimensions from an equation involving physical quantities by a suitable substitution of variables.This technique can simplify and parameterize problems where measured units are involved.

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  8. Euler's critical load - Wikipedia

    en.wikipedia.org/wiki/Euler's_critical_load

    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.

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