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  2. Euler–Bernoulli beam theory - Wikipedia

    en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory

    This vibrating glass beam may be modeled as a cantilever beam with acceleration, variable linear density, variable section modulus, some kind of dissipation, springy end loading, and possibly a point mass at the free end. Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) [1] is a simplification of the ...

  3. Macaulay's method - Wikipedia

    en.wikipedia.org/wiki/Macaulay's_method

    Simply supported beam with a single eccentric concentrated load. An illustration of the Macaulay method considers a simply supported beam with a single eccentric concentrated load as shown in the adjacent figure. The first step is to find . The reactions at the supports A and C are determined from the balance of forces and moments as

  4. Shear and moment diagram - Wikipedia

    en.wikipedia.org/wiki/Shear_and_moment_diagram

    Shear and Bending moment diagram for a simply supported beam with a concentrated load at mid-span. Shear force and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear forces and bending moments at a given point of a structural element such as a beam.

  5. Direct integration of a beam - Wikipedia

    en.wikipedia.org/wiki/Direct_integration_of_a_beam

    Simply supported beam with a constant 10 kN per meter load over a 15m length. Take the beam shown at right supported by a fixed pin at the left and a roller at the right. There are no applied moments, the weight is a constant 10 kN, and - due to symmetry - each support applies a 75 kN vertical force to the beam. Taking x as the distance from ...

  6. Deflection (engineering) - Wikipedia

    en.wikipedia.org/wiki/Deflection_(engineering)

    The deflection at any point, , along the span of a center loaded simply supported beam can be calculated using: [1] = for The special case of elastic deflection at the midpoint C of a beam, loaded at its center, supported by two simple supports is then given by: [ 1 ] δ C = F L 3 48 E I {\displaystyle \delta _{C}={\frac {FL^{3}}{48EI}}} where

  7. Conjugate beam method - Wikipedia

    en.wikipedia.org/wiki/Conjugate_beam_method

    This beam has the same length as the real beam and has corresponding supports as listed above. In general, if the real support allows a slope, the conjugate support must develop shear; and if the real support allows a displacement, the conjugate support must develop a moment. The conjugate beam is loaded with the real beam's M/EI diagram.

  8. Read the Luigi Mangione federal criminal complaint - AOL

    www.aol.com/read-luigi-mangione-federal-criminal...

    Luigi Mangione was charged with four federal crimes Thursday in the killing of UnitedHealthcare CEO Brian Thompson. The federal charges are significant because they open the possibility of him ...

  9. Theorem of three moments - Wikipedia

    en.wikipedia.org/wiki/Theorem_of_three_moments

    The moment M1, M2, and M3 be positive if they cause compression in the upper part of the beam. (sagging positive) The deflection downward positive. (Downward settlement positive) Let ABC is a continuous beam with support at A,B, and C. Then moment at A,B, and C are M1, M2, and M3, respectively.