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  2. 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

  3. 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.

  4. Euler–Bernoulli beam theory - Wikipedia

    en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory

    The bending moments and shear forces in Euler–Bernoulli beams can often be determined directly using static balance of forces and moments. However, for certain boundary conditions, the number of reactions can exceed the number of independent equilibrium equations. [5] Such beams are called statically indeterminate.

  5. Cavendish experiment - Wikipedia

    en.wikipedia.org/wiki/Cavendish_experiment

    The large weights can be rotated to the other side of the torsion beam (w, w), causing the beam to rotate in the opposite direction. The Cavendish experiment , performed in 1797–1798 by English scientist Henry Cavendish , was the first experiment to measure the force of gravity between masses in the laboratory [ 1 ] and the first to yield ...

  6. Bending moment - Wikipedia

    en.wikipedia.org/wiki/Bending_moment

    Computing the moment of force in a beam. An important part of determining bending moments in practical problems is the computation of moments of force. Let be a force vector acting at a point A in a body. The moment of this force about a reference point (O) is defined as [2]

  7. Timoshenko–Ehrenfest beam theory - Wikipedia

    en.wikipedia.org/wiki/Timoshenko–Ehrenfest_beam...

    A caveat to this Ansatz damping force (resembling viscosity) is that, whereas viscosity leads to a frequency-dependent and amplitude-independent damping rate of beam oscillations, the empirically measured damping rates are frequency-insensitive, but depend on the amplitude of beam deflection.

  8. Beam (structure) - Wikipedia

    en.wikipedia.org/wiki/Beam_(structure)

    A stiffer beam (high modulus of elasticity and/or one of higher second moment of area) creates less deflection. Mathematical methods for determining the beam forces (internal forces of the beam and the forces that are imposed on the beam support) include the "moment distribution method", the force or flexibility method and the direct stiffness ...

  9. 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 ...