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Euler-Bernoulli Beam Theory: Exploring Bending Moment and Shear Force

Discover the Euler-Bernoulli Beam Theory (1750) detailing bending moment, shear force, and slope deflection in beams. Explore the coefficients at the beam's center and their relation to double factorials. Dive into the construction of the Eiffel Tower (1887-1889) as an application of this theory.

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Euler-Bernoulli Beam Theory: Exploring Bending Moment and Shear Force

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  1. One Three hundred and Eighty Fourth John Read @johndavidread

  2. 2

  3. + = + = = = 2 + = +

  4. q q Leonard Euler 1707 - 1783 Daniel Bernoulli 1700 - 1782 w x Eiffel Tower under construction 1887-1889 The Euler Bernoulli Beam Theory 1750

  5. Bending moment Shear force slope deflection

  6. w q w q w q w q q w

  7. For q(x) = a constant, setting q = 1 , and setting both E = 1 and I = 1 and for a unit length beam l = 1 = 1

  8. For q(x) = a constant, setting q = 1 , and setting both E = 1 and I = 1 and for a unit length beam l = 1 = 1

  9. For q(x) = a constant, setting q = 1 , and setting both E = 1 and I = 1 and for a unit length beam l = 1 = 1

  10. At the centre of the beam where x = ½

  11. At the centre of the beam where x = ½

  12. At the centre of the beam where x = ½

  13. The coefficients are the reciprocals of the double factorials !! of n, for n = 0 to 4

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