ME85-Lecture23

# ME85-Lecture23 - Lecture 22 Differential Equation for Beam...

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Lecture 22 Differential Equation for Beam Deflection

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Euler-Bernoulli beam theory (also known as Engineering beam theory , Classical beam theory or just beam theory ) is a simplification of the linear theory of elasticity, which provides a means of calculating the load-carrying and deflection characteristics of beams. It was first enunciated circa 1750, but was not applied on a large scale until the development of the Eiffel Tower and the Ferris wheel in the late 19th century. Following these successful demonstrations, it quickly became a cornerstone of engineering and an enabler of the Second Industrial Revolution.
Leonhard Euler Jacob Bernoulli Daniel Bernoulli

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The Da Vinci-Euler-Bernoulli Beam Theory?

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Eiffel Tower
The original Chicago Ferris Wheel (80 m) Ferris Wheel In London (94m)

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164 meter tall Singapore Ferris Wheel

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The second tallest building in the world

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How to measure vibrations of shaking table ?
Deformation of a Beam Under Transverse Loading Relationship between bending moment and curvature for pure bending remains valid for general transverse loadings. EI x M ) ( 1 = ρ Cantilever beam subjected to concentrated load at the free end, EI Px = 1 Curvature varies linearly with x At the free end A , = = A A ρ ρ , 0 1 At the support B , PL EI B B = , 0 1

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Deformation of a Beam Under Transverse Loading Overhanging beam Curvature is zero at points where the bending moment is zero, i.e., at each end and at
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## This note was uploaded on 01/21/2012 for the course C 85 taught by Professor Papadopoulos during the Spring '08 term at University of California, Berkeley.

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ME85-Lecture23 - Lecture 22 Differential Equation for Beam...

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