One Three hundred and Eighty Fourth
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One Three hundred and Eighty Fourth. John Read @johndavidread. 2. +. =. +. =. =. =. 2. +. = +. q. q. Leonard Euler 1707 - 1783. Daniel Bernoulli 1700 - 1782. w. x. Eiffel Tower under construction 1887-1889. The Euler Bernoulli Beam Theory 1750. Bending moment.

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One Three hundred and Eighty Fourth

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One three hundred and eighty fourth

One Three hundred and Eighty Fourth

John Read

@johndavidread


One three hundred and eighty fourth

2


One three hundred and eighty fourth

+

=

+

=

=

=

2

+

= +


One three hundred and eighty fourth

q

q

Leonard Euler 1707 - 1783

Daniel Bernoulli

1700 - 1782

w

x

Eiffel Tower under construction 1887-1889

The Euler Bernoulli Beam Theory 1750


One three hundred and eighty fourth

Bending moment

Shear force

slope

deflection


One three hundred and eighty fourth

w

q

w

q

w

q

w

q

q

w


One three hundred and eighty fourth

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


One three hundred and eighty fourth

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


One three hundred and eighty fourth

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


One three hundred and eighty fourth

At the centre of the beam where x = ½


One three hundred and eighty fourth

At the centre of the beam where x = ½


One three hundred and eighty fourth

At the centre of the beam where x = ½


One three hundred and eighty fourth

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


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