Question 4 For small deflections, the shape of a beam is modelled by the equation: El y" - w, where E is Young's modulus for the material, I is the second moment of area of a cross section of the beam, and y is the displacement from the straight line position. A uniform heavy beam of length L metres, with downward force density w N/m, is built in at the end x = 0, and hangs free at its other end. (al Sketch a diagram that models this situation. (0) State all the boundary conditions that apply and explain fully their meaning.

Structural Analysis
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Author:KASSIMALI, Aslam.
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Chapter2: Loads On Structures
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Question 4
For small deflections, the shape of a beam is modelled by the equation:
El y" = w,
where E is Young's modulus for the material, I is the second moment of area of a cross section
of the beam, and y is the displacement from the straight line position.
A uniform heavy beam of length L metres, with downward force density w Nim, is built in at the
end x = 0, and hangs free at its other end.
(a) Sketch a diagram that models this situation.
(0) State all the boundary conditions that apply and explain fully their meaning.
(c) Show, by integration, that the deflection of the beam x metres from one end is described by
the equation
24 EI
(d) State the value of x at which the maximum deflection occurs and hence show the maximum
deflection, ymars of a heavy beam of length L is given by
Ymax =
8EI
You are given the following details.
Transcribed Image Text:Question 4 For small deflections, the shape of a beam is modelled by the equation: El y" = w, where E is Young's modulus for the material, I is the second moment of area of a cross section of the beam, and y is the displacement from the straight line position. A uniform heavy beam of length L metres, with downward force density w Nim, is built in at the end x = 0, and hangs free at its other end. (a) Sketch a diagram that models this situation. (0) State all the boundary conditions that apply and explain fully their meaning. (c) Show, by integration, that the deflection of the beam x metres from one end is described by the equation 24 EI (d) State the value of x at which the maximum deflection occurs and hence show the maximum deflection, ymars of a heavy beam of length L is given by Ymax = 8EI You are given the following details.
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