Question

7. The beam AB is constructed from a lightweight material with Young's modulus E. It has a total length of L and a second moment of area I. (a) Consider Figure 9(a), where a moment M acts at point B. Find the rotation of point B in terms of M, E, I and L. [7 marks] (b) The rotational stiffness k of the beam is defined as the ratio of moment M to the rotation of point B. Express k in terms of E, I and L. [1 mark] (c) Figure 9(b) shows a heavy flywheel with mass Q in the form of a solid circular disc of radius R, which is attached to point B using a bearing. While spinning at constant angular velocity $\omega$, the bearing jams and the flywheel stops spinning. Find the resulting rotation at point B in terms of Q, R, $\omega$ and k. [4 marks] (d) Determine the vertical reaction force at A in terms of Q, R, $\omega$, E, I and L. Draw the bending moment diagram of the beam. [3 marks]

          7.
The beam AB is constructed from a lightweight material with Young's modulus E. It has a
total length of L and a second moment of area I.
(a) Consider Figure 9(a), where a moment M acts at point B. Find the rotation of point B
in terms of M, E, I and L.
[7 marks]
(b) The rotational stiffness k of the beam is defined as the ratio of moment M to the
rotation of point B. Express k in terms of E, I and L.
[1 mark]
(c) Figure 9(b) shows a heavy flywheel with mass Q in the form of a solid circular disc of
radius R, which is attached to point B using a bearing. While spinning at constant
angular velocity $\omega$, the bearing jams and the flywheel stops spinning. Find the resulting
rotation at point B in terms of Q, R, $\omega$ and k.
[4 marks]
(d) Determine the vertical reaction force at A in terms of Q, R, $\omega$, E, I and L. Draw the
bending moment diagram of the beam.
[3 marks]

7.
The beam AB is constructed from a lightweight material with Young's modulus E. It has a
total length of L and a second moment of area I.
(a) Consider Figure 9(a), where a moment M acts at point B. Find the rotation of point B
in terms of M, E, I and L.
[7 marks]
(b) The rotational stiffness k of the beam is defined as the ratio of moment M to the
rotation of point B. Express k in terms of E, I and L.
[1 mark]
(c) Figure 9(b) shows a heavy flywheel with mass Q in the form of a solid circular disc of
radius R, which is attached to point B using a bearing. While spinning at constant
angular velocity ω, the bearing jams and the flywheel stops spinning. Find the resulting
rotation at point B in terms of Q, R, ω and k.
[4 marks]
(d) Determine the vertical reaction force at A in terms of Q, R, ω, E, I and L. Draw the
bending moment diagram of the beam.
[3 marks]

Added by Andrea M.

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