Answer Happy

Q4)
A cantilevered aluminium beam is shown in Figure Q.4a. The beam
has length 𝐿 = 1.5 m
and thickness 𝑡 = 15 mm. It has a linear coefficient of thermal
expansion (CTE) of 12 × 10−6 K-1, second moment of area 𝐼 = 8000
mm4, and Young’s modulus 𝐸 = 70 GPa. The beam initially sits a
height h = 30 mm above one of the outer panels of the spacecraft to
which the beam is attached, as shown in Figure Q.4a(i). The bottom
surface of the beam is held at a temperature of 200 K, while the
temperature of the top surface varies depending on the orbit of the
spacecraft. A difference in temperature between the top and bottom
surface of the beam will cause it to curve. The global coordinate 𝑥
has value 𝑥 = 0 at the beam root.
(i) Estimate the temperature of the top surface of the beam at
which the beam will just begin to make contact with the lower
panel, as shown in Figure Q.4a
(ii) Find the deflection angle to the horizontal of the tip of
the beam in the situation described in part 4(a) above
(iii) The vertical displacement of the tip of a cantilevered
beam subjected to a vertical tip
load 𝐹 can be estimated as:
𝛿 = 𝐹𝐿^3 / 3𝐸𝐼
If the top surface of the beam reaches 250 K, estimate the force
of contact between the tip of the beam and the lower panel. You may
assume that the lower panel is rigid. State any assumptions you are
making.
L (i) L (ii) Figure Q.4a. h