A cantilevered aluminium beam is shown in Figure Q.4a. The beam
has length ๐ฟ = 1.5 m
and thickness ๐ก = 15 mm. It has a linear coefficient of thermal
expansion (CTE) of 12 ร 10โ6 K-1, second moment of area ๐ผ = 8000
mm4, and Youngโs modulus ๐ธ = 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 ๐ฅ
has value ๐ฅ = 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 ๐น can be estimated as:
๐ฟ = ๐น๐ฟ^3 / 3๐ธ๐ผ
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.
- 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 1 (32.25 KiB) Viewed 10 times