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ENGR5002 / Week 1
ENGR217 2019 Q B1Past paperOld spec ENGR2172:125 marks30 min

ENGR217 Summer 2019 Q B1[VALID] official answers

Answer ALL parts (a) - (d).

[Data Book: water ρ=1000 kg m−3\rho = 1000\ \mathrm{kg\,m^{-3}}.]

Figure B1-1: vertical tank end made of an 11.6 m wide x 6.6 m deep rectangle (water surface at its top edge) above a triangle 3.6 m deep with its apex downward; C1, C2 and C are the centroids, O-O the horizontal axis through C.
Figure B1-1: vertical tank end made of an 11.6 m wide x 6.6 m deep rectangle (water surface at its top edge) above a triangle 3.6 m deep with its apex downward; C1, C2 and C are the centroids, O-O the horizontal axis through C.
Formulas you may need
  • Force on a plane surface: F=ρgzCGAF = \rho g z_{CG} A (on the formula sheet)
  • Centre of pressure: lCP=lCG+IGA lCGl_{CP} = l_{CG} + \dfrac{I_G}{A\, l_{CG}} (on the formula sheet)
  • Shape table: rectangle A=bhA = bh, IG=bh3/12I_G = bh^3/12; triangle A=bh/2A = bh/2, centroid h/3h/3 from the base, IG=bh3/36I_G = bh^3/36 (on the formula sheet)
  • Composite centroid: yˉ=∑Aiyi∑Ai\bar y = \dfrac{\sum A_i y_i}{\sum A_i} (learn this)
  • Parallel axis theorem: I=IG+Ad2I = I_G + A d^2 (learn this)
  1. (a)
    Find the depths y1y_1 and y2y_2, to the centroids C1C_1 and C2C_2 of the rectangle and triangle shown in Figure B1-1 below, and then find the depth yy to the centroid C of the whole figure.
    [5]
  2. (b)
    The plane figure shown forms the vertical end of the water tank. What is the magnitude of the force exerted on the plane by the water?
    [5]
  3. (c)
    Find the second moment of area of the figure about the horizontal axis O-O through the centroid C. (This will involve the use of the parallel axis theorem in both the triangle and the rectangle).
    [10]
  4. (d)
    Finally find the position of the centre of pressure P of the complete figure.
    [5]