ENGR216 2017 Q A1Past paperOld spec ENGR2162:225 marks30 min

ENGR216 Summer 2017 Q A1[VALID] official answers

Answer ALL parts (a) - (e)

Figure A1 (dimensions in mm): horizontal stepped bar between rigid walls at A (left) and E (right). Rod (1), the larger diameter, runs from A to C; rod (2), the smaller diameter, runs from C to E. Axial loads P1 at B and P2 at D both act to the right. Lengths AB = 180, BC = 135, CD = 90, DE = 90.
Figure A1 (dimensions in mm): horizontal stepped bar between rigid walls at A (left) and E (right). Rod (1), the larger diameter, runs from A to C; rod (2), the smaller diameter, runs from C to E. Axial loads P1 at B and P2 at D both act to the right. Lengths AB = 180, BC = 135, CD = 90, DE = 90.
Formulas you may need
  • Axial deformation of a uniform segment δ=NLAE\delta = \dfrac{NL}{AE}, summed over segments δ=∑iNiLiAiEi\delta = \sum_i \dfrac{N_i L_i}{A_i E_i} (learn this)
  • Normal stress σ=N/A\sigma = N/A and Hooke's law σ=Eϵ\sigma = E\epsilon (learn this)
  • Area of a solid circle A=πr2=πd2/4A = \pi r^2 = \pi d^2/4 (on the formula sheet)
  • Equilibrium along the bar ∑Fx=0\sum F_x = 0 (learn this)
  • Compatibility for a bar between rigid supports: total change in length =0= 0; method of superposition (release a redundant support, then restore it) (learn this)
  1. (a)
    Explain what the difference between statically determinate and statically indeterminate structures is, and explain what is the standard procedure for determining all reactions for these two types of systems.
    [4]Third
  2. (b)
    Consider the structure depicted in Figure A1. The structure is made up of two cylindrical rods denoted by (1) and (2) joined at C and restrained by rigid supports at A and E. State whether the structure of Figure A1, constrained to maintain the same overall lengths between positions A and E before and after applications of the concentrated loads P1P_1 and P2P_2, is statically determinate or indeterminate, and justify your answer.
    [3]Third
  3. (c)
    Explain which conditions can be used to determine the reactions at the rigid supports A and E.
    [3]Third
  4. (d)
    The cross section diameter and Young's modulus of rod (1) are respectively E1=70 GPaE_1 = 70\ \mathrm{GPa} and d1=40 mmd_1 = 40\ \mathrm{mm}, and the corresponding parameters of rod (2) are respectively E2=200 GPaE_2 = 200\ \mathrm{GPa} and d2=30 mmd_2 = 30\ \mathrm{mm}. The values of the axial loads P1P_1 and P2P_2 indicated in Figure A.1 are P1=90 kNP_1 = 90\ \mathrm{kN} and P2=120 kNP_2 = 120\ \mathrm{kN}, and all four lengths indicated in the figure are in millimetres. Determine the reactions at the rigid supports A and E, providing their magnitude and orientation (left or right).
    [8]
  5. (e)
    Determine the magnitude and direction (left or right) of the displacement of point c.
    [7]