ENGR20004 Engineering Mechanics, mid-semester test 1 2021
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ENGR20004 Engineering Mechanics, mid-semester test 1
Wednesday, 1 September 2021
Instructions
1. Correctly answer all three questions for the full 100 marks.
2. Substantial marks are awarded for free-body diagrams, so draw and label them with unambiguously defined boundaries and with unam- biguously applied loads.
3. Substantial marks are also awarded for the approach, so ensure that the steps are clear, logical and legible, accompanied by discussions where necessary.
Question 1 (25 marks)
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(a) |
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(b) |
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Figure 1: (a) Side view of a walnut cracker and enlarged view (from the top looking downwards) of Section A–A showing pin B. The force F is applied to the handle to crack the walnut C between fixed and movable pistons. A walnut cracks when crushed by a force exerted by the pistons that exceeds 500N. (b) Photograph of walnut cracker taken from https://www.aliexpress.com/item/4000877902088.html. If the handle is vertical when the walnut C cracks, indicate the location along the axis of pin B where the maximum average shear stress occurs and determine the minimum diameter of circular pin B given the maximum allowable average shear stress in the pin is 30MPa. (Free-body
diagrams: 15 marks; approach: 8 marks; numerical solution: 2 marks)
Question 2 (35 marks)
(a)
(b)
Figure 2: (a) A beach chair ABCDEFH is supporting Joe via the hammock FH. Joe’s weight is 700N, centred at G and dis- tributed equally over both left- and right-sides of the chair. The hammock is attached to F at angle 30O downwards from the hor- izontal. Joe’s head does not touch F, and Joe’s feet do not touch the ground. The chair contacts the ground at A and D. ABEF, DCBH and CE are rigid and straight members, held together by joints at B, C and E. (b) Photograph of the beach chair taken from https://www.templeandwebster.com.au/Natural-Acacia-Wood-Beach-Chair-QF-BEACH-QUFU1005.html.
(i) Determine the loads on the chair at F and H that act on one side of the chair resulting from Joe’s weight. (Free-body diagram: 10 marks; approach: 4 marks; numerical solution: 1 mark)
(ii) Draw the free-body diagrams of ABEF, DCBH and CE representing one side of the chair and label all the loads acting on them. For
the purpose of assessing the structural integrity of the chair, you can assume that A is a pinned joint and D is a roller joint. Assuming that the loads at F and H are known from part (i), and that the dimensions of the chair (lengths AB, BE, EF, DC, CB, BH and CE) are given, show that you have enough equations (name but do not write them, e.g. F_ = 0 for member XYZ) to solve for the remaining unknown loads. (Free-body diagrams: 15 marks; approach: 5 marks)
Question 3 (40 marks)
Figure 3: A crane lifts a 200kN load. The boom ABC is at angle 30O upwards from the horizontal, the luffing cylinder BG is at angle 15O at B from the boom ABC and the hoist wire segment CF is at angle 10O from the boom ABC. A, B, C, D and G are pin joints. The hoist wire FCDED runs around the pulleys mounted to the pins at C and D and around the free pulley E. The hoist wire is attached to the pin D at one end, and reeled at the drum F at the other end. The load is attached to the centre of the free pulley E. The boom ABC and boom tip CD are one L-shaped body and CD is perpendicular to ABC.
(i) Draw an appropriate free-body diagram to show that the tension in the hoist wire FCDED is 100kN. (Free-body diagram: 5 marks)
Figure 4: A simply supported beam of length L subject to a force P applied at distance b from one end.
(ii) Given the free-body diagram in figure 4, calculate the shear force and bending moment along the axis of the beam in terms of P, b and L, and draw them as diagrams. (Free-body diagrams: 10 marks; approach, analytical and diagram solutions: 5 marks)
(iii) Calculate all the loads acting on the 15m-long boom ABC, neglecting the boom-tip dimension, a = 0 (D a C). (Free-body diagrams:
10 marks; approach and numerical solutions: 5 marks)
(iv) Suggestion: check and upload your solutions up to here before proceeding. This last part is only worth 5% of the test. Now, allowing for a = 0.5m that separates the pulleys C and D at the boom tip, determine the shear-force and bending-moment diagrams of the boom ABC by superposition of
(1) your diagrams drawn for (ii) using your loads calculated for (iii), and
Figure 5: An overhanging beam supported by pins spaced apart by distance b subject to a moment C. V is the shear force and M is the bending moment drawn under the free-body diagram, according to the sign convention shown on the right.
(2) the diagrams drawn in figure 5 using the value of the moment C that you calculate from an appropriate free-body diagram. For this part only, you can use a graphical approach to superpose the bending-moment and shear-force diagrams.
(Free-body diagrams, approach and numerical solution: 5 marks)
2022-08-29