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Q1 MECHANICAL ENGINEERING SCIENCE 2 - Strengths Tutorial 1 A 2mm cube of a certain material is subjected to a compressive force of 40kN acting on...

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MECHANICAL ENGINEERING SCIENCE 2 - Strengths Tutorial 1 Q1 A 2mm cube of a certain material is subjected to a compressive force of 40kN acting on each of its faces. If the bulk modulus and Poisson’s ratio for the cube material are 200 GPa and 0.33 respectively, calculate (a) Volumetric strain in the cube. (b) Change in length of each side of the cube. (Ans: -0.05, -0.033mm) Q2 Two titanium rods (Figure 1) AB and BC are supporting the vertical force, F = 30kN. Determine the required diameters of the two rods (to the nearest mm) if the allowable tensile stress is σ allow =130MPa. [ans: AB 21 mm and BC 23 mm] Q3 Two titanium rods (Figure 1) AB and BC have diameters 16 mm and 20 mm respectively. Determine the largest vertical force, F, that can be supported if the allowable tensile stress in the rods is σ allow =130MPa. [ans: 18.3 kN] Figure 1 Q4 A simplified diagram of a racing cars suspension and wheel is used to design the bars and pins. The force that the suspension must withstand can be considered to be a vertical force, F = 1.5 kN, acting vertically upwards at B. Calculate the minimum radius of the bars AB and BC if the maximum allowable stress σ allow = 80 MPa. Also, calculate the minimum radius of the pin at A if this pin is in Double Shear and the maximum allowable shear stress τ allow = 50 MPa [ans: Radius AB = 3.58mm; Radius BC = 3.76mm ; Radius PIN A = 3.20 mm] A C B F 25 o Wheel A C B F 25 o Wheel A C B F 35 o A C B F 35 o
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Q5 If the allowable bearing stress for the concrete under the supports at A and B is σ allow = 3.5 MPa, calculate the size of the square bearing plates C and D required to spread the load from the supports so the concrete is not damaged. Take F = 17kN and determine the dimensions of the square plates to the nearest 10mm. The reactions at the supports are vertical. [ans: C needs to be 90 mm x 90 mm; D needs to be 130 mm x 130 mm] Q6 A crane is hoisting a 500 kg crate. The boom OA is 12 m long with a mass of 150 kg which acts at the mid-point. A cable CB of circular cross section is attached to the boom at B where the length OB is 9 m. The hinge at O is a smooth pin-joint which is free to turn (g=9.81ms -2 ). Calculate the minimum diameter required for the cable CB if the maximum allowable tensile stress in the cable is σ allow = 150 MPa. The pin at O is in Double Shear calculate the minimum diameter of this pin if the maximum allowable shear stress in the pin is τ allow = 60 MPa. [ ans: 7.6 mm; 10.5 mm] F 15 kN 15 kN 15 kN 20 kN 2 m 2.5 m 2 m 2 m C D A B F 15 kN 15 kN 15 kN 20 kN 2 m 2.5 m 2 m 2 m C D A B O B C A 55 o 15 o crate
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