4.5 The principal stresses induced at a point in a machine component made of steel 50C4 (S, = 460 N/mm2) are as follows: oj = 200N/mm? O2=150 N/mm? 03 =0 Calculate the factor of safety by (i) the maximum shear stress theory, and (ii) the distortion energy theory. (6) 2.3 (ii) 2.55]

3. Assume the plane stress state: ơ1 = 0, 02 = 20, T12 = 15 (all stresses in ksi). If oz alone is increased until the maximum shear stress t1, in the material reaches ±20 ksi, what is the value of o, at this point? HINT: this is relatively easy to figure out if you construct a Mohr's circle for the initial stress state and then consider what happens if o, is replaced with Ao2 and you solve for A when the maximum shear stress (from the circle geometry) reaches ±20 ksi.

P2.12 (WP A thin triangular plate PQR forms a right angle at point Q. During deformation, point Q moves to the right by u = 0.8 mm and upward by v = 1.3 mm to new position Q', as shown in Figure P2.12. Determine the shear strain y at corner Q' after deformation. Use a = 225 mm, b = 455 mm, and d = 319.96 mm. v7 d FIGURE P2.12

Q2 The shaft in Figure Q2.1 consists of three sections of different diameters and shear moduli as shown. It is fixed to a wall at A and loaded at points B.C and D. GAB 50 GPa dAB = 60 mm 30 kNm ++ 0.1 m Q2 contd. B ** GRC = 70 GPa dac = 80 mm 0.2 m Fig. Q2.1 Gcp= 50 GPa dep 40 mm C 20 kNm Fig. Q2.2 0.1 m D (a) Draw the Torque diagram for the shaft AD. Show all of your working and indicate all key values. (b) Determine the angle of twist for each section of the shaft (AB, BC and CD) and the total angle of twist between A and D. 5 kNm (c) If the shear strength for the entire shaft is 400 MPa, determine the maximum torque each section can withstand. Ø 120 mm 3 bolts equally spaced MEE1004/2021 (d) The shaft is to be fixed to the wall at end A via a flange with 3 equally spaced bolts, on a pitch circle diameter of 120 mm, as shown in Figure Q2.2. If the bolt material has a shear strength of 300 MPa, determine the minimum diameter of the bolts.

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Q2(c) The steel alloy shaft having a diameter of 38 mm is used to transmit torque, T as shown in Figure Q2(c). If the allowable shear stress of the shaft is 80kPa, i)Determine the maximum torque T that can be transmitted by the shaft. ii)What would be the maximum torque T' if a 25 mm diameter hole is bored through the shaft? Figure Q2(c.) |Q2 c) (i) T c The torsion formula :7 = J Т (0.019) T (0.019)^4 ; Therefore, the max torque T = x10 Nm 80 2 Q2 c) (ii) For point lying on the outside suurface of the shaft: x10 ="(0.019) * (0.019*-0.0125 ) ; Therefore the max torque T' Nm 80 2 Q2 c) (iii) The shear stress at point located at inner surface of shaft, T'c T = -= J ) (0.0125) = 7 (0.019*-0.01254) T'c kPa 4. 2 2.