Strength of Materials, mech0402227Prob1: The axially loaded bar ABCD shown in the figure is held between rigid supports. The bar has cross-sectional area A1 from A to C and 2A1 from C to D. (a) Derive formulas for the reactions RA and RD at the ends of the bar. (b) Determine the displacements ᵟ B and ᵟ C at points B and C, Respectively. Prob2: A plastic rod AB of length L = 0.5 m has a diameter d1 = 30 mm (see figure). A plastic sleeve CD of length c =0.3 m and outer diameter d2 = 45 mm is securely bonded to the rod so that no slippage can occur between the rod and the sleeve. The rod is made of an acrylic with modulus of elasticity E1 = 3.1 GPa and the sleeve is made of a polyamide with E2= 2.5 GPa. (a) Calculate the elongation _ of the rod when it is pulled by axial forces P = 12 kN. (b) If the sleeve is extended for the full length of the rod, what is the elongation? (c) If the sleeve is removed, what is the elongation? Prob3: A brass sleeve S is fitted over a steel bolt B (see figure), and the nut is tightened until it is just snug. The bolt has a diameter dB = 25 mm, and the sleeve has inside and outside diameters d1 = 26 mm and d2= 36 mm, respectively. Calculate the temperature rise ∆T that is required to produce a compressive stress of 25 MPa in the sleeve. (Use material properties as follows: for the sleeve, αS = 21 × 10×6/°C and ES = 100 GPa; for the bolt,αB = 10×10×6/°C and EB= 200 GPa. E=210 GPa is loaded as shown in Fig. if the bolt is now tightened by a quarter turn of the nut? The copper tube has length L= 16 in.2.2 The pitch of the threads of the bolt is p = 52 mils (a mil is one-thousandth of an inch). What stresses Ϭs and Ϭc will be produced in the steel and copper.0 k-ft acting midway between the supports at B and C. respectively Prob5: . The x-sectional area of the pipe is 1800 mm2 (a) Find the displacement at the free end (b) Find the distance x from the left-hand support to the point at which the displacement is zero. Also. the moduli of elasticity of the steel and copper are Es =30 × 106 psi and Ec = 16 × 106 psi.2 in. A=1800 mm2 Prob6: A beam ABC with an overhang at the left-hand end is shown in Fig. and the steel bolt has cross-sectional area As = 0.6 in. . The beam is subjected to a uniform load of intensity q = 1. Draw the shear-force and bending-moment diagrams for this beam.Prob4: A copper tube is fitted around a steel bolt and the nut is turned until it is just snug (see figure). and cross-sectional area Ac = 0.0 k/ft on the overhang AB and a counterclockwise couple M0 = 12. Given : E= 210 GPa . A 4 m long steel pipe . respectively.