34 80 AN -500 mm CHAPTER 2 Shear Stresses 10 mm 500 mm. Fig. 2.18 2.16. Consider the two plates of equal thickness joined by two fillet welds as indicated in Fig. 2-19. Determine a expression for the maximum shearing stress in the welds. Ans. 0.707 Plab P Fig. 2-19 2.17. A copper tube 55 mm in outside diameter and of wall thickness 5 mm fits loosely over a solid steel circula har 40 mm in diameter. The two members are fastened together by two metal pins each 8 mm in diameter and 40°C. Calculate the average shear stress in the pins. For copper E-90 GPa, a 18 x 10"/C; for steel E=200 GP the assembly is just stress free when the pins are in position. The temperature of the entire assembly is then raises passing transversely through both members, one pin being near each end of the assembly. At room temperature a=12x 10ºC. Ans. 132 MPa 2.18. In automotive as well as aircraft applications, two pieces of thin metal are often joined by a single lap shear joint, as shown in Fig. 2-20. Here, the metal has a thickness of 2.2 mm. The ultimate shearing strength of the epoxy adhesive joining the metals is 2.57 x 10' kPa, the shear modulus of the epoxy is 2.8 GPa, and the epoxy is effective over the 12.7 x 25.4-mm overlapping area. Determine the maximum axial load P the joint can carry. 12.7 mm Ans. 8290 N 22mm 25.4 mm- Fig. 2-20 2.2 mm Epoxy 0.127 mm 2.19. If the shear modulus of the epoxy in Problem 2.18 is 2.8 GPa, determine the axial displacement of one piece of metal with respect to the other just prior to failure of the epoxy if the epoxy is 0.127 mm thick. Ans. 0.0017 mm