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hw5soln - 2.15[2.2 A horizontal shaft transmits a torque T...

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Unformatted text preview: 2.15. [2.2] A horizontal shaft transmits a torque T of 50 N7 m to a tube, as shown in Fig. P.2.15, thmugh a rubber can» hector glued to both members What is the shear stress on elements of cylindrical surfaces in the rubber connector cone centric with the shaft as a function of r, the radius of the aforementioned cylindrical surface? 2.11. [2.2] Shown in Fig. P.2.l7 are two plates fastened together by three rivets in what is called a lap joint, What is the average shear stress river the sections of the rivets in the plane of the Interface between the two plates assuming that each rivet transmits the same load? In rivet calculations it is American practice to discount frictional forces between the plates (this gives an added measure of safety in deSign). If across all cross sections of the plates (i.e., along cuts across the width of the plates including those like 14—11) the normal stress is assumed unitonn for each such section, What section has the largest stress. and what is the value of this stress? Again, do not consider friction. 17:125mn Figure thus 12.5 mm \ 12.5mm \ 7 Will/”III,” h‘“\“\\“\ V l 40033 N Figure ”.17. Shear Stress "3:25 i = 40,000 3(13) “ is = 1,086 x 103 Pa Section with largest tensile stress is ' along centerliue of rivets. Thus (t")(.0125)[.15D-(3)(.0125)] = 40.090 Tn = 2.844 X 107 Pa 2.39. What is the maximum torque T transmitted by the flange connection in Fig. P239? There are eight bolts each having a diameter of 5 mm The maximum allowable stress per bolt is 300 MPa. FBD Fball F 501! = TA 7z'(0.005)2 =(300x10‘) =5890N 2T = 0 ' T = ngBult = (8)(O.200)(5890) 2.49. In Fig. 132.49 we show a section of a shaft A rotating concentrically with speed to inside a journal bearing B and separated from B by a film of oil of thickness e and viscosity u. Newton’s viscosity law r = Mall/er) gives the shear stress on interfaces normal to radius r in the oil. If there is a linear profile of the oil and if it “sticks" to the metal surfaces (i.e., it has the same speed as the surface at the surface), what is the torque T needed to rotate the shaft? Take the length of the hearing to be L. Velocity profile < The velocity profile is determined as fol- lows: _ (r-r) V=mt" - 0 0 (or 0) Note profile is linear and V = 0 at r = r0 + e as required. Simplifying: r-r . _ _ o . . V — wroU e ] Use Newton's viscosity law: d it ind—l = ulmrolt— 1,) The shear stress is thus the same for all interfaces having a radial direction. Hence, to get torque T noting diagram we can say dT It dA To our ( E°)(rD de L)r° il ...
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