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# Mechanics of Deformable Bodies 057 019

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This 7 page Class Notes was uploaded by Rahsaan Hoppe on Friday October 23, 2015. The Class Notes belongs to 057 019 at University of Iowa taught by Colby Swan in Fall. Since its upload, it has received 37 views. For similar materials see /class/228005/057-019-university-of-iowa in General Engineering at University of Iowa.

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Date Created: 10/23/15

057019 Mechanics ofDeformable Bodies College ofEngineering Instructor CC Swan University of Iowa Period 9 Spring 2009 Semester Sections 5153 of Textbook Topic Torsion of Axial Members Objectives Overview of Material Covered Twist and resulting shear strains Torque and resulting shear stresses Torquetwist and shear stress shear strain Power transmission via torque Example applications O DU39lhUJNH 1 Material Covered From Chapter 4 you are encouraged to read sections 47 stress concentrations 48 inelastic deformation and 49 residual stresses While the information therein is good to be aware of you will not be held responsible for it in this course Torsion behavior of long axial members is important in many power transmission applications and in structural applications as well 2 Twist and resulting shear strains Circles remain circular T Longitudinal T lines become twisted Before deformation I 1 Radial lines remain straight After deformation 057019 Mechanics ofDeformable Bodies College ofEngineering Instructor CC Swan University of Iowa dammitax lt V plum Dy 4 iquot fanny 7 i n quot39H dtlbrlllcd I flme 39 The Imgli ur mm mm inurcilxb UK incmwc d 7 P g 57mm where 7 is the material 5 shear strain p is the distance of a material point from the centroidal axis c is the radius of the circular cross section is the angle of twist in the member X is the coordinate variable along the member s centroidal axis The shear slruin for the material increases linearly Wilh p is y pcwlmx 057019 Mechanics of Deformable Bodies College of Engineering Instructor CC Swan University of Iowa 3 Torque and Shear Stresses Assuming for the time being that the material that comprises the axial member is linearly elastic and isotropic then the relation between shear stress and shear strain of a material point on a cross section of the axial member is rGy p 7 7mm l h o V E N l I l Shear stress varies linearly along each radial line of the cross section lb 59 Integrating the moment of shear stresses over a circular crosssection about the longitudinal axial of the member we obtain the relation between shear stresses and torque T pm A E J 261A T J27rrp2dp p Tmax 76 0 C c Tp max 27rp3dp 1 c 2njp3dp I J j 7rcquot E i 2 7mg 2 dx G c 2 The polar moment of inertia J about the centroidal axis of simple cross sections circular crosssection annular cross section solld Shaft tubular shaft 4 J 2 m J M 2 057019 Mechanics of Deformable Bodies College of Engineering Instructor CC Swan University of Iowa 4 Power Transmission It is often the case that a source of power such as an engine exists at one location but work must be done at a different location Power can be transmitted from the engine to the location where work needs to be done using drive shafts The rate of power transmission by shaft is PT TmT2 f dt where T is the torque in the shaft a is the rate at which the shaft turns radians f is the rate at which the shaft turns cycles 057019 Mechanics of Deformable Bodies College of Engineering Instructor CC Swan University of Iowa 5 Example Problems Example 1P5 9 from text The assembly consists of two sections of galvanized steel pipe connected together using a reducing coupling at B The smaller pipe has an outer diameter of075 in and an inner diameter of 068 in whereas the larger pipe has an outer diameter of 1 in and an inner wall diameter of 086 in If the pipe is tightly secured to the wall at C determine the maximum shear stress developed in each section of the pipe when the couple shown is applied to the 151391 handles ofthe wrench Prob 5 9 057019 Mechanics of Deformable Bodies College of Engineering Instructor CC Swan University of Iowa Example 2 PS 13 from text A steel tube having an outer diameter of 25 in is used to transmit 350 hp when turning at 27 revmin Determine the inner diameter cl ofthe tube to the nearest 18 in if the allowable shear stress is Ta0w10 ksi Prob 5 13 057019 Mechanics of Deformable Bodies College of Engineering Instructor CC Swan University of Iowa Example 3 PS 17 from text Ifthe applied torque on shaft CD is T 75 Nm determine the absolute maximum shear stress in each shaft The bearings B C and D allow free rotations of the shafts and the motor holds the shafts fixed from rotating Prohs 5 1617

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