mechanics of materials ch 3
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Mechanics of Materials SlideTRANSCRIPT
Nondestructive Evaluation in Aerospace Examples of Current and Future Research Avenues
MAE 3083Lecture #6
Stress and Strain: Axial loadingTorsionDr. Catalin Mandache
February 2nd, 2015
Review of the previous lecture (Stress and Strain)Dr. Catalin [email protected] strainApplications involving temperature changesPoissons ratioMultiaxial loadingGeneralized Hookes lawSaint-Venant principleShearing strain2Lecture objectivesDr. Catalin [email protected] applications on stress and strain, thermal strain, statically indeterminate problems
Chapter #3: TorsionCircular shaftsStress in a shaftDeformation in a circular shaft angle of twistApplicationsProblem 2.68Dr. Catalin [email protected]
sx=18 ksisz=24 ksiE=12.6X10^6 psin=0.34
Find change in lengths of AB, BC and ACProblem 2.98Dr. Catalin [email protected]
P=100 kN. Determine the minimum plate thickness t required if the allowable stress is 125 MPa.Chapter #3: TorsionDr. Catalin [email protected] of circular cross section (shafts and tubes) are subject to twisting couples (or torques of opposite directions). - circular planes remain undistorted
Transmission shafts used to transfer power from one point to another.Need to determine:stress and strain distributionangle of twistlinear-elastic behaviourinelastic behaviour
Torques in shaftsDr. Catalin [email protected]
Turbine exerts a torque on the shaft, torque that is transmitted to the generator.
Stress and strains are generated in the shaft due to the twisting torques.Internal shearing stressesDr. Catalin [email protected]
Torques acting on a shaftEquilibrium considerationsCannot determine the stress distribution: statically indeterminate problemNeed to consider deformationsUnlike the normal stress due to axial loads, the distribution of shearing stresses due to torsional loads cannot be assumed uniform.Shaft deformation, twist angleDr. Catalin [email protected]
Based on observation:
f ~ Tand~ L
Cross-sections for hollow and solid circular shafts remain plain and undistorted because a circular shaft is axisymmetric.
Shearing strainDr. Catalin [email protected]
circular shaft of length L and radius c
shearing strain is proportional to radius and length of the shaft
Shearing stress and strain in the elastic limitDr. Catalin [email protected] law for shearing stress:
elastic torsion formulas
Concept application 3.1Dr. Catalin [email protected]
Hollow circular shaft, outer diameter of 60 mm, inner diameter of 40 mm.Length of the shaft, L=1.5 m.Find torque that can be applied if the shearing stress is not to exceed 120 MPaThe corresponding minimum value of the shearing stress in the shaft.