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 Mandachecmandache@fit.eduThermal strainApplications involving temperature changesPoissons ratioMultiaxial loadingGeneralized Hookes lawSaint-Venant principleShearing strain2Lecture objectivesDr. Catalin Mandachecmandache@fit.eduMore 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 Mandachecmandache@fit.edu

sx=18 ksisz=24 ksiE=12.6X10^6 psin=0.34

Find change in lengths of AB, BC and ACProblem 2.98Dr. Catalin Mandachecmandache@fit.edu

P=100 kN. Determine the minimum plate thickness t required if the allowable stress is 125 MPa.Chapter #3: TorsionDr. Catalin Mandachecmandache@fit.eduMembers 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 Mandachecmandache@fit.edu

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 Mandachecmandache@fit.edu

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 Mandachecmandache@fit.edu

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 Mandachecmandache@fit.edu

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 Mandachecmandache@fit.eduHookes law for shearing stress:

elastic torsion formulas

Concept application 3.1Dr. Catalin Mandachecmandache@fit.edu

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.