CSULB MAE 374 Lab study
stress by moment
(Moment due to bending [M] *c)/Polar moment of Inertia I=(1/12)b*(h^3)
3 Assumptions been made prior to derivation of torsion equations
1) assume stay in same cross section. 2) Torque applied is constant on sample 3) torque stopped at 5 degrees and sample unloaded back to initial position
3 limitations of Torsion Formula
1) must have circular cross section 2) Material is linearly elastic 3) equations only applicable within elastic range
What thickness (for given pressure vessel diameter) does thin shell assumption become inaccurate?
5% accuracy if <0.1 and 10% accuracy if <0.2, can use thin wall equation. At 0.35 in thickness, can't be considered thin walled
Ultimate Strength/tensile strength
Amount of stress that can handle before material ruptures/failure
Differences of experimental strains and theoretical strains in cantilever beam
Difference occurred due to loading applied. Axial strain more since bigger displacement of force and transverse strain smaller displacement due to distance. Human error in measurements.
Types of fracture that occur for different materials
Ductile fracture common for tested materials: elastic deformation, necking, complete failure. Steel was rupture without visible deformation.
Experimental ways to determine Young's Modulus
Dynamic testing (resonant frequency method), wave propagation ( ultrasonic echo pulse method), nanoindentation
Elastic behavior vs Inelastic behavior
Elastic behavior is ability to deform under a load, yet returns back to original shape. Inelastic behavior is ability to resist deformation, but once deforms does not return back to original.
Contribution of Poisson's Ratio in stress analysis and structural design?
Has a direct relationship between negative transverse strain and axial strain. Shows thickness of material deflection while cross sectional area of material deforms perpendicular to thickness.
Proportional limit
Highest stress which stress is proportional to strain. Elastic limit before permanent deforming
Large shafts for ocean liners are often hollow. Why?
Hollow shafts and rods can withstand higher torsion than solid ones. Hollow has higher torsional stiffness and this would hold better where solid rods would snap.
Why is oil used as a medium for pressurizing instead of air or oxygen?
Hydrogen has an explosive nature, thus would act like a bomb if pressure reaches critical point. Oil is not explosive and thus not a safety hazard. Also easier to see a leak with oil instead of hydrogen which is clear.
What properties of the material are measured or indicated by the modulus of elasticity?
Indicates the material's rigidity
Reciprocity theorem in Flexure Test
Instrument utilize metal strips placed along length of aluminum beam. As beam deformed so did strips. Charges changed as instrument lengthen or shortened. Change in currents expressed in length.
Deflection vs Young's Modulus: proportional or inversely proportional?
Inversely proportional to each other
Is it possible to determine point of intersection of an ISO clinic with free boundary? How about isochromatic?
It is possible for isoclinic, by using angle of inclination of the polarizer. Possible for isochromatic to intersect a free boundary for ring but not disk.
Yield point/strength
Load at which material begins to change shape permanently
Modulus of Resilience
Maximum energy that can be absorbed per unit volume without creating permanent distortion. Steel has a lower one, less energy per unit volume than aluminum. Steel stronger than aluminum
Modulus of elasticity (Youngs modulus) E
Measures the resistance of a material to elastic (Recoverable) deformation under load. High modulus changes shape barely under load like steel. Low modulus is like rubber. Tensile stress to tensile strain ratio.
Shear Modulus of Elasticity
Modulus of Rigidity (G). Ability to withstand torsion during torque. Shear stress to shear strain.
Can Isostatics intersect a free boundary at an angle other than 90 degrees?
No, isostatics can only intersect at 90 degree angle due to principle stresses always occur at perpendicular angle.
Can torsion equations be used in square shaft?
No, no constant radius on square shaft. In addition shaft would warp and not have same plane,unlike circular surface area of cylinder.
Negative Poisson's ratio
Possible. Auxetics are materials that have negative Poisson's Ratio. When force applied, material stretches and increases in thickness perpendicular to force.
Isostatic
Principle stress trajectories that come in pairs of perpendicular sets.
Isoclinics
Principle stress trajectories that don't come in pairs and identify directions of stress.
Complete Calculation of Poisson's Ratio?
Require both axial strain and lateral/transverse strain. Also need Uniform cross-section
How does shearing strain vary with distance from axis of shaft?
Shear strain increases farther way from the center of the shaft. Highest strain occurs in outer part or radius. With more bending the shear strain increases the farther away from the center of twist.
Why is an extensometer required for tensile tests or metals and alloys? Why not plastics?
The reason is because metals and alloys have an inelastic region where there is nonlinear relationship between stress and strain. Plastic plot would be linear
Use of areas beneath bending moment and shear force diagrams
Used to analyze and determine material and material properties. Deflection of beam calculated by area under bending moment diagram.
Can two isoclinics of different parameters intersect? What is the state of stress at intersection point?
Yes they can. First case when isoclinics are equal. Stress same. Second case when stresses located at same point, all basically zero. Last case when all stresses have same but opposing loads.
Can torsional procedure be used with hollow shaft?
Yes, it is possible since constant radius. Polar moment equation will be different though.
Cantilever beam vs simply supported beam
cantilever beam is beam fixed on one end, allowing deflect on other end. Simply supported is supported each end, deflection at center under loading.
