Need To Learn Flashcards
What are the thin walled pressure vessel assumptions
Thin walled cylinder assumptions:
→ Stresses are uniform through radius
→ Magnitude of radial stress is so small compared to the hoop and longitudinal stresses it can be neglected
→ Isotropic linear elastic material properties
→ Ends of cylinder and any riveted joints have no effect on stresses
Perfectly cylindrical geometry which is axisymmetric
What are the assumptions and limitations of thick walled cylinder assumptions
→ A perfectly cylindrical geometry which is axisymmetric
→ Used Hooke’s Law, so assumed homogenous isotropic linear elastic material properties
→ Longitudinal stress is constant throughout the section, so assumes the ends of the cylinder and any riveted joints have no effect on the stresses
→ Any changes in cylinder dimension as a result of the pressure will remain in plane and not cause distortion
Only pressure loads are applied to the cylinder
What are the methods of assembling compound cylinders
→ Axial force (for small interference)
→ Heat up outer cylinder
→ Cool inner cylinder
→ Use hydraulic pressure to expand outer cylinder
→ Use materials with different degrees of thermal expansion then heat both
Work harden inner section of one thick cylinder, causing plastic deformation and residual stress formation upon cooling (autofretage)
Rotating disc assumptions
→ A perfectly cylindrical geometry which is axisymmetric
→ Homogenous isotropic linear elastic material properties
→ Longitudinal stress equal to zero
Any change in dimension will remain in plane and not cause distortion
Thermal gradient in rotating discs
T = a + br
Lame constant for a solid rotating disc
B = 0
Hydrostatic vs deviatoric
→ Hydrostatic stress is the same in all directions, but deviatoric stress can vary with direction
→ Deviatoric stress can cause plastic flow but hydrostatic stress does not
→ Hydrostatic stress relates to a volume change but deviatoric stress does not
→ Hydrostatic stress is a 1D line on a 3D yield surface plot, whereas deviatoric stress relates to the distance from that line
- To calculate the hydrostatic stress from a stress tensor, only the direct stresses are required, but to find the deviatoric stress then the whole stress tensor is needed for the calculation
comparison of failure criteria
Tresca and von mises work well for ductile metals under static loading, where tresca is more conservative
what can tresca and von mises not predict failure of
Brittle materials such as ceramics
Metals under fatigue loading
Many plastics and elastomers
Components with small defects or notches causing stress concentrations (such as those caused by corrosion, or manufacturing issues)
Failure under high load rates
assumptions of calcs in plastic flow regime
→ Proportional loading
→ Material is not affected by loading rate (cannot apply to viscoelastic materials)
→ Isotropic material properties
→ Purely plastic behaviour, with zero elastic strains and constancy of volume
Beam assumptions
→ The beam is initially straight and all bending is in-plane
→ The neutral axis remains the same length
→ Bending stress distribution is linear throughout the thickness
→ Constant bending moment along beam
→ After bending the changes in curvature of the beam is small (radius of curvature R is large)
Perfect elastic - plastic assumptions
→ Material is perfectly elastic during loading
→ When yield stress is reached, material is perfectly plastic and undergoes no strain hardening
Unloading is perfectly linear
what is shape factor
Shape factor: ratio of how much partial plastic deformation can withstand before collapse and can be used to select beam for a certain application
what is load factor
load to cause collapse/ working load
assumptions of limit analysis of beams
→ No elastic deformation occurs before plastic deformation
→ When a plastic hinge develops, the hinge occupies a length which is small in comparison to the length of the member
→ After the plastic hinge has formed, the section will allow free rotation without any increase in the moment
→ The number of ‘hinges’ which form will depend upon the beam support conditions and the applied loads, but never less than 2 for a statistically indeterminate beam
- The number and position of the plastic hinges must be correct for the beam and the loading conditions, otherwise the predicted plastic collapse load will be too high
stiffness vs strength
→ Strength can represent many different states of loading (e.g. elastic, plastic, fatigue). Stiffness only relates to elastic loading
→ A material which has a high UTS or yield is not necessarily stiff, and vice versa
→ Stiffness relates to how much deformation occurs, strength is largely independent of deformation (assuming no tensile instability)
→ Both strength and stiffness are dependent on geometry, but Young’s modulus is not.
→ The units are different, strength is always measured in Pascals (whether yield, UTS, fatigue strength), whereas stiffness is measured in N/m
