ME222 Formula Sheet 4 PDF

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last exam formula sheet that is provided...

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FormulaSheet   Table1:GeometricPropertiesofcommonshapes Rectangle Circle 



 

1   12











Semi‐circle



4  3    2

   

 



       



 ParallelAxisTheorem:         Table2:MaterialDatainEnglishandSIunits.  Steel Cupronickel Aluminum 20x106 psi 10x106psi Young’sModulus 30x106psi (210GPa) (140GPa) (70GPa) 6 7.5x106 psi 4x106psi ShearModulus 11x10 psi (80GPa) (52GPa) (28GPa) CoefficientofThermal 6.5x10‐61/F 9.75x10‐61/F 13x10‐61/F ‐6 ‐6 Expansion (18x10 1/ C) (24x10‐61/ C) (12x10 1/C)   CombinedLoading: Alternativeapproachforshearstressesonyor       zaxes:



 

 



   









  | |     



SphericalPressureVessel:

  





  | |     

 CylindricalPressureVessel: 





   

 

 

        

        

        2     



  2



Stresstransformations(2D):

 󰆓 

  

   cos 2   sin 2 2 

2        󰆓   cos 2   sin 2 2 2     󰆓  󰆓   sin 2   cos 2 2

Straintransformations(2D):

 󰆓

  

 sin 2    cos 2  2 2 2         cos 2   sin 2 2 2 2

 󰆓 



 󰆓  󰆓   󰇛   󰇜sin 2   cos 2

Straintransformationsusedwithstraingagerosettes(fortheithdirection): 

   cos     sin    sin  cos  

 2Dprincipalstresses:

, 

2              󰇢    󰇡 tan 2       2 2 2

 Staticdesigncriteriabasedonmaterialfailure: MaxPrincipalStressCriterion(Rankine):



Designissafewhen:  Andwhen:

Designissafewhen:

AngleofTwist:







 

   

  





 

 Hooke’sLaw:                                                     

  

 Radiusofcurvature: 1       ThermalDeformation:   󰇛Δ󰇜



 

  

     

  

  

MaxShearStressCriterion(Tresca):

  AxialDeformation:





  





 2󰇛1  󰇜

 





 

Eulerbuckling:



 

 













...