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IX.) Combined Stresses A.) Biaxial Bending    b  =  M x   +  M y S x   S y
B.) Combined Bending & Axial Stresses    =  +   P   +   M A  S
C.) Eccentrically Loaded Axial Members M = Pe , where  “e” = “eccentricity”    =  +   P   +   Mc  ,  A  I Replace M with Pe:    =  +   P   +   Mc   A  I
D.) Stress Element  x   = Normal Stress in x direction  y   = Normal Stress in y direction   xy  = Shear Stress in x and y direction   y  xy  x  xy x  xy  xy  y  x
D.) Combined Normal & Shear Stresses  n   =   x  cos 2  y  sin 2  xy  sin   cos   v   = (  x  y  sin   cos  xy  cos 2  sin 2   y  n  v  xy  x  xy y x 
E.) Maximum Normal Stresses  (Principal Stresses)  1,2   =  0.5(  x  y    (  x  y   +   xy    The maximum  normal  stresses occur on a plane whose normal is at the angle   p  with the x-axis, determined from: tan(2  p ) =   xy   (  x   y 
F.) Maximum Shear Stress   v,max   =      (  x  y   +   xy   The maximum shear stress occurs on a plane whose normal is at the angle   v  with the x-axis, determined from: tan(2  v )  =  (  x   y   xy 
[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object]
G.)Mohr’s Circle
G.)Mohr’s Circle

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311 Ch17

  • 1. IX.) Combined Stresses A.) Biaxial Bending  b = M x + M y S x S y
  • 2. B.) Combined Bending & Axial Stresses  = + P + M A S
  • 3. C.) Eccentrically Loaded Axial Members M = Pe , where “e” = “eccentricity”  = + P + Mc , A I Replace M with Pe:  = + P + Mc A I
  • 4. D.) Stress Element  x  = Normal Stress in x direction  y  = Normal Stress in y direction  xy  = Shear Stress in x and y direction  y  xy  x  xy x  xy  xy  y  x
  • 5. D.) Combined Normal & Shear Stresses  n  =  x  cos 2  y  sin 2  xy  sin  cos   v  = (  x  y  sin  cos  xy  cos 2  sin 2   y  n  v  xy  x  xy y x 
  • 6. E.) Maximum Normal Stresses (Principal Stresses)  1,2  = 0.5(  x  y    (  x  y   +  xy   The maximum normal stresses occur on a plane whose normal is at the angle  p with the x-axis, determined from: tan(2  p ) =  xy   (  x  y 
  • 7. F.) Maximum Shear Stress  v,max  =   (  x  y   +  xy  The maximum shear stress occurs on a plane whose normal is at the angle  v with the x-axis, determined from: tan(2  v ) = (  x  y   xy 
  • 8.
  • 9.