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For all the problems describe all pieces to the equations. 1.What is the equation for normal stress? 2.What is the equation for shear stress? 3.What is the equation for cross sectional area of a beam? 4.What is the equation for cross sectional area of a shaft? 5.What is the equation for shear stress at an angle to the axis of the member? 6.What is the equation for normal stress at an angle to the axis of the member? 7.What is the equation for the factor of safety? 8.What is the equation for strain under axial loading?

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Answer:

  1. stress equation : [tex]\frac{p}{A}[/tex]    
  2. Shear stress equation : [tex]\frac{Qv}{Ib}[/tex]  
  3. cross sectional area of a beam equation : b*d  
  4. cross sectional area of a shaft equation : [tex]\frac{\pi }{4} (d)^{2}[/tex]  
  5. shear stress at an angle to the axis of the member equation: [tex]\frac{P}{A}[/tex] sin∅cos∅.
  6. Normal stress at an angle to the axis of the member equation: [tex]\frac{P}{A} cos^{2}[/tex]∅
  7. factor of safety equation : [tex]\frac{ultimate stress}{actual stress}[/tex]  
  8. strain under axial loading equation: [tex]\frac{PL}{2AE}[/tex]    

Explanation:

The description of all the pieces to the equations

  1. stress equation : [tex]\frac{p}{A}[/tex]     p = axial force, A = cross sectional area
  2. Shear stress equation : [tex]\frac{Qv}{Ib}[/tex]  Q = calculated statistical moment, I = moment of inertia, v = calculated shear, b = width of beam
  3. cross sectional area of a beam equation : b*d     b=width of beam,       d =depth of beam
  4. cross sectional area of a shaft equation : [tex]\frac{\pi }{4} (d)^{2}[/tex]   d = shaft diameter
  5. shear stress at an angle to the axis of the member equation: [tex]\frac{P}{A}[/tex] sin∅cos∅.  P = axial force, A = cross sectional area  ∅ = given angle
  6. Normal stress at an angle to the axis of the member equation: [tex]\frac{P}{A} cos^{2}[/tex]∅  p = axial force , A = cross sectional area, ∅ = given angle
  7. factor of safety equation : [tex]\frac{ultimate stress}{actual stress}[/tex]  
  8. strain under axial loading equation: [tex]\frac{PL}{2AE}[/tex]    P = axial force, L = length, A = cross sectional area, E = young's modulus

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