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<ul><li>II)  Properties of Materials </li></ul><ul><li>A.) Tension Test </li></ul> Stress   ), ksi Strain (  ), in/in...
<ul><li>B. Mechanical Properties of Materials </li></ul><ul><li>1.) Ultimate Strength (   U ) - The  maximum stress a mat...
<ul><li>3.) Proportional Limit (   PL ) - The  maximum stress a material will  withstand before stress-strain  relationsh...
<ul><li>5.) Ductility </li></ul><ul><li>Ductile Material - will undergo plastic  deformation before failing </li></ul> S...
<ul><li>6.)Brittleness </li></ul><ul><li>Brittle Material - will fail without any plastic deformation (opposite of ductile...
C.)  Allowable Stress, Actual Stress,    Factor of Safety
<ul><li>1.) The Actual Stress,    is the amount of stress in a member due to the applied load.  </li></ul><ul><li>  = P/...
<ul><li>2.) Allowable Stress (continued) </li></ul><ul><li>The allowable stress is determined by applying a Factor of Safe...
<ul><li>- FS depends on the </li></ul><ul><li>a.) Material - properties & variability </li></ul><ul><li>b.) Importance of ...
<ul><li>Example:  Suspending yourself from a 300’ high building with a cable.  </li></ul><ul><li>How big must  the cable b...
<ul><li> all  =   Y  _ =  36,000 psi  = 9,000 psi </li></ul><ul><li>  FS 4.0 </li></ul><ul><li>In structural design, we ...
<ul><li>The absolute smallest  Area (A) we can safely use is when the actual stress is equal the allowable stress.  </li><...
<ul><li>So the bare minimum diameter is 0.168” </li></ul><ul><li>Readily available sizes are in diameter increments of 1/1...
 
Spreadsheet   for HW # 10-4 256.7577 0.21 53.9 0.42 10.8 322.017 0.2 64.4 0.4 12.9 388.3064 0.18 69.9 0.36 14 433.7244 0.1...
<ul><li>Example:  Hyd. Piston Rod Stainless Steel </li></ul><ul><li> y  = 40 ksi  FS = 1.5 </li></ul><ul><li>A  = ( 10,00...
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311 Ch10

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311 Ch10

  1. 1. <ul><li>II) Properties of Materials </li></ul><ul><li>A.) Tension Test </li></ul> Stress  ), ksi Strain (  ), in/in  PL  Y  U E =  =slope
  2. 2. <ul><li>B. Mechanical Properties of Materials </li></ul><ul><li>1.) Ultimate Strength (  U ) - The maximum stress a material will withstand before fracture. </li></ul><ul><li>2.) Yield Strength (  Y ) - The maximum stress a material will withstand before deforming permanently. </li></ul>
  3. 3. <ul><li>3.) Proportional Limit (  PL ) - The maximum stress a material will withstand before stress-strain relationship becomes non-linear. </li></ul><ul><li>4.) Modulus of Elasticity - the ratio of stress over strain in the linear region of the stress-strain curve. </li></ul>
  4. 4. <ul><li>5.) Ductility </li></ul><ul><li>Ductile Material - will undergo plastic deformation before failing </li></ul> Stress Strain Ductile Material
  5. 5. <ul><li>6.)Brittleness </li></ul><ul><li>Brittle Material - will fail without any plastic deformation (opposite of ductile) </li></ul> Stress Strain Brittle Material
  6. 6. C.) Allowable Stress, Actual Stress, Factor of Safety
  7. 7. <ul><li>1.) The Actual Stress,  is the amount of stress in a member due to the applied load. </li></ul><ul><li> = P/A </li></ul><ul><li>2.) Allowable stress  all of a material is the maximum stress that may be considered safe for a given structural member. </li></ul><ul><li>  = P/A <  all </li></ul>
  8. 8. <ul><li>2.) Allowable Stress (continued) </li></ul><ul><li>The allowable stress is determined by applying a Factor of Safety (FS) to the yield strength or ultimate strength. </li></ul><ul><li> all =  Y or  all =  U </li></ul><ul><li>F.S. F.S. </li></ul><ul><li>FS varies from 1.5 to 3 in typical design situations. </li></ul>
  9. 9. <ul><li>- FS depends on the </li></ul><ul><li>a.) Material - properties & variability </li></ul><ul><li>b.) Importance of the product </li></ul><ul><li>c.) Uncertainty of the load </li></ul><ul><li>- FS ensures the yield strength will not be </li></ul><ul><li> exceeded. </li></ul><ul><li>- FS allows for flaws in the material & </li></ul><ul><li>workmanship. </li></ul>
  10. 10. <ul><li>Example: Suspending yourself from a 300’ high building with a cable. </li></ul><ul><li>How big must the cable be to hold you? </li></ul><ul><li>Assume the cable has a solid circular cross-section and is made of A36 steel . </li></ul><ul><li> Y = 36,000 psi (p617) </li></ul><ul><li> </li></ul><ul><li>F.S. = 4.0 ( safe enough?) </li></ul><ul><li>P = 200 lb (your weight) </li></ul>
  11. 11. <ul><li> all =  Y _ = 36,000 psi = 9,000 psi </li></ul><ul><li> FS 4.0 </li></ul><ul><li>In structural design, we want to find the smallest cross-sectional area (A) that will safely hold a known force (P). </li></ul><ul><li>The smaller the area (A) is, the higher the actual stress (  ) will be. </li></ul><ul><li> = P </li></ul><ul><li> A </li></ul>
  12. 12. <ul><li>The absolute smallest Area (A) we can safely use is when the actual stress is equal the allowable stress. </li></ul><ul><li>200 lb = 9,000 psi </li></ul><ul><li> A </li></ul><ul><li>A = 200 lb __ = 0.0222 in 2 </li></ul><ul><li> 9,000 psi </li></ul><ul><li> d = [4(0.0222 in 2 )  1/2 = 0.168 in </li></ul>
  13. 13. <ul><li>So the bare minimum diameter is 0.168” </li></ul><ul><li>Readily available sizes are in diameter increments of 1/16”. </li></ul><ul><li>2/16” = 0.125” (too small) </li></ul><ul><li>3/16” = 0.188” > 0.168” (OK) </li></ul>
  14. 15. Spreadsheet for HW # 10-4 256.7577 0.21 53.9 0.42 10.8 322.017 0.2 64.4 0.4 12.9 388.3064 0.18 69.9 0.36 14 433.7244 0.16 69.4 0.32 13.9 559.5056 0.116 64.9 0.232 13 907.7293 0.055 49.9 0.11 10 2212.747 0.01805 39.9 0.0361 8 6490.265 0.006 38.9 0.012 7.8 18182.03 0.00215 39.1 0.0043 7.83 31952.07 0.00125 39.9 0.0025 8 31531.65 0.00095 30.0 0.0019 6 30723.15 0.00065 20.0 0.0013 4 33283.41 0.0003 10.0 0.0006 2 0 0.0 0 0 (ksi) (in) (kips) E Strain Stress Deformation Load
  15. 16. <ul><li>Example: Hyd. Piston Rod Stainless Steel </li></ul><ul><li> y = 40 ksi FS = 1.5 </li></ul><ul><li>A = ( 10,000 lb )(1.5) = 0.375 in 2 </li></ul><ul><li>(40,000 psi) </li></ul><ul><li>D =[ (4 )( .375 in 2 )/  ] 1/2 = 0.69” = 3/4” </li></ul>10000lb 10000 lb

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