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Crack Pattern Development

Crack Pattern Development. CRC Pavement Vetter, C.P. 1933 Reinforced Concrete Drying Shrinkage Temperature Drop. Consider a unit Length (L) between cracks . is restrained by the reinforcement . Causes tension in concrete & compression in the steel.

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Crack Pattern Development

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  1. Crack Pattern Development Rigid Pavement Design Course

  2. CRC Pavement • Vetter, C.P. 1933 • Reinforced Concrete • Drying Shrinkage • Temperature Drop • Consider a unit Length (L) between cracks • . is restrained by the reinforcement • . Causes tension in concrete & compression in the steel. • . Bond stress between steel & concrete and the concrete & subgrade Rigid Pavement Design Course

  3. (1) Bond stress in the vicinity of crack (2) Compression in steel and tension in the concrete increases until steel = concrete. In this region there is no bond slip or stress. d. Subsequent crack form in concrete when bond stress exceeds the concrete tensile strength. Rigid Pavement Design Course

  4. Traverse Crack Longitudinal Joint C L L ‘t’ Free Edge Rigid Pavement Design Course

  5. Crack Asfsc Asfs Acft Section YY Section XX Forces Acting on CRC Pavement Section Probable Strain Distribution Adjacent to a Crack Rigid Pavement Design Course

  6. Extensive bond slip Good bond Crack L/2=nSmin Rigid Pavement Design Course

  7. Strain Steel strain Crack width: equation 2.10a Tension Smin or (L-2x)/2 Crack width: equation 2.10b Compression Concrete strain Unrestrained shrinkage strain Rigid Pavement Design Course

  8. L Condition of no stress c b/2 h Stressed, full restraint cw c.g. of bond Steel stress Concrete Stress Stresses and Strains in Fully Restrained, Cracked Reinforced Concrete for Decreasing Temperature Rigid Pavement Design Course

  9. Assumptions of Vetter Analysis • 1. Volumetric ‘s are uniformly distributed. • 2. Compatibility exists in bonded region. • 3. Total bond force= • Total Tensile Force= • Total change in the steel stress • 4. Total length of steel will remain unchanged. Total elongation = Total shortening • 5. Equilibrium exists between forces at crack & the forces in the fully bonded region. • In partially bonded region; compatibility of deformation does not exist. • Crack width results from relative displacement between the steel and the concrete. Rigid Pavement Design Course

  10. fsz Compression fsz Tension Tension x1 a) Steel Stresses C of Crack L ftz Tension b) Concrete Stresses u Bond Stress Bond Stress x L c) Bond Stresses Stress Distribution Between Cracks Subject to Shrinkage Rigid Pavement Design Course

  11. (1) Center of crack spacing (2) Bond Force = Concrete tensile force = Change in steel force (3) Total length of steel bars remain unchanged total shortening= total elongation Rigid Pavement Design Course

  12. Total Shortening = Total Elongation Note Rigid Pavement Design Course

  13. For temp. drop Both Rigid Pavement Design Course

  14. Tension a) Steel Stresses C of Crack L b) Concrete Stresses u Bond Stress Bond Stress y L c) Bond Stresses Stress Distribution Between Cracks Subject to Temperature Drop Rigid Pavement Design Course

  15. (1) Center of crack spacing (2) Bond Force = concrete tensile force = change in steel force (3) Total length of steel bars remain unchanged total shortening= total elongation Rigid Pavement Design Course

  16. For temp. drop Both Rigid Pavement Design Course

  17. 20 18 16 12 8 4 0 Pavements Placed During Winter = Summer = Average Crack Spacing (ft) 2 3 4 5 6 7 Ratio of Steel bond Area to Concrete Volume x 10-2 (in.2/in.3) Rigid Pavement Design Course Relationship Between Steel Bond Area and Crack Spacing

  18. Development Length Allowable Bond Stress Design Strength of the Bar ACI Definition of Development Length (a) Assumed and Actual Bond Stress-Slip Relationships. Rigid Pavement Design Course

  19. Development Length Actual Bond Stress Vetter Allowable Bond Stress Force in Bar Under Working Stress Condition Stress Transfer Length (b) Rigid Pavement Design Course

  20. Actual bond Stress-Slip Relationship As Modeled in Computer Program Bond Stress Relative Slip Between Concrete and Steel (c) Rigid Pavement Design Course

  21. concrete tension specimen steel bar a b P (a) • x-Displ. • Slip (b) ACI x (c) Sb Determination of Slip from Strain Functions Rigid Pavement Design Course

  22. Rigid Pavement Design Course

  23. Rigid Pavement Design Course

  24. Relative to temperature drop Max. drop to cause L = 2x substitute for in equation  For a greater temp. drop t2……only if otherwise Rigid Pavement Design Course

  25. Rigid Pavement Design Course

  26. Rigid Pavement Design Course

  27. Structural Response Models Uniform Bond Stress Distribution Vetter: Shrinkage and Temperature Drop Zuk: Shrinkage Friberg: Temperature Drop Rigid Pavement Design Course

  28. Hughes: Shrinkage and temperature Drop (concrete only) Rigid Pavement Design Course

  29. CRCP-2: Computer Model for Shrinkage and Temperature Drop (force equilbrium) Regression Equations: Rigid Pavement Design Course

  30. Non-Uniform Bond Stress Distribution TTICRCP: Computer model for Shrinkage and Temperature Drop (force equilibrium and energy balance) Reis: Shrinkage and Temperature Drop Um u x L Percent Steel (p) ; prevent yielding ; p=pmin fs=fy Rigid Pavement Design Course

  31. 2002 AASHTO Guide CRC Design K2  K1  Rigid Pavement Design Course

  32. Crack Width Rigid Pavement Design Course

  33. Crack Spacing Distribution %P v c. spc Rigid Pavement Design Course

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