1. Structural Equivalency Lecture 10

2. Subbase Thickness, inches LTE=10% DC-10 Gear k=100 Subbase E=1x10 6 psi h- Varies LTE=10% 0510152025 25 20 15 10 5 0 18” 21” 24” Subgrade Stress, psi

3. Conventional Plate Theory o Single Placed Layer 1) Regard the base as contributing exclusively to the stiffness of the subgrade  k composite o Based of PCA tests (1950’s) o Volumetric approach o Backcalculation- matching Defl. Basin Basin Area

4. h1E1h1E1 h2E2h2E2 11 k heEeheEe ee k

6. Slab Action:  - Value

7. Equivalent Thickness h e-p  Equivalent Thickness  m  Measured Value k b  Back-calculated E c  Based on Cores

8. Unbonded Layers No separation during bending

9. Bonded System

10. unbonded or bonded Tandem Dual Tridem Tied or Extended Shoulder DoDo W L slab  = 0 or f

11. Bending Moment

12. Bending Moment - with Subbase

13. Bending Stress - with Subbase

14. Partially Bonded System cc ee  e-p hchc h e-p Transformed Section

15. Summary

16. Westergaard Special Theory

17. Basis of b and a correction factors Ordinary Theory: plane sections remain plane Special Theory: where vertical distortion is accounted for. Stress under a point loads tends to infinity (a & b were provided as correction factors)

18. for interior load:

19. Equation for b - b is a fictitious radius in the stress equation which yields the same tensile stress as the solutions by Nadai Point Loada=1/4 h b=0.3254hb=0.3709h b=0.705hb=0.504h b=1.456h b=0.944h b=1.967h a=h/2 a=3h/4 a=h a=1.5h a=2h

20. Nadai examined the area close to the load a small portion of the slab impressed with a uniform pressure and subgrade reaction pressure Boundary conditions used by Nadai not clear. - Used simple support reaction Westergaard selected n=5 For n  5, the subgrade reaction is small in comparison to the load on the surface and can be neglected. c uniform press. Vicinity close to loaded area Nadai Subgrade reaction (empirical soln.)

21. Westergaard Recommended In plotting against the following expression for b resulted where a=1.724h is where a=b; but a=0.5h may be just as appropriate. a=1.724h appears to be arbitrary.

22. 0 0.25 0.5 0.75 1 1.5 2 1 2 1.724h (c=b) 1.967 1.456 0.944 0.705 0.504 0.3709 0.3254 c/h Hyperbola Analytical results Figure 6-2. Relation among true radius b, slab thickness h (16).