Structural Equivalency Lecture 10

Subbase Thickness, inches LTE=10% DC-10 Gear k=100 Subbase E=1x10 6 psi h- Varies LTE=10% ” 21” 24” Subgrade Stress, psi

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

h1E1h1E1 h2E2h2E2 11 k heEeheEe ee k

Slab Action:  - Value

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

Unbonded Layers No separation during bending

Bonded System

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

Bending Moment

Bending Moment - with Subbase

Bending Stress - with Subbase

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

Summary

Westergaard Special Theory

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)

for interior load:

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

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.)

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.

h (c=b) c/h Hyperbola Analytical results Figure 6-2. Relation among true radius b, slab thickness h (16).