CHAPTER 5 CONCRETE PAVEMENTS - TU Delft

The value of the limit temperature gradient ∆tl follows from equalizing the equations
5.3 and 5.4 for both the center of the longitudinal slab edge and the center of the
transverse slab edge.
5.3.4 Stresses due to traffic loadings:
The basic theory for the structural design of plain concrete pavements has been
developed by Westergaard in 1926 (8). Westergaard considers a single, fully
supported slab (without any load transfer to adjacent slabs) of the concrete
pavement. The slab is resting on an elastic foundation, i.e. vertical elastic springs
with a stiffness k (the modulus of substructure reaction k, see 5.3.2).
Westergaard developed equations for the maximum flexural tensile stress in the
concrete slab and the maximum vertical displacement (deflection) of the concrete
slab due to a single wheel load, located in the interior (middle), along the edge or in a
corner of the slab (figure 5.9). In the cases that the single wheel load is in the interior
or along the edge of the slab, the flexural tensile stress is maximal at the bottom of
the slab in the center of the wheel load. In the case that the single wheel load is in a
corner of the slab, the flexural tensile stress is maximum at the top of the slab at
some distance (around 1 m) of the corner.
Figure 5.9: Positions of the load in Westergaard’s theory.
The edge loading case is most important for the structural design of plain concrete
pavements. There exist numerous Westergaard-equations for this loading case, but
the most correct equations (which yield nearly the same result) are the following
‘new’ Westergaard-equations from 1948 (9,10):
circular loading area
( 1 + υ)
( 3 + υ)
3
3 P ⎧ ⎛ E h ⎞ 4 1 − υ
σ =
⎨l
n ⎜
⎟ + 1.
84 − υ + + 1.
18 2
4
π h ⎩ ⎝100
k a ⎠ 3 2
semi-circular loading area
( 1 + υ)
( 3 + υ)
( ) ⎬
⎭ ⎫ a
1 + υ
2 (5.5)
3
3 P ⎪⎧
⎛ E h ⎞ 4
a ⎪⎫
2
σ =
⎨l
n
+ − + ( + ) ⎬
⎪⎩
⎜
⎟ 3.
84 υ 0.
5 1 2 υ
(5.6)
2
4
π h ⎝100
k a2
⎠ 3
l ⎪⎭
l
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