CT4860 STRUCTURAL DESIGN OF PAVEMENTS

3.4 Stresses and displacements due to traffic loadings
3.4.1 Introduction
In 1926 Westergaard published his original equations for the calculation of the
maximum flexural tensile stress and the maximum vertical displacement due
to a single wheel load in the interior, at the edge or at the corner of a single
concrete slab. In latter years Westergaard himself as well as other
researchers published several ‘modified’ Westergaard-equations. Until today
this Westergaard-theory is widely used all over the world to calculate the
stresses and displacements in concrete pavement structures due to traffic
loadings. The Westergaard-theory is described in 3.4.2.
In reality a concrete pavement structure does not exist of a single concrete
slab, but of a number of concrete slabs with longitudinal and transverse joints
(plain concrete pavements) or longitudinal joints and transverse cracks
(reinforced concrete pavements). The load transfer in these joints and cracks,
and the consequences for the stresses and displacements of the concrete
pavement structure, are discussed in 3.4.3.
3.4.2 Single concrete slab (Westergaard-theory)
Westergaard developed a theory for the maximum stress (flexural tensile
stress) and the maximum vertical displacement (deflection) due to a single
wheel load, located in the interior (middle), along the edge or in a corner of a
single (concrete) slab on an elastic foundation (springs with a stiffness equal
to the modulus of substructure reaction k).
The fully supported slab is assumed to be such large, that the edges and
corners don’t have any significant influence on the maximum stress and
deflection.
In the cases that the single wheel load is in the interior or along the edge or
crack of the concrete slab, both the flexural tensile stress and deflection are
maximum at the bottom of the concrete slab in the load centre. In case of a
single wheel load in the corner of the slab, the deflection is maximum exactly
in the corner while the flexural tensile stress is maximum at some distance of
the corner at the top of the concrete slab (figure 13).
Figure 13. Loading positions in Westergaard’s theory.
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