CT4860 STRUCTURAL DESIGN OF PAVEMENTS

'
4 y ( W − y)
transverse edge: R = (20b)
'2
W
where: L’ = slab span (mm) in the longitudinal direction
W’ = slab span (mm) in the transverse direction
X = distance (mm) of the point under consideration at the longitudinal
edge to the nearest transverse edge minus 1/3 of the support
length C
y = distance (mm) of the point under consideration at the transverse
edge to the nearest longitudinal edge minus 1/3 of the support
length C
The equations 17 to 19 make clear why nowadays relatively small concrete
slabs are applied in plain concrete pavements, with horizontal dimensions
smaller than about 5 m (roads) or 7.5 m (airports) respectively. For these slab
dimensions the span of the slabs both in the longitudinal (L’) and the
transverse (W’) direction is much smaller than the critical slab length lcrit,
''
resulting in reduced warping stresses σ (equation 19).
3.3.4 Temperature gradient stresses (Dutch method)
In the Netherlands originally VNC (Cement Industry Association) has
developed an analytical design method for plain concrete pavements (11,12).
Recently the method has been upgraded, and extended with continuously
reinforced concrete pavements, by CROW (5).
One has realized that the most critical point of the pavement structure is
somewhere at an edge of the plain concrete slab or at a crack of the
reinforced concrete slab. At the edges or cracks there is by definition a
uniaxial stress situation in the concrete slab (only stresses parallel to the edge
or crack and no stress perpendicular to the edge or crack). For the calculation
of the temperature gradient stresses this means that only a concrete beam
(with unit width) along the edge or crack needs to be taken into account and
not an entire plain concrete slab or a whole part of the reinforced concrete
pavement between two transverse cracks.
In the case of a small positive temperature gradient ∆t the warping (upward
displacement) of the concrete slab along the edge or crack is smaller than the
compression (downward displacement) of the substructure (characterized by
the modulus of substructure reaction k) due to the deadweight of the concrete
slab. This implies that the concrete slab remains fully supported (figure 12
left). The flexural tensile stress σt at the bottom of the concrete slab in the
center of a slab edge or crack can then be calculated by means of the
equation:
h⋅∆t
σ t = α E
(21)
2
t
28