| Design principle
The tie bars are designed to withstand tensile stresses, the maximum tensile force in the tie bar is made equal to the force required to overcome frictional force between the bottom of the adjoining pavement slab and the soil subgrade. Estimation of spacing and length of tie bar is explained in the following. Estimation of spacing of tie bar
Since the purpose of the tie bar is to tie
concrete slabs together, the area of steel per unit length
of longitudinal joint is obtained by equating the total friction
to the total tension developed in the tie bar system (as
explained in Figure 24).
Thus,
 |
(29) |
where μ = co-efficient of friction between
concrete slab and the sub-base, W = weight of the concrete
slab per unit length (say per meter), σst =
allowable working stress in tension for the steel used as
tie bar, Ast= cross-sectional area of steel per
unit length (say per meter). The weight of concrete slab
per unit length can be written as,
 |
(30) |
where, w = weight of
slab per unit volume (say, cubic meter), B = width
of the slab, and h = height of the slab. Thus,
from Equation (29) and (30), the area of steel per unit length,
 |
(31) |
Assuming suitable diameter of tie bar, the spacing of tie bar can be found out so as to the requirement of steel per unit length.
Estimation of length of tie bar
Consider a single tie bar. The tensile force
developed in the tie bar should not exceed the bond strength
between the tie bar and the concrete, otherwise it can be
pulled out of concrete. Thus, considering one end of the
tie bar,
 |
(32) |
where, as = cross-sectional area of one tie-bar, P = perimeter of one tie bar, l = length of tie bar inside the concrete slab, Sb = allowable bond strength between the concrete and the tie bar.
Thus, total length of the tie bar, can be
written as,
 |
(33) |
where z = allowance due to inaccurate
centering of the tie bar.
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