# AS 5100.2:2017 Clause 18.3 Differential temperature

## Surfacing reduction factors

NOTE: These design temperature gradients have been derived for cases where decks are unsurfaced or where surfacing will be limited to 50 mm of bituminous concrete. For substantially greater thicknesses of surfacing, some reduction in design temperature gradients may be warranted.

There is no guidance on potential reduction factors in AS 5100, but Eurocode 2 Table 6.2 provides reduction factors for surfacing thicknesses other than 50mm.

Surfacing (mm) Concrete Heating Concrete Cooling Composite Heating Composite Cooling
unsurfaced 0.8 1.1 0.9 1.0
water-proofed 1.5 1.0 1.1 0.9
50 1.0 1.0 1.0 1.0
100 0.7 1.0 1.0 1.0
150 0.5 1.0 1.0 1.0
ballasted (750mm) 0.6 1.0 0.8 1.2

## Derivations

\begin{align} T(D) & = T(t) \\ & = (T+5)(1 - \frac{t}{1200})^{5} \end{align}
$D' = min(300, D)$
\begin{align} \frac{T(y) - T_{1}}{T_{2} - T_{1}} & = \frac{y - y_{1}}{y_{2} - y_{1}} \\ \frac{T(y) - (0.4T - 3)}{0 - (0.4T - 3)} & = \frac{y - 0}{D' - 0} \\ T(y) - 0.4T + 3 & = (-0.4T + 3)\frac{y}{D'} \\ T(y) & = (0.4T - 3)(1 - \frac{y}{D'}) \end{align}
\begin{align} T(D) & = T(t) \\ & = (0.4T - 3)(1 - \frac{t}{D'}) \geq 0 \\ & = (0.4T - 3)(1 - \frac{t}{min(300, D)}) \geq 0 \end{align}