AASHTO 8th 2017 Figure 3.12.3-2 Temperature Gradient

Figure 1: From AASHTO
Figure 1: From AASHTO

What AASHTO refers to as “Steel Girder Structures” implies composite as \(t\) is stated as the depth of the concrete deck.

Symbol Description
\(H\) Depth of superstructure

Value of A

For composite sections:

\[ A = 12'' \]

For concrete sections:

\[ A = max(16'' - H, 12'') \]

Intersection between Segments 1 and 4

\[\begin{align} \frac{t - 0''}{4'' - 0''} & = \frac{T_{seg1} - T_{1}}{T_{2} - T_{1}} \\ T_{seg1} & = \frac{t}{4''}(T_{2} - T_{1}) + T_{1} \end{align}\]

Intersection between Segments 2 and 4

\[\begin{align} \frac{t - 4''}{A + 4'' - 4''} & = \frac{T_{seg2} - T_{2}}{0 - T_{2}} \\ \bigg(\frac{t - 4''}{A}\bigg)(-T_{2}) + T_{2} & = T_{seg2} \\ T_{seg2} & = T_{2}\bigg(1 - \frac{t - 4''}{A}\bigg) \end{align}\]

Value of \(T_{4}\)

\[ T_{4} = max(T_{seg1}, T_{seg2}, 0) \]

Intersection between Segments 3 and 4

Figure 2: Where T3 > 0 and T4 > 0 and T4 < T3
Figure 2: Where T3 > 0 and T4 > 0 and T4 < T3