Consider a $20$ m span deck unit and a design load combination of $1\mathrm{.}2$xDead load $+1$xTruck load calculate the following:

a$)$ Maximum reaction $($upward positive$)$

b$)$ Maximum positive moment at mid$-$span

c$)$ Maximum positive shear at quarter span length from the supports.

The bottom side of the beam can be heated to $250$ degrees Celsius, while the top side is at $40$ degrees Celsius. Considering the load combination of $1\mathrm{.}2x$ fire:

d$)$ Calculate the deflection at mid$-$span of $19$ m bridge deck. Assume the coefficient of thermal expansion for concrete is $1\frac{{10}^{-5}}{?}$ degrees Celsius.

Assume:

Deck units take only asphalt weight above them.

The bridge deck consists of deck units that are tied through post$-$tensioning tendons. The dead load on the deck units includes the self$-$weight and the asphalt weight.

Asphalt thickness is uniform across the deck and equals $110$ mm $,$ unit weight of asphalt is $21\mathrm{.}2k\frac{N}{m_{{?}_{?}}^3}$

Use the cross section given in the drawings to calculate area $($cross section $10$ m and $19$ m spans$)-$ concrete material has $25k\frac{N}{m^3}$ unit weight.

Assume truck load is equally distributed between deck units. To find the share of each unit, divide the total response by number of units across the deck.

There is a live load represented by a T$44$ truck on the bridge.