$($a$)$ Develop a formulation for estimation of thermal bending stress $(\{$:$D^3)$ in coneretes$($a$)$ The governing equation of a rheological material is given as $=Re+$nhat$(f),$ Thie mialsial

is subjected to a stress situation as shown in Figure $1.$ Prediet its strain respanse cidevelyp

expressions and also show schematically$).$

Spavement slab $($assume one dimensional structure$).$ Explain the sign convention adopted.

$($b$)$ For, $T_B=T_0-\frac{T_1-T_b}{h}z,$ calculate ${}^{BT}$ at the bottom fibre $(z=+\frac{h}{2})$ under perfect

restrained condition.

$($c$)$ For the sign convention adopted in Q$\mathrm{.}4($a$),$ show that the $d^{.T}$ calculated in Q$\mathrm{.}4($b$)$ will

Te tensile, if $T_1>T_6.$

$($d$)$ For partial restrained condition $($that is$,$ when self weight has some finise value$),$

schematically draw $($calculations not necessary$)$ the variation between $({}^{\text{'}\text{'}})$ med, along the

length of the slab $(x),$ and explain the trend.

$($e$)$ If $T_c-T_b=T_c($say$),$ and if $T_c>T_o,$ estimate the length of the conserete slab $).$

$3$ Considering smooth movement of vehicles on the pavement, permissble gap in this,

expansion joint is stipulated as $g($refer Figure $2).$