Q$3.$ A $2-$span semi$-$integral bridge consists of a $7\mathrm{.}5m$ wide superstructure, a square pier $(1\mathrm{.}41\mathrm{.}4m),$

and seat$-$type abutments at the ends. Assume the bridge to be located in Bhuj, Gujarat and pier

foundation as open type isolated footing resting on soil having SPT value, $N=9.$ Assume DL of

superstructure $=280k\frac{N}{m}$; Wearing coat load $=22k\frac{N}{m}.$ Given forces on pier due to IRC Class $70$R

wheeled loading; Axial force $=700kN,$ Longitudinal live load moment $=650kN-m$; Transverse live

load moment $=1200kN-m.$ Grade of concrete $=$ M$35$; Grade of Steel $=$ Fe $415$; Clear cover $=40mm$;

Importance factor $=1\mathrm{.}2$; Depth of superstructure $=2m.$ Also, assume unconstrained rotational and

translational boundary conditions at the abutment. Marks$]$

$($a$)$ Calculate the design forces on the bridge pier in the transverse direction using the seismic coefficient

method by idealizing it as SDOF with the mass of superstructure and $80\%$ mass of pier lumped at the

top of the pier. Neglect $30\%$ longitudinal direction earthquake load while calculating design forces

$($DL$+$LL$+$EQ$)$ using partial safety factors for verification of structural strength.

$($b$)$ Is ductile reinforcement detailing necessary for the bridge pier in part $($a$)?$ If yes, why is it required,

and what are the steps to be followed such that brittle mode of failure is avoided? Why did we consider

the overstrength factor while assessing the plastic moment capacity of the bridge pier?

$($c$)$ Calculate the wind forces on the superstructure in longitudinal, transverse, and vertical directions.

Also, calculate the total wind force and moment at the base of bridge pier in the transverse direction.

$($d$)$ Calculate the water current force on bridge pier. Assume the pier to be parallel to the direction of

water current, velocity of flow $=1\mathrm{.}2\frac{m}{s},$ and $HFL=4m$ above the base of pier. Assume velocity of

water as zero at the base of pier.

$($e$)$ To reduce the seismic forces, the structural engineer decided to change the bridge type to a multi$-$

span continuous $($MSC$)$ bridge. In the MSC bridge, the superstructure is supported on four numbers

elastomeric bearings $($EB$)$ which are used to transmit horizontal seismic forces. The bearings $(4$ nos.$)$

are located on the top of the pier. The dimension of the bearing is $600400100mm$ and consists of

$6$ numbers of $5mm$ steel plates. Calculate the change in the time period of the bridge and seismic

coefficient $A_h$ in the transverse direction.