$($a$)$ Explain the techniques of pre $-$tensioning.

$($Or$)$

$($b$)$ Describe briefly about systems of post tensioning.

$($a$)$ A concrete beam of dimension $100mm300mm$ is post$-$tensioned with $5$ straight wires of $7mm$ diameter. The average prestress after short$-$term losses is $0\mathrm{.}7fpk=1200\frac{N}{m}m2$ and the age of loading is given as $28$ days. Given that Ep $=200103$MPa,$E_c=35000$MPa, find out the losses of prestress due to creep, shrinkage and relaxation. Neglect the weight of the beam in the computation of the stresses.

$($Or$)$

$($b$)$ Elaborate about the effects of long$-$term deflection of prestressed concrete members due to creep and shrinkage.

$($a$)$ A pre stressed concrete $T$ section has $1800mm200mm$ flange. $450mm1500mm$ rib and $100$ nos of $8mm$ HTS wires are located at $1600mm$ from the top of flange. Estimate the flexural strength of the beam using M$40$ grade concrete and Fe$1600$ grade steel.

$($Or$)$

$($b$)$ The support section of a pre$-$stressed concrete beam $100mm$ wide and $250mm$ deep is required to support an ultimate shear force of $60kN.$ The compressive pre$-$stress at the centroidal axis is $5\frac{N}{m}{m}^2.$ The characteristics cube strength of concrete is $40\frac{N}{m}{m}^2.$ The cover to the tension reinforcement is $50mm.$ If the characteristic tensile strength of steel in stirrups is $250\frac{N}{m}{m}^2.$ Design suitable reinforcement at the section using IS $1343$ recommendations.

$14.($a$)$ Design a cylindrical prestressed concrete water tank to suit the following data: Capacity of tank $=24500106$ litres. Maximum compressive stress in concrete at transfer not to exceed $13\frac{N}{m}{m}^2($compression$).$ Minimum compressive stress under working load to be $1\frac{N}{m}{m}^2.$ The prestress is to be provided by circumferential winding of $7mm$ dia with an initial stress of $1000\frac{N}{m}{m}^2$ and by vertical cables of $12$ wires of $8mm$ diameter which are stressed to $1200\frac{N}{m}{m}^2.$ Loss ratio $=0\mathrm{.}75.$ The cube strength of concrete is $40\frac{N}{m}{m}^2.$ Design the walls of the tank and details of circumferential wire winding and vertical cables for the following joint condition at the base: elastomeric pads $($assume coefficient of friction as $0\mathrm{.}5).$

$($Or$)$

$($b$)$ A prestressed concrete pipe of $1\mathrm{.}2m$ diameter, having a core thickness of $75mm$ is required to withstand a service pressure intensity of $1\mathrm{.}2\frac{N}{m}{m}^2.$ Estimate the pitch of $5mm$ diameter high tensile wire winding if the initial stress is limited to $1000\frac{N}{m}{m}^2.$ Permissible stresses in concrete being $12\frac{N}{m}m2$ in compression and zero in tension. The loss ratio is $0\mathrm{.}8,$ if the direct tensile strength of concrete is $2\mathrm{.}5\frac{N}{m}{m}^2,$ estimate load factor against cracking.

$15.($a$)$ Write step by step procedure for the design of two way concrete prestressed slab $($Or$)$

$($b$)$ Summarize the primary design consideration in the design of prestressed concrete one way slabs.