$00$:$56$

$584$

Introduction

You are a graduate engineer of a design team. Your team is currently working for a project about design of a highways bridge using precast beams. You are assigned to design the prestressing system based on the following information given by your supervisor.

Design Basis

General Arrangement of precast beam

Total length of the beam is $30m.$

Precast beams are simply supported on bearings.

Bearings center to center spacing is $29\mathrm{.}2m$

Relevant drawings are shown in appendix $1.$

Materials

$ENC_{40}$ concrete

Unit weight of concrete is $25k\frac{N}{m^2}$

Reinforcement grade $S500,$ i$.$e$.f_k=500$MPa

Prestressing steel, $f_{pk}=1860$MPa and $f_{p0\mathrm{.}1k}=1640$MPa

Loading

Construction: Imposed loads are composed of

a$)$ Dead load of the beam, and

b$)$ Concrete slab $3\mathrm{.}5m$ wide and $0\mathrm{.}15m$ thick, constructed on top of the beam.

Operation: Imposed loads are composed of

a$)$ surfacing load of $3\mathrm{.}5m$ wide and $0\mathrm{.}1m$ thick.

b$)$ Traffic load of $5$kPa

SLS and ULS Design requirement

SLS $-$ Assume $1\mathrm{.}0$ for all loadings.

ULS $-$ Assume $1\mathrm{.}35$ for structural dead load, $1\mathrm{.}5$ for superimposed dead load and $1\mathrm{.}35$ for live load

All stress limitation criteria shall comply with EN$1992-1-1$

Environmental Factor

Annual Average Relative Humidity $=70\%$

Annual Average temperature is $20C$

Construction Sequence

The beam is precast at day $0$ and cured for $7$ days.

Post$-$tensioning force is applied to the beam at age $90$ days