Prestressed Concrete Bridge Design — Worked Examples

Example 1: Transfer Stress at the Bottom Fiber

A pretensioned girder has $A=0.62\text{ m}^2$, bottom section modulus $S_b=0.19\text{ m}^3$, transfer prestress $P_t=6200\text{ kN}$, and tendon eccentricity $e=0.52\text{ m}$ below the centroid. At the section being checked, girder self-weight produces $M_g=1450\text{ kN}\cdot\text{m}$.

Take compression as negative and use the stage-consistent elastic stress expression.

Example 2: Effective Prestress After a Consistent Loss Estimate

A girder is stressed to an initial force of $P_i=7200\text{ kN}$. A code-approved loss calculation gives a total effective reduction of $18\%$ for the service stage.

Example 3: Stage-Specific Composite Stress Bookkeeping

A precast girder carries three categories of moment at one section: $M_1=2200\text{ kN}\cdot\text{m}$ from girder plus wet-deck construction before composite action, $M_2=900\text{ kN}\cdot\text{m}$ from superimposed dead load after composite action, and $M_3=1800\text{ kN}\cdot\text{m}$ from service live load after composite action.

Example 4: Organize the Ultimate Flexural Check

A verified bridge-analysis model reports a factored positive moment demand $M_u=8.6\text{ MN}\cdot\text{m}$ at a critical section.

Example 5: Interpret Camber Through Construction Stages

A precast girder has an estimated upward prestress camber of $+52\text{ mm}$ at release, self-weight deflection of $-18\text{ mm}$, time-dependent prestress/creep adjustment of $+14\text{ mm}$ by erection, and wet-deck construction deflection of $-31\text{ mm}$.