Prestressed Concrete Examples

A $300\text{ mm}\times600\text{ mm}$ rectangular beam has $P_i=1200\text{ kN}$ at $e=+100\text{ mm}$. At transfer, self-weight produces $M_i=30\text{ kN-m}$. Calculate both extreme-fiber stresses on the gross, uncracked section.

For the beam in Example 1, take $P_e=0.80P_i=960\text{ kN}$ and a total sagging service moment $M_{\mathrm{ser}}=150\text{ kN-m}$. Calculate both fiber stresses.

Use the same section, $P_e=960\text{ kN}$, and $e=+100\text{ mm}$, but increase the service moment to $250\text{ kN-m}$. Determine the bottom stress and interpret it.

A $300\text{ mm}\times600\text{ mm}$ beam carries only a prestress force $P=1500\text{ kN}$. Find the eccentricity that makes the bottom-fiber stress zero.

A post-tensioned tendon is jacked to $P_j=2000\text{ kN}$. At the section of interest, $\mu\alpha+kx=0.080$. Anchorage seating is represented by a further $40\text{ kN}$ force reduction there. Subsequent creep, shrinkage, and relaxation reduce the transfer force by a combined $15\%$. Find $P_i$ and $P_e$ under these explicitly supplied simplifications.

At transfer, the concrete stress at the tendon level is $f_{cgp}=8.0\text{ MPa}$. Use $E_c=30{,}000\text{ MPa}$ and $E_p=200{,}000\text{ MPa}$ to estimate the compatible tendon stress loss.

A simply supported $12\text{ m}$ beam has a symmetric parabolic tendon with zero end eccentricity, midspan drape $h=0.250\text{ m}$, and constant effective force $P_e=1800\text{ kN}$. The uniform dead load is $10\text{ kN/m}$.

For a symmetric two-span beam with $L=10\text{ m}$ per span, prestressing produces a downward secondary reaction of $50\text{ kN}$ at the interior support. The balancing end reactions are $25\text{ kN}$ upward at each exterior support. Find the secondary moment at the interior support.