Cables and Arches - Examples & Applications

Determine the tension in the segments of a cable spanning $20\text{ m}$ between two supports at the same elevation. A single vertical load of $100\text{ kN}$ is applied at the midspan, causing a sag of $5\text{ m}$ at the load point.

A symmetrical three-hinged semicircular arch has a radius of $10\text{ m}$ and spans $20\text{ m}$ between two pinned supports at the same elevation. A vertical point load of $50\text{ kN}$ is applied at the crown hinge. Determine the horizontal thrust at the supports.

Determine the maximum tension ($T_{max}$) in a parabolic suspension cable spanning $L=100\text{ m}$ between two supports at the same elevation. The cable is subjected to a uniformly distributed horizontal load of $w=20\text{ kN/m}$. The sag at the midspan is $h=10\text{ m}$.

Determine the equation of the parabolic profile $y(x)$ for a cable spanning $L=40\text{ m}$ and carrying a uniform horizontal load $w=15\text{ kN/m}$. The minimum sag at the center is $h=5\text{ m}$. Place the origin of the coordinate system at the lowest point of the cable.

Case Study: Classification of Arches in Historic Bridge Construction.

Case Study: Selection of a Two-Hinged vs. Three-Hinged Arch for a Long-Span Hangar.