BeginnerTopic 18 of 106Engineering Mechanics
Cables and arches
Flexible cables carry load by tension in parabolic or catenary shapes.
In depth
An ideal cable carries only tension. Under uniform horizontal load it forms a parabola with sag d: T=wL²/(8d) at the horizontal tension. Under its own weight it forms a catenary. Arches carry load mainly in compression.
Key points
- Longer sag lowers tension
- Suspension bridge main cables are nearly parabolic
- Arches thrust horizontally on abutments
ExampleA cable with span 100 m and sag 10 m under 2 kN/m has H=2×100²/(8×10)=250 kN.
What is Cables and arches?
Flexible cables carry load by tension in parabolic or catenary shapes.
Why is it important to understand cables and arches?
Cables and arches show how structures carry load through pure tension or pure compression, which is the principle behind suspension bridges and stone vaults.
Why does a suspension cable take a parabolic shape?
Under uniform load along the horizontal, a cable forms a parabola. Under its own weight alone, it forms a catenary.
Why are arches good for compression?
Stone and concrete are strong in compression and weak in tension, and a well-shaped arch keeps the internal force in compression.
How is Cables and arches used in practice?
Typical applications include designing the main cable of a suspension bridge, estimating the tension in a power line between two towers and designing a masonry arch to carry a bridge deck in compression.
What should I learn before Cables and arches?
Study "Frames and machines" first (topic 17 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
What are the key points of Cables and arches?
Longer sag lowers tension. Suspension bridge main cables are nearly parabolic. Arches thrust horizontally on abutments.
Can you give an example of Cables and arches?
A cable with span 100 m and sag 10 m under 2 kN/m has H=2×100²/(8×10)=250 kN.
What comes after Cables and arches?
The next topic is "Moment of inertia of area", which builds directly on this one.
How difficult is Cables and arches?
It is classed as Beginner in Engineering Mechanics (topic 18 of 106). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.