Chapter 18, Problem 33A

Why is cement not needed between the stone blocks of an arch that has the shape of an inverted catenary?

To determine

To Explain: The reason that cement is not used between stone block while making the shape of inverted catenary arches.

Explanation of Solution

Introduction:

One of the famous problems in the physics is the catenary problem. Catenary is the curve shape arrangement of the chain or object which supports at its two ends and hanging under the influence of gravity. Since from long time catenary arches are used by people to build kilns. The architecture arts that follows the catenary curve is known as catenary arches.

Ideal catenary arch is the ability to withstand and supports its weight without collapsing. Ideal catenary arch is made up of same cross-sectional blocks. The blocks of arch don’t side fall, because the forces between the blocks are along the curve of the arch itself. Therefore, no shear stress on the blocks to make them fall sideways. Normal force acts along the line of the arch is equivalent to the pressure force between blocks in contact. In the vertical catenary arches, compression force applies the pressure along the curve of the arch. This pressure force balances the vertical force of gravity.

Conclusion:

Therefore, normal force acts along the line of the arch is equivalent to the pressure force between stone blocks. This force holds the block together and avoids side way fall. Due to this reason, there is no need of using cement in between stone blocks for holding them together.