Two Hinged Arch and Temperature Induced Bending

Two Hinged Arch
A two hinged arch is a structural element that is used to transfer loads from one point to another. It is made up of a curved arch rib that is supported on two hinges or pivots at either end. The arch rib is usually made of steel or reinforced concrete and is designed to withstand compressive loads.

Temperature Induced Bending in Two Hinged Arch
When the temperature of a two hinged arch increases, the arch rib expands and this causes it to bend. This is because the hinges at the ends of the arch rib prevent it from expanding freely, and this results in the arch rib bending upwards.

Types of Bending in Two Hinged Arch
The bending that occurs in a two hinged arch due to temperature changes can be of different types depending on the location of the maximum bending moment. These include:

1. No Bending Moment
If the temperature increase is uniform throughout the length of the arch rib, there will be no bending moment induced in the arch rib. This is because the arch rib expands uniformly and there is no change in the shape of the arch.

2. Uniform Bending Moment
If the temperature increase is not uniform throughout the length of the arch rib, there will be a uniform bending moment induced in the arch rib. This is because the arch rib expands unequally, and this results in a constant bending moment throughout the length of the arch.

3. Maximum Bending at the Crown
If the temperature increase is greater at the crown of the arch rib than at the hinges, there will be a maximum bending moment induced at the crown. This is because the arch rib expands more at the crown than at the hinges, and this results in a maximum bending moment at the crown.

4. Maximum Bending Moment at the Hinges
If the temperature increase is greater at the hinges than at the crown, there will be a maximum bending moment induced at the hinges. This is because the arch rib expands more at the hinges than at the crown, and this results in a maximum bending moment at the hinges.

Conclusion
In a two hinged arch, an increase in temperature can induce bending in the arch rib. The type of bending that occurs depends on the location of the maximum bending moment, which can be at the crown, hinges or uniform throughout the length of the arch rib. It is important to consider temperature effects when designing two hinged arches to ensure their structural integrity.