7.2.1. Solution: Reactions of the Statically Determined Arch

Try these first

1. 1.

   What is the formula for the vertical reaction V in a statically determined arch?

   Hint

   Look for the relationship involving vertical forces and span.

2. 2.

   Define a three-hinged arch.

   Hint

   Think about the advantages of having supports in arch design.

3. 3.

   What does the horizontal force H in an arch directly depend on?

   • A) The width of the arch
   • B) The height of the arch
   • C) The length of the arch

   Hint

   Consider how increasing the height changes the force.

4. 4.

   True or False: In a three-hinged arch, internal bending moments can exist.

   • True
   • False

   Hint

   Think about the design flexibility of three-hinged structures.

5. 5.

   For a three-hinged arch spanning 50 m with a rise of 8 m and under a uniform load of 15 kN/m, calculate the vertical reaction V and horizontal force H.

   Hint

   Remember to use each formula correctly based on definitions.

6. 6.

   Discuss the effects of varying the rise while keeping the span constant on the internal stresses and stability of the arch.

   Hint

   Consider structural stability in your analysis; changing dimensions can lead to varying stress responses.