In two-hinged arch, how many unknown forces exist?

Explanation:

Three hinge arch :

• In the case of a three-hinged arch, we have three hinges, two at the support and one at the crown and there are four reaction components in the three-hinged arch.
• One more equation is required in addition to three equations of static equilibrium for evaluating the four reaction components.
• Taking moment about the hinge of all the forces acting on either side of the hinge can set up the required equation, making 3  hinge arch determinate.

Two hinge arch :

• In the two hinge arch, we have 2 hinges at two support of the arch and have four reaction or unknown components, as in a 3 hinge arch.
• But here we don't have an additional equation to solve the structure and hence our 2 hinge arch is indeterminate by degree 1.

​Hinge less/ Fixed arch :

• In the fixed arch, both the support are fixed. So, in a fixed arch six reaction forces ( One moment extra on each support ).
• But, we have only 3 equilibrium equations. So, the degree of indeterminacy of fixed arch becomes 6 - 3 = 3. 

​​