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Which of the following is a statically indeterminate structure? 

Which of the following is a statically indeterminate structure?  Correct Answer Two hinged arch

Concept:

A two-dimensional structure in general is classified as a statically indeterminate structure if it cannot be analyzed by conditions of static equilibrium.

The conditions of equilibrium for 2D structures are:

  1. The Sum of vertical forces is zero (∑Fy = 0).
  2. The Sum of horizontal forces is zero (∑Fx = 0).
  • The Sum of moments of all the forces about any point in the plane is zero (∑Mz = 0).

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Simply supported beam:

Number of unknowns = 3

Degree of static indeterminacy = 3 - 3 = 0. Hence it is statically determinate.

Cantilever beam:

Number of unknowns = 3

Degree of static indeterminacy = 3 - 3 = 0. Hence it is statically determinate.

Three hinged arches:

Number of unknown = 4

Degree of static indeterminacy = 4 - 3 -1 = 0. (Additional equation due to internal hinge ∵ B.M = 0)

Hence it is statically determinate.

Two hinged arches:

Number of unknown = 4

Degree of static indeterminacy = 4 - 3 = 1.

Hence it is statically indeterminate.

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