Question
Download Solution PDFWhich of the following is a statically indeterminate structure?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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:
- The Sum of vertical forces is zero (∑Fy = 0).
- 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).
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.
Last updated on May 28, 2025
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