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Architecture Engineering QUESTION #2363
Question 1
In the analysis of indeterminate structures using the Flexibility (Force) Method, the compatibility equation for a structure with \(n\) redundants is expressed in matrix form as:
  • \([F]\{X\} = \{D_0\}\)
  • \([K]\{D\} = \{P\}\)
  • \([F]\{X\} + \{D_0\} = \{0\}\)✔️
  • \([K]\{X\} = -\{D_0\}\)
Correct Answer Explanation
The compatibility equation in the Force Method is \([F]\{X\} + \{D_0\} = \{0\}\) (or equivalently \([F]\{X\} = -\{D_0\}\)), where \([F]\) is the flexibility matrix (flexibility coefficients \(f_{ij}\) = displacement at \(i\) due to unit force at \(j\)), \(\{X\}\) is the vector of redundants, and \(\{D_0\}\) is the displacement vector of the released structure (primary structure) under applied loads. Option B is the stiffness method equation.