To generate the j th column of the flexibility matrix

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BPSC AE Paper 5 (Civil) 25 March 2022 Official Paper
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  1. a unit force is applied at coordinate j and the forces are calculated at all coordinates
  2. a unit force is applied at coordinate j and the displacements are calculated at all coordinates
  3. a unit displacement is applied at coordinate j and the displacements are calculated at all coordinates
  4. a unit displacement is applied at coordinate j and the forces are calculated at all coordinates

Answer (Detailed Solution Below)

Option 2 : a unit force is applied at coordinate j and the displacements are calculated at all coordinates
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Detailed Solution

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Explanation:

Stiffness Matrix Method

1. This method is also known as displacement method or equilibrium method.

2. It is suitable if static indeterminacy (Ds) > kinematic indeterminacy (D) for the structure.

Stiffness is defined as Force required to produce unit displacement, \(k = \frac{P}{{\rm{\Delta }}}\)

K12 → Force at 2 due to unit displacement at 1

Flexibility Matrix Method

1. This method is also known as force method or compatibility method.

2. It is suitable if kinematic indeterminacy (Dk) > static indeterminacy (Ds) for the structure.

Flexibility is defined as Displacement caused due to unit Force.

δ12 → Displacement at 2 due to Force at 1

∴ To generate a jth column of flexibility matrix a unit force is applied at coordinate j and the displacement are calculated at all coordinates.
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