What is the condition for the degree of static indeterminacy of space frame, where m is the number of members, n is the number of joints and r is the number of reaction?
- A3m + r – 3j
- Bm + r – 3j
- C6m + r – 6jCorrect
- Dm + r – 6j
Solution
Concept
Static Indeterminacy of Space Frame
Formula
Ds = 6m + r – 6j
Step-by-step solution
1. Identify the number of members (m), support reaction components (r), and total joints (j) in the space frame. 2. Calculate the total unknown forces as the sum of members and reactions: (m + r). 3. Calculate the total available equilibrium equations by multiplying the number of joints by 6 (since each 3D joint yields 6 equilibrium equations): 6j. 4. Subtract the total equilibrium equations from total unknown forces: Ds = 6m + r – 6j
Explanation
For a 3D pin-jointed space frame, the total number of unknown forces is the sum of member forces (m) and support reactions (r). Since each joint in three dimensions provides 3 independent equilibrium equations, the total available equations are 3j (where j is the number of joints). The degree of static indeterminacy is the total unknowns minus the available equations, given by 6m + r – 6j
Correct answer: C) 6m + r – 6j