Static Equilibrium in a Space Structure

Introduction:
When analyzing the static equilibrium of a space structure, we need to consider the forces and moments acting on the structure to ensure that it remains balanced and stable. To determine the number of independent equations required for static equilibrium, we need to consider the conditions that must be satisfied.

Conditions for Static Equilibrium:
For a space structure to be in static equilibrium, the following conditions must be satisfied:

1. Sum of Forces in X-direction: The algebraic sum of all the forces acting in the X-direction must be equal to zero.
2. Sum of Forces in Y-direction: The algebraic sum of all the forces acting in the Y-direction must be equal to zero.
3. Sum of Forces in Z-direction: The algebraic sum of all the forces acting in the Z-direction must be equal to zero.
4. Sum of Moments: The algebraic sum of all the moments acting about any point must be equal to zero.

Explanation:
In a space structure, there are three dimensions (X, Y, and Z), and each dimension has two independent equations (sum of forces and sum of moments). Therefore, the total number of independent equations required for static equilibrium in a space structure is:

3 dimensions * 2 equations per dimension = 6 equations

These six equations are necessary to ensure that the structure is in static equilibrium. Each equation represents a different aspect of the forces and moments acting on the structure, and all six equations must be satisfied simultaneously for the structure to remain balanced and stable.

Conclusion:
In conclusion, the correct answer is option 'B' - 6. Six independent equations are required for static equilibrium in a space structure. These equations ensure that the sum of forces and moments in each dimension (X, Y, and Z) is equal to zero, ensuring the structure's stability and balance.