The degree of static indeterminacy of a pin-jointed space frame is given by the formula r - 3j, where r is the number of reaction components and j is the number of joints. In this case, the correct answer is option 'B'.

Explanation:

- Pin-jointed space frames are structures that consist of interconnected members connected by pins at each joint. These frames are commonly used in civil engineering for various applications such as bridges, roofs, and trusses.
- To determine the degree of static indeterminacy of a pin-jointed space frame, we need to count the number of unknowns and the number of equations available to solve them.
- The number of unknowns is given by the number of reaction components (r) and the number of member forces. In this case, we are only considering pin-jointed frames, so the number of unknowns is equal to the number of reaction components.
- The number of equations is given by the number of equilibrium equations for each joint. Each joint is in equilibrium, so the number of equations is equal to the number of joints (j).
- The degree of static indeterminacy is calculated by subtracting the number of equations from the number of unknowns, which gives us r - j.
- However, in the case of pin-jointed space frames, there are three additional conditions that need to be satisfied for the frame to be in equilibrium. These conditions are known as the conditions of static indeterminacy and are related to the fact that the frame is a rigid body in space.
- These three conditions can be expressed as equations, which add three additional equations to the system. Therefore, the number of equations becomes j + 3.
- Substituting this value into the formula, we get r - (j + 3), which simplifies to r - 3j.
- Therefore, the correct answer is option 'B', which states r - 3j as the degree of static indeterminacy of a pin-jointed space frame.