Pre-tensioning of a bolted joint is used to

The correct option is increase stiffness of the bolted joint.

Explanation:

Pre-tensioning, also known as preload, refers to the initial tensile force applied to a bolt when it is tightened during installation. This tension stretches the bolt and creates a corresponding compressive clamping force on the connected members or components of the joint.

When an external tensile load is applied to a pre-tensioned joint, the assembly behaves like a system of springs in parallel: the bolt acts as a tension spring, and the clamped members act as a compression spring. Since the members are pre-compressed under a high force, they remain tightly pressed together as long as the external load does not exceed the preload.

Because the clamped members typically have a much higher stiffness than the bolt, they absorb a significant portion of any external tensile load. The division of the external load between the bolt and the members can be expressed as:
$$P_b=P·\frac{k_b}{k_b+k_m}$$
where P_b is the additional load experienced by the bolt, P is the external load, k_b is the stiffness of the bolt, and k_m is the stiffness of the clamped members.

By keeping the joint members in compression, pre-tensioning prevents joint separation and ensures the members contribute actively to resisting the load. This effectively increases the overall stiffness of the bolted joint assembly under operation, prevents loosening, and improves fatigue resistance.