### What is the design criteria of Fully Restrained (PR) Connection? Explain in details step by step procedure of a design of Fully Restrained (PR) Connection with required formula and an example of calculation.

In structural engineering, a fully restrained (FR) connection refers to a connection that provides complete rotational and translational restraint between members. The design of fully restrained connections involves determining the required connection stiffness, moment and shear capacities, and verifying the connection’s ability to provide full restraint. Here is a step-by-step procedure for designing a fully restrained connection:

Step 1: Identify the Member Configuration Determine the specific configuration of the members involved in the connection, including the beam and the column. Gather information about their dimensions, material properties, and the connection requirements.

Step 2: Determine Applied Loads Identify the loads that will be applied to the connection, such as axial loads, moments, and shear forces. Determine the magnitude, direction, and distribution of these loads.

Step 3: Analyze the Structure Perform a structural analysis of the entire structure to determine the forces and moments acting on the connection. Consider the loading conditions, support conditions, and member stiffness.

Step 4: Determine Connection Stiffness Calculate the required stiffness of the connection to achieve full restraint. The connection stiffness is influenced by factors such as the beam-column geometry, beam and column stiffness, and design code provisions.

Step 5: Check Moment Capacity Check the moment capacity of the connection to ensure it can safely resist the applied bending moments. Consider factors such as the connection type (e.g., bolted, welded), moment transfer mechanism, and design code provisions.

Step 6: Check Shear Capacity Check the shear capacity of the connection to ensure it can safely resist the applied shear forces. Consider factors such as the connection type, shear transfer mechanism, and design code provisions.

Step 7: Verify Connection Performance Perform a performance verification of the connection to ensure it provides full restraint. This involves evaluating the connection’s rotation and translation characteristics under applied loads and confirming that they meet the specified design criteria for fully restrained connections.

Step 8: Design Verification Perform a design verification to confirm that the fully restrained connection meets the desired safety and performance requirements. This may involve performing structural analysis or calculations to confirm the adequacy of the connection stiffness, moment and shear capacities, and the connection performance.

Example: Consider the design of a fully restrained connection between a steel beam and a column. The beam has a maximum positive moment of 150 kNm, and the desired level of full restraint requires limiting the beam rotation to 0 radians under this moment. The material properties are as follows: beam and column yield strength = 300 MPa.

Step 1: Identify the Member Configuration The member configuration consists of a steel beam and a column, both with known dimensions and material properties.

Step 2: Determine Applied Loads The beam has a maximum positive moment of 150 kNm.

Step 3: Analyze the Structure Perform a structural analysis of the entire structure to determine the forces and moments acting on the connection.

Step 4: Determine Connection Stiffness Calculate the required stiffness of the connection to achieve full restraint. The stiffness can be determined by considering factors such as the beam-column geometry, beam and column stiffness, and design code provisions.

Step 5: Check Moment Capacity Check the moment capacity of the connection to ensure it can safely resist the applied bending moments. This may involve considering the connection type, moment transfer mechanism, and design code provisions.

Step 6: Check Shear Capacity Check the shear capacity of the connection to ensure it can safely resist the applied shear forces. Consider factors such as the connection type, shear transfer mechanism, and design code provisions.

Step 7: Verify Connection Performance Evaluate the connection’s rotation and translation characteristics under the applied loads. For a fully restrained connection, the beam rotation must be limited to 0 radians.

Step 8: Design Verification Perform a design verification to confirm that the fully restrained connection meets the desired safety and performance requirements.

Please note that the example provided is simplified, and actual design calculations for a fully restrained connection can be more complex, considering additional factors such as load combinations, connection details, and various design code provisions. It is essential to consult the relevant design code or consult with a qualified structural engineer to ensure accurate and compliant connection design.