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### What is the design criteria of Pinned Joint? Explain in details step by step procedure of a design of Pinned Joint with required formula and an example of calculation.

A pinned joint, also known as a hinged joint, is a type of connection where two members are joined together and allowed to rotate freely about a common axis. The design criteria for pinned joints include determining the forces and moments acting on the joint and ensuring that the joint can safely transmit these forces without failure. Here is a step-by-step procedure for designing a pinned joint:

Step 1: Identify the Joint Configuration and Geometry Determine the specific configuration of the pinned joint, including the type of members being connected and their dimensions. Identify the geometry of the joint, such as the distance between the pin and the applied loads.

Step 2: Determine Applied Forces and Moments Identify the forces and moments that will be applied to the joint. These can include axial forces, shear forces, bending moments, and torsional moments. Consider both static and dynamic loads.

Step 3: Determine Reactions at the Joint Analyze the forces and moments acting on the joint to determine the reaction forces and moments. Apply the principles of static equilibrium to calculate the reactions. The reactions will depend on the type and magnitude of the applied loads and the geometry of the joint.

Step 4: Check Joint Strength Check the strength of the joint components, such as the pins, bolts, or fasteners, to ensure they can withstand the applied forces and moments. Consider the material properties, dimensions, and allowable stresses of the components.

Step 5: Check Joint Stability Check the stability of the joint to ensure that it can resist buckling or instability under the applied loads. Consider the slenderness ratio and critical buckling load of the joint members.

Step 6: Check Joint Deflection Check the deflection of the joint under the applied loads to ensure it is within acceptable limits. Calculate the deflection using appropriate formulas or numerical methods, considering the geometry and material properties of the members.

Step 7: Design Verification Perform a design verification to ensure that the joint meets the desired safety and performance requirements. This may involve performing structural analysis or calculations to confirm the adequacy of the joint components and their connections.

Example:

Let’s consider a pinned joint consisting of two steel members connected by a pin. The members have a rectangular cross-section with dimensions of 100 mm by 50 mm and a length of 2 meters. The joint is subjected to an axial force of 50 kN and a bending moment of 100 kNm.

Step 1: Identify the Joint Configuration and Geometry The joint consists of two rectangular steel members connected by a pin.

Step 2: Determine Applied Forces and Moments The applied forces are an axial force of 50 kN and a bending moment of 100 kNm.

Step 3: Determine Reactions at the Joint The axial force will result in an equal and opposite reaction force at the joint. The bending moment will cause a reaction moment at the joint.

Step 4: Check Joint Strength Check the strength of the pin and the members to ensure they can withstand the applied forces. Verify that the stresses in the members and the pin are within the allowable limits for the material.

Step 5: Check Joint Stability Check the stability of the joint to ensure it can resist buckling. Consider the slenderness ratio of the members and check that it is below the critical buckling limit.

Step 6: Check Joint Deflection Check the deflection of the joint under the applied loads to ensure it is within acceptable limits. Calculate the deflection using appropriate formulas or numerical methods.

Step 7: Design Verification Perform a design verification to confirm that the joint meets the desired safety and performance requirements. This may involve performing structural analysis or calculations to confirm the adequacy of the joint components and their connections.

It is important to note that the specific design criteria, formulas, and calculations for pinned joints may vary depending on the specific application, design codes, and standards being used. It is recommended to consult the relevant design code or consult with a qualified structural engineer to ensure accurate and compliant joint design.