The failure of a key is due to:

Explanation:

Key

• A Key is a machine element that is used along with coupling in order to transmit power from one shaft to another.
• Key is the weakest member in the assembly of shaft, pulley and key.
• Key acts as a safety device, whenever there is excess load appears on the pulley key fails first and it keeps safer to shaft and pulley.
• A key is the piece of low carbon steel inserted between shaft and hub to connect these together in order to prevent relative motion between them.
• It is always inserted parallel to the axis of the shaft.
• Keys are used as temporary fastenings and are subjected to considerable crushing and shearing stresses.
• A keyway is a slot or recess in a shaft or hub of the pulley to accommodate a key.

Forces acting on a key

Assumption: Exact location of force P on face AC is not exactly known. Therefore, to simplify analysis it is considered that P is tangential to the shaft diameter.

Now P =     ----(1)

Case (a): Shearing in the key:

τ =   

where τ = shear stress of the material

Case (b): Crushing in key:

Crushing will occur if 

Out of given options, only shearing is present therefore option 1 is correct.