A pile weighing W₁ kg penetrates S metres with its last blow. If W₂ is the weight of the hammer having a drop of H metres, the pile can carry a maximum external load

ANS:B -

To determine the maximum external load that the pile can carry, we can use the concept of the "pile driving formula" in foundation engineering. This formula relates the penetration of the pile to the energy imparted to it during driving. The potential energy imparted to the pile by the hammer is given by: E=W2​×H Where:

• E = Potential energy imparted to the pile (joules)
• W2​ = Weight of the hammer (kg)
• H = Drop of the hammer (meters)

This energy is expended in overcoming the resistance of the soil and in raising the pile: E=(W1​+W2​)×S Where:

• W1​ = Weight of the pile (kg)
• S = Penetration of the pile (meters)

At the point of maximum efficiency, the potential energy imparted to the pile is equal to the work done in driving it: W2​×H=(W1​+W2​)×S From this equation, we can solve for the maximum external load Wext​ that the pile can carry: Wext​=SW2​×H​−W1​ This represents the maximum load that the pile can support without further penetration. However, it's important to note that the pile's load-bearing capacity may also be influenced by factors such as soil conditions, pile diameter, and pile material. Therefore, additional analysis and considerations may be required in practical engineering applications.