While an oil well is being drilled at a depth of 2500 m, it is observed that the top of the 200

step 1 So we have got Yung's modulus is F over A delta L over L equals FL over a delta L. So from here

While an oil well is being drilled at a depth of 2500 m, it...

While an oil well is being drilled at a depth of $2500 \mathrm{m},$ it is observed that the top of the 200 -mm-diameter steel drill pipe $(G=77.2 \mathrm{GPa})$ rotates through 2.5 revolutions before the drilling bit starts to operate. Determine the maximum shearing stress caused in the pipe by torsion.

Key Concepts

Torsion

Torsion refers to the twisting action applied to a structural member or shaft, which results in shear stresses within the material. It is a key concept in mechanics of materials and plays an important role in determining the strength and safe operation of cylindrical structures under rotational loads.

Shear Stress in Torsion

When a cylindrical object like a pipe is subjected to a twisting moment, the induced stress distribution is primarily shear in nature. The maximum shearing stress occurs at the outer surface of the member and is determined by the applied torque, the radius of the object, and its geometric resistance to twisting, typically using the formula ?_max = T·r/J.

Polar Moment of Inertia

The polar moment of inertia is a geometric parameter that quantifies a circular cross-section's resistance to torsional deformation. It is essential for calculating the shear stresses induced by a given torque and depends on both the shape and dimensions of the cross-section.

Angle of Twist

The angle of twist is a measure of the rotational deformation a shaft undergoes under a torsional load. It is influenced by the applied torque, the length of the shaft, the shear modulus of the material, and the polar moment of inertia. This concept helps in understanding and predicting the performance of structures under torsional loading.

Shear Modulus (Modulus of Rigidity)

The shear modulus is a material property that quantifies the material's resistance to shear deformation. It defines the relationship between shear stress and shear strain in a material and is crucial for designing components subjected to torsional loading.

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