Vertical Stress on the Solid Cylindrical Test Apparatus

The vertical stress on the solid cylindrical test apparatus is applied by the major principal stress. This can be understood by considering the stress distribution in a cylindrical body subjected to axial loading.

Stress Distribution in a Cylindrical Body

When a cylindrical body is subjected to axial loading, the stress distribution is not uniform across the cross-section. The stress is highest at the center of the cross-section and decreases towards the outer edges. This distribution of stress is known as the stress profile.

Principal Stresses

In a three-dimensional stress state, there are three principal stresses: the major principal stress (σ1), the intermediate principal stress (σ2), and the minor principal stress (σ3). These principal stresses are mutually perpendicular and can be represented by a stress tensor.

Stress Distribution in a Solid Cylindrical Test Apparatus

In the case of a solid cylindrical test apparatus, the major principal stress acts along the vertical axis of the cylinder. This is because the load is applied vertically, leading to the highest stress at the center of the cross-section.

The intermediate principal stress acts horizontally and is due to the confining pressure applied to the sides of the cylinder. The minor principal stress is negligible in this case.

Vertical Stress

The vertical stress is the stress acting in the vertical direction, perpendicular to the cross-section of the cylindrical test apparatus. As mentioned earlier, the major principal stress acts along the vertical axis, making it the primary contributor to the vertical stress.

Conclusion

In summary, the vertical stress on the solid cylindrical test apparatus is applied by the major principal stress. This is because the major principal stress acts along the vertical axis and is responsible for the highest stress at the center of the cross-section. The intermediate principal stress, acting horizontally, contributes to the confining pressure but does not directly affect the vertical stress. The minor principal stress is negligible in this case.