Introduction:
When a long shaft of diameter D is subjected to a twisting moment T at its ends, it experiences shear stress and torsional deformation. The maximum normal stress acting in the cross-section of the shaft can be determined using the torsion formula.

Torsion Formula:
The torsion formula relates the torque or twisting moment applied to a shaft to the shear stress induced in the shaft. It can be expressed as:

τ = (T*r) / (J)

Where:
- τ is the shear stress (N/m^2 or Pa)
- T is the applied torque or twisting moment (N-m)
- r is the radial distance from the axis of rotation to the point of interest (m)
- J is the polar moment of inertia of the cross-section (m^4)

Maximum Normal Stress:
The maximum normal stress in the cross-section of the shaft occurs at the outermost fiber. This can be calculated using the following equation:

σ_max = (τ * r) / (c)

Where:
- σ_max is the maximum normal stress (N/m^2 or Pa)
- τ is the shear stress at the outer fiber (N/m^2 or Pa)
- r is the radius of the shaft (m)
- c is the distance from the neutral axis to the outermost fiber (m)

Explanation:
To determine the maximum normal stress acting in the cross-section of the shaft, follow these steps:

1. Calculate the shear stress at the outermost fiber using the torsion formula.
- Determine the applied torque or twisting moment T.
- Calculate the radial distance r from the axis of rotation to the outermost fiber.
- Determine the polar moment of inertia J for the cross-section of the shaft.

2. Calculate the maximum normal stress using the equation σ_max = (τ * r) / (c).
- Determine the radius of the shaft r.
- Calculate the distance c from the neutral axis to the outermost fiber.

3. Substitute the values into the equation to find the maximum normal stress σ_max.

4. The resulting value represents the maximum normal stress acting in the cross-section of the shaft.

Conclusion:
In summary, the maximum normal stress acting in the cross-section of a long shaft subjected to a twisting moment can be determined using the torsion formula and the equation for maximum normal stress. By calculating the shear stress at the outermost fiber and considering the geometry of the shaft, the maximum normal stress can be evaluated. This information is crucial for designing and analyzing the strength and stability of the shaft under torsional loading.