The shaft is supported by a smooth thrust bearing at A and...

The shaft is supported by a smooth thrust bearing at $A$ and smooth journal bearing at $B$. If $P=10 \mathrm{kN}$ and the shaft is made from steel having an allowable normal stress of $\sigma_{\text {allow }}=150 \mathrm{MPa}$ and an allowable shear stress of $\tau_{\text {allow }}=85 \mathrm{MPa}$, determine the required minimum wall thickness $t$ of the shaft to the nearest millimeter to safely support the load.

Key Concepts

Bearing Reaction Analysis

Bearing reaction analysis involves determining the forces and moments transmitted through the supports of a shaft, such as thrust and journal bearings. By understanding how bearings transfer loads to the shaft, engineers can accurately calculate the maximum internal forces and design the shaft dimensions to safely carry the applied loads.

Thin-Walled Cylinder Analysis

This concept is used when designing hollow or tubular shafts where the wall thickness is small relative to the diameter. It involves simplified formulas to calculate properties like the moment of inertia and section modulus, which are essential in stress analysis, and helps in efficiently determining the minimum wall thickness required for structural integrity.

Shear Stress in Shafts

Shear stress in shafts typically occurs due to torsional loads and transverse forces, where the internal shear force causes deformation. Analyzing shear stress involves determining the distribution across the cross-section and ensuring that the induced shear remains within the material's allowable shear stress, which is critical for avoiding failure under twisting loads.

Flexural (Bending) Stress

Flexural bending stress arises in a beam or shaft when it is subjected to external moments, causing one side to be in tension and the other in compression. The stress is calculated using the bending moment, the distance from the neutral axis, and the section modulus of the cross-section, emphasizing the importance of cross-sectional geometry in resisting bending.

Allowable Stress Design

This concept involves designing a component such that the calculated stresses under load do not exceed the material's allowable stress limits. In practice, the maximum stresses produced by bending, torsion, or combined loading are compared to the specified allowable stresses to ensure a safe design with an adequate safety margin.

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