The section of shaft shown in the figure is to be designed...

The section of shaft shown in the figure is to be designed to approximate relative sizes of $d=0.75 D$ and $r=D / 20$ with diameter $d$ conforming to that of standard rollingbearing bore sizes. The shaft is to be made of SAE 2340 steel, heat-treated to obtain minimum strengths in the shoulder area of $175 \mathrm{kpsi}$ ultimate tensile strength and 160 kpsi yield strength with a Brinell hardness not less than 370 . At the shoulder the shaft is subjected to a completely reversed bending moment of $600 \mathrm{lbf}$ - in, accompanied by a steady torsion of $400 \mathrm{lbf} \cdot$ in. Use a design factor of $2.5$ and size the shaft for an infinite life using the DE-Goodman criterion.

Key Concepts

Material Strength and Properties

The material properties, including ultimate tensile strength, yield strength, and hardness, are essential factors in shaft design. These properties determine the material’s ability to withstand both static and cyclic loads. In high-performance applications, selecting a material with the appropriate heat treatment and strength levels ensures that the shaft will perform reliably under significant bending, torsion, and fatigue loads.

Shaft Geometry and Sizing

The geometric design of the shaft, including its diameter, shoulder radius, and other dimensional ratios, plays a pivotal role in determining how stresses are distributed under load. Proper sizing not only aligns with standard bearing sizes and manufacturing practices but also ensures that stress concentrations are minimized, promoting uniform stress distribution and reducing the likelihood of failure under combined loading conditions.

Combined Loading Analysis

When designing a shaft, it is crucial to consider the effects of multiple loadings acting simultaneously, such as bending and torsion. This analysis involves determining the individual stress contributions from bending moments and torsional moments, and then combining them—often using methods such as the von Mises criterion—to check that the resultant stresses remain within safe limits for the material in use.

Fatigue Failure Analysis (DE-Goodman Criterion)

The DE-Goodman criterion is a fatigue failure analysis method used in design to ensure that components subjected to cyclic loading achieve an infinite life. By comparing the actual applied cyclic stresses with the material's endurance limits, adjusted for mean stress effects, the DE-Goodman criterion helps designers account for fatigue damage and enhance reliability under repeated loading conditions.

Design and Safety Factor Considerations

A design or safety factor is incorporated into engineering calculations to account for uncertainties in the design parameters, material properties, and loading conditions. By applying a design factor, the calculated stresses are kept significantly below the material's strength limits, thereby enhancing the reliability and safety of the structure over its intended life.

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