The assembly consists of three disks A, B, and C that are...

The assembly consists of three disks $A, B,$ and $C$ that are used to support the load of 140 kN. Determine the smallest diameter $d_{1}$ of the top disk, the largest diameter $d_{2}$ of the opening, and the largest diameter $d_{3}$ of the hole in the bottom disk. The allowable bearing stress for the material is $\left(\sigma_{b}\right)_{\text {allow }}=350 \mathrm{MPa}$ and allowable shear stress is $\tau_{\text {allow }}=125 \mathrm{MPa}$

Key Concepts

Bearing Stress

Bearing stress refers to the pressure or compressive force per unit area exerted on a material at points of contact. In structural design, it is critical to ensure that the contact surfaces between components, such as disks or plates, can support the applied load without failure or excessive deformation. Engineers calculate bearing stress by dividing the load by the effective contact area and then comparing it to the material's allowable bearing strength to ensure safety and proper function.

Shear Stress

Shear stress is the force per unit area acting parallel to a material's surface, which tends to cause layers of the material to slide relative to one another. In structural connections and load-bearing assemblies, it is important to analyze shear stress to prevent shear failure, which can occur when the applied load exceeds the material's shearing capacity. This analysis is crucial for ensuring that connections and joints within a structure remain intact under service loads.

Allowable Stress and Safety Factors

Allowable stress is a concept used in engineering design to define the maximum stress that a material or component can safely withstand under a particular load, accounting for uncertainties and potential variations in material properties and loading conditions. It forms the basis of safe design practices by incorporating safety factors, ensuring that the structure remains within conservative limits compared to the material's ultimate strength.

Design Considerations for Structural Openings

In mechanical design, structural members such as disks often include openings or holes for assembly, weight reduction, or passage of components. The design of these openings must consider the redistribution of stresses around the cut-outs, as stress concentrations can occur at edges leading to potential failure points. Proper sizing and placement of openings are essential to maintain the integrity of the load-bearing assembly while achieving the design requirements.

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