The cotter is used to hold the two rods together. Determine...

The cotter is used to hold the two rods together. Determine the smallest thickness $t$ of the cotter and the smallest diameter $d$ of the rods. All parts are made of steel for which the failure normal stress is $\sigma_{\text {tail }}=500 \mathrm{MPa}$ and the failure shear stress is $\tau_{\text {fail }}=375 \mathrm{MPa}$. Use a factor of safety of $(\mathrm{F} \cdot \mathrm{S} \cdot)_{t}=2.50$ in tension and $(\mathrm{FS} .)_{s}=1.75$ in shear

Key Concepts

Geometric Design and Sizing

Geometric design and sizing deal with determining the appropriate dimensions of components, such as the cotter thickness and rod diameters, to ensure that they can safely sustain the expected loads. By applying stress formulas and incorporating factors of safety, designers compute the minimum sizes required to avoid material failure under both tensile and shear loading conditions.

Material Failure Criteria

Material failure criteria involve determining the maximum stress levels a material can endure before failing, including tensile and shear failure stresses. These criteria are used in conjunction with the factor of safety to guide the design of components so that the stresses under operational loads remain below the adjusted failure thresholds.

Normal (Tensile) Stress

Normal stress, in the context of tensile loading, is defined as the force acting perpendicular to the cross-sectional area of a component divided by that area. It is crucial to assess this stress to ensure that the material does not exceed its allowable tensile stress and risk fracture or permanent deformation.

Factor of Safety

The factor of safety is a design parameter used to ensure that a component can reliably withstand loads beyond the expected maximum during operation. It is calculated by dividing the material's failure stress by the applied stress, thereby providing a margin that accounts for uncertainties in load estimations, material variability, and potential flaws in design or construction.

Shear Stress

Shear stress is the force applied parallel to a material's cross-section divided by the area over which it acts. In design, it is important to calculate shear stress to ensure that the component does not experience excessive sliding forces that could lead to a shear failure, particularly in fasteners or connections like cotters.

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