Two steel plates are to be held together by means of 16-mm diameter high-strength steel bolts fi

step 1 the allowable shear flow at the joint interface is limited to the shear force in each ball. So f

Two steel plates are to be held together by means of 16-mm...

Two steel plates are to be held together by means of $16-\mathrm{mm}$ diameter high-strength steel bolts fitting snugly inside cylindrical brass spacers. Knowing that the average normal stress must not exceed $200 \mathrm{MPa}$ in the bolts and $130 \mathrm{MPa}$ in the spacers, determine the outer diameter of the spacers that yields the most economical and safe design.

Key Concepts

Stress Analysis

This concept involves determining the distribution of force over a material's cross-sectional area. In engineering design, knowing the average normal stress is critical because it must remain below the material's allowable stress limit to avoid yielding or failure. The analysis is performed by dividing the applied load by the effective area, and it is fundamental in ensuring the strength and integrity of structural components such as bolts and spacers.

Cross-sectional Area Calculation

The calculation of cross-sectional areas for circular components is essential to determine the stress levels experienced by the materials. The area is typically computed using the formula for the area of a circle, ?d²/4, where d is the diameter. This calculation helps in assessing whether the geometry of components like bolts and spacers can safely carry the applied loads, thus ensuring a robust design.

Material Properties and Allowable Stress

Understanding material properties, particularly the maximum allowable stress, is key to safe engineering design. Each material, such as high-strength steel for bolts or brass for spacers, has its specific stress limits. The design must ensure that operational stresses remain below these allowable values to prevent permanent deformation or failure, which is crucial for reliability and safety.

Design Optimization for Safety and Economy

This concept revolves around achieving a balance between safety requirements and material efficiency. In engineering design, especially when dealing with bolted connections, it is important to optimize dimensions (like the outer diameter of spacers) to meet strength criteria while minimizing unnecessary material usage. This optimization leads to an economical design that still adheres to all safety standards.

Mechanical Fastener Design

In the context of joining structural elements, the design of mechanical fasteners involves considering factors such as load transfer, compatibility between different components, and the differing material properties. Properly designed fasteners, including the selection and dimensioning of bolts and spacers, ensure the joint performs effectively under expected service loads and environmental conditions.

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