Determine The Smallest NPI Profile Used In Member

Determine the smallest NPI profile that can be used in members 1, 3, 5, 7, 10, 16 and 18

This assignment focuses on selecting the smallest NPI steel profile suitable for specific members in a structural framework, considering allowable stresses in tension and compression. The problem provides the members' positions, their length, and the applied loads, along with the allowable stress limits in tension (260 N/mm²) and compression (190 N/mm²). The task involves calculating the minimal cross-sectional area necessary for the profiles to safely withstand the applied forces without exceeding the specified stresses, subsequently identifying the appropriate NPI profile dimensions.

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The structural design process for steel frameworks necessitates meticulous selection of appropriate profiles that can withstand various load conditions while adhering to safety limits. In this context, the primary goal is to determine the smallest NPI profile that can be employed in members 1, 3, 5, 7, 10, 16, and 18, given the specified loadings and allowable stresses in tension and compression. This task involves a series of calculations to ensure the profile chosen possesses sufficient cross-sectional area to carry the applied forces without surpassing the permissible stress thresholds.

The initial phase involves understanding the applied forces and the relevant stress parameters. The members in question are subjected to axial tension or compression, with the maximum force specified as 150 kN acting in tension in some members and in compression in others. The applied maximum force, therefore, guides the stress analysis, which checks whether the selected profile will remain within safe stress limits during operation. The permissible stress in tension (σ_tension) is 260 N/mm², and in compression (σ_compression) is 190 N/mm², forming the basis for the cross-sectional calculations.

The fundamental equation used to determine the minimum cross-sectional area (A_min) for each member is derived from the basic stress formula:

σ = Force / Area → A_min = Force / σ_allowable

Applying this formula to each member, the calculation proceeds as follows:

Given the maximum axial load (Force) of 150 kN (which is 150,000 N), the minimum cross-sectional area based on tension stress limit is:

A_tension = 150,000 N / 260 N/mm² ≈ 577 mm²

Similarly, for members subjected to compression, the area should be based on the compression allowable stress:

A_compression = 150,000 N / 190 N/mm² ≈ 789 mm²

Since several members are under tension while others under compression, the actual profile must satisfy the most restrictive condition, i.e., the larger of the two areas. Considering this, the minimal cross-sectional area required is approximately 789 mm².

Next, identifying the appropriate NPI profile involves considering standard profile dimensions available in the market. NPI profiles are characterized by their height, width, and web and flange thicknesses; these dimensions influence their cross-sectional areas. Reference tables of standard NPI profiles indicate that typical NPI profiles start from sizes like NPI 80, NPI 100, NPI 120, etc., with increasing cross-sectional areas.

For instance, the NPI 80 profile has an approximate cross-sectional area of around 485 mm², which is below the required 789 mm². Therefore, it is insufficient. The NPI 100 profile has a typical area around 629 mm², still below the safety threshold, but closer. The NPI 120 profile, which generally has an area exceeding 800 mm², aligns with the minimal area found necessary from calculations. Hence, the smallest suitable NPI profile is NPI 120. This selection ensures the members can carry the applied loads safely within the allowable stress limits, providing a margin for unforeseen stresses and manufacturing tolerances.

In conclusion, selecting the appropriate NPI profile involves a combination of stress calculations and reference to standard profile dimensions. Based on the applied loads and permissible stresses, the minimum cross-sectional area required is approximately 789 mm², pointing towards the use of at least an NPI 120 profile to ensure safety and structural integrity.

References

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  • American Society for Testing and Materials (ASTM). (2020). Standard Specification for Steel Structural Shapes. ASTM A6/A6M-20.
  • Steel Construction Institute (SCI). (2019). Structural Steel Profiles and Design Tables. SCI Publications.
  • Eurocode 3: Design of steel structures. (2005). European Committee for Standardization.
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