Structural Analysis of Cantilever Truss

Summary

The primary objective of this coursework is to design a lightweight cantilever structure capable of supporting a 500 g mass positioned 500 mm away from a vertical wall. Additionally, the task involves predicting which structural member is the most vulnerable and determining its failure load. In this study, we consider the structure as a perfect pin-jointed truss. We employ free body diagrams and symmetry to calculate the forces within each truss member. While the truss successfully supported the 500g mass, the low buckling load for member HD (5.

57N) limits the maximum load capacity to 6.17N.

Introduction

A truss is a structural framework constructed from beams and other elements in a manner that the entire assembly behaves as a single unit. Trusses are widely used in various applications, including antenna towers, cranes, and bridges, owing to their ability to create robust structures while optimizing material usage. The main objective of this study is to predict the failure point and load capacity of a truss structure before it fails under axial loads, thereby ensuring that the structure remains within material stress limits.

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Design of Structure

The design constraints imposed on the truss stipulate that it must have no attachment points along its members, no redundancy in member placement, and all non-zero force members should exhibit symmetry about the XZ mirror plane. Throughout our calculations, we assume that the truss behaves as a perfect pin-jointed structure. This simplification is acceptable for the analysis of relatively simple trusses like the one under consideration. Our truss design follows the principles of a Howe truss, where diagonal members are subjected to compressive forces, while the vertical members are in tension.

The selection of the Howe truss design is based on its simplicity, cost-effectiveness, and predictability of member behaviors, as compression and tension members are clearly defined.

Calculations

Our structural analysis involves calculations using the equations of equilibrium, namely, ∑MA = 0 and ∑MD = 0. For example:

^FEx × 0.1 - 4.905 × 0.5 = 0

^FEx × 0.5 - ^FAx × 0.5 = 0

These equations yield the following results:

^FEx = 24.525 N

^FAx = 24.525 N

^FEy = 4.905 N

For calculating the buckling load of member EB:

LEB = Fb1L1² = Fb2L2²

4.905 = FEB × (0.273 × 9.81) × (0.260)²

FEB = 10.968 N

Member AB would buckle due to its buckling load of 3.621 N for a length of 223.6 mm, with a load of 5.484 N.

Final Design

The final design of the truss involved shortening horizontal members, resulting in shorter diagonal members. This alteration increased the buckling load of the members, consequently enhancing the maximum load capacity of the truss. We hypothesized that the longest diagonal member, HD, would be the first to buckle due to its low buckling load and high applied force. Our calculations confirmed this hypothesis.

For instance, FEx = 24.525 N, FAx = 24.525 N, FEy = 4.905 N, and FAy = 0 N. The results indicate that HD is indeed the most vulnerable member, with a buckling load of 5.57 N and an axial force of 4.42 N.

Results and Discussion

Members under Compression

Maximum Load

The member HD is the most vulnerable due to its low buckling load of 5.57 N and the high axial force acting on it. The buckling scaling law indicates that the buckling load is inversely proportional to the square of the member length. Since HD is the longest member, it has the lowest buckling load. As the truss is symmetric with symmetric vertical members, we can double the buckling load of HD (5.57 N) and use trigonometric ratios to determine the maximum load:

(5.57 × 2) × sin(45°) = maximum load

Maximum load = 6.179 N

This result confirms our hypothesis that member HD is the most vulnerable. However, it's essential to note that this analysis assumes ideal pin-jointed connections, which may not always apply in real-life scenarios. Additionally, neglecting the weight of the structure can lead to errors, especially when dealing with small loads. Future studies could consider the inclusion of bending moments, shear stresses, and the weight of the truss for a more accurate analysis.

Conclusion

In conclusion, this coursework aimed to design and analyze a cantilever truss structure. By employing the principles of a perfect pin-jointed truss and considering the buckling loads of individual members, we successfully predicted the most vulnerable member and its failure load. The study revealed that member HD is the weakest link in the truss, with a buckling load of 5.57 N and a maximum load capacity of 6.179 N. Nevertheless, it's important to acknowledge the limitations of this analysis, such as the idealized pin-jointed connections and neglecting the structure's weight. Future research could address these limitations for a more comprehensive understanding of truss behavior under various conditions.

References

• Smith, J. R. (2010). Structural Analysis and Design of Trusses.
• Brown, A. C. (2015). Engineering Mechanics: Principles of Truss Analysis.