Assignment 2 Exercise 3: Catenary Vault Student Name You Are ✓ Solved

Assignment 2exercise 3 Catenary Vaultstudent Nameyou Are Designing

Design a catenary masonry vault over an alpine road situated on steep terrain. Ensure the design respects the two support locations at the start and end of the vault, and maintains sufficient clearance for road traffic below. Develop the form diagram for the vault and create a corresponding force diagram, choosing an appropriate scale for the force diagram to accurately represent the load distribution and structural behavior. The design should utilize principles of graphic statics to achieve a structurally sound and visually effective catenary form that adheres to site constraints and structural requirements.

Sample Paper For Above instruction

The design of a catenary masonry vault over an alpine road on steep terrain presents unique structural challenges and opportunities. Using principles of graphic statics, the vault must be meticulously shaped to follow the natural catenary curve, which is the ideal form for withstand ing loads primarily due to its property of distributing compressive forces along a curved line. This paper explores the conceptualization, form finding, and force analysis necessary to develop an effective catenary vault that meets the constraints of support locations and traffic clearance requirements.

In the initial phase of the design process, precise survey data of the terrain and support points must be acquired. The support locations, as specified, serve as the foundational anchor points for the vault, defining the span and shape of the form diagram. By applying the principles of graphic statics, the form diagram visually represents the geometry of the vault derived from the load conditions, with the catenary curve embodying the equilibrium of forces. The force diagram complements this by illustrating the distribution of compressive forces within the vault structure when subjected to external loads such as traffic weight and environmental factors like snow or wind.

The form diagram is constructed by connecting the support points with a smooth curve that follows the natural catenary, which can be achieved using weighted string or digital modeling techniques to ensure precise curvature. The force diagram is then generated by translating the load and support reactions into force polygons, which reveal the internal force distribution. This diagram guides the adjustment of the vault's form, ensuring that the masonry blocks are oriented to handle the compression effectively, thereby facilitating stability and durability.

Given the steep terrain, considerations for foundation stability, drainage, and thermal expansion are critical. The curved vault must be designed with appropriate thickness and material selection to withstand the compressive stresses while fitting within the limited footprint imposed by the terrain and traffic clearance requirements. The integration of graphic statics allows for iterative refinement of the form and force diagrams, optimizing the structural form to minimize material use while maximizing safety and functionality.

Ultimately, the vault's shape, as dictated by the form diagram, should harmonize with the natural landscape and demonstrate engineering efficiency through the application of the catenary principle. This structural form leverages compressive forces along a curved line, reducing bending moments and material stresses. The resulting design not only ensures structural integrity but also embodies aesthetic harmony with the surrounding environment, showcasing the synergy between form, function, and site context.

References

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