Verifica statica dell'arco: metodo grafico di Mery e curva delle pressioni

Summary

This video explains the static verification of an arch, focusing on the determination of the pressure curve to ensure the arch remains fully compressed without any tension. It introduces the graphical method developed by Engineer Du Armeri in 1840 to trace the pressure curve using equilibrium polygons and force vectors. The video demonstrates the process of calculating the resultant forces and determining the pressure curve, ensuring the arch's compressive stress is below the material's resistance. Viewers are encouraged to subscribe for more updates on similar topics.

Takeaways

• 😀 The static verification of an arch involves determining the pressure curve to ensure it remains within the central core of inertia.
• 😀 If the pressure curve is contained within the core of inertia, the arch will be fully compressed without any tensile zones.
• 😀 The compression stress must be lower than the material's resistance to satisfy the verification.
• 😀 The graphical method for determining the pressure curve was developed by Engineer Du Armeri in 1840.
• 😀 The static equilibrium of a symmetric, symmetrically loaded, and constrained arch can be analyzed using an equilibrium polygon with forced passage through two points.
• 😀 The study of a symmetric arch can be limited to half of its structure, simplifying the analysis by applying the forces in the key section and determining the pressure curve.
• 😀 The weight of individual segments of the arch and the weight of the superstructure must be considered to determine the resultant forces acting on the arch.
• 😀 The resultant of each applied force can be found using the tip-to-tail method, with an arbitrary pole chosen to calculate the resultant force line of action.
• 😀 The action lines of each vertical load are drawn from the pole, and by extending these lines, the intersection will reveal the resultant's line of action.
• 😀 Once the resultant and thrust lines of action are known, the pressure curve can be determined graphically using these lines to ensure the arch stays fully compressed.
• 😀 The final verification checks whether the maximum compression stress for each segment of the arch is lower than the material’s resistance, confirming the arch’s stability.

Q & A

What is the main purpose of the static verification of the arch?

The static verification of the arch aims to ensure that the pressure curve is contained within the central core of inertia, ensuring the arch is fully compressed without any sections subjected to tensile stress.

What is the method used for determining the pressure curve in this video?

The method used is a graphical technique developed by engineer Du Armeri in 1840. It involves determining the pressure curve through a balance of forces and leveraging the equilibrium polygon method.

What does the verification of compression tension require?

The verification requires that the compression tension be less than the material's compressive strength to ensure structural integrity.

What kind of loading and boundary conditions are assumed in the analysis of the arch?

The analysis assumes that the arch is symmetrically loaded and symmetrically supported, which allows the study to be limited to half of the arch.

How is the equilibrium of the arch determined in this method?

The equilibrium of the arch is determined using the equilibrium polygon, where the forces are resolved graphically by connecting the action lines of individual loads.

What is the method used to determine the resultant of vertical loads on the arch?

The method used is the 'tip-to-tail' graphical method, where vectors representing individual forces are drawn from an arbitrary pole, and the resultant is determined by connecting the vectors.

What is the role of the arbitrary pole in determining the forces?

The arbitrary pole is used to draw the action lines of the forces, and by connecting the vectors, it helps determine the resultant force and the line of action for the arch's thrust.

How is the thrust line determined in this method?

The thrust line is determined by imposing that the line of action passes through the third median point of the arch at the lower section, and the intersection of this line with the resultant action line defines the thrust direction.

What happens if the pressure curve is contained within the core of inertia?

If the pressure curve is contained within the core of inertia, it means the arch is fully compressed without any part being under tensile stress, which satisfies the static verification.

What is the final step in verifying the arch's structural integrity?

The final step is to ensure that the maximum compression stress in each section of the arch is lower than the material's compressive strength, completing the verification process.