This document analyzes the structural safety of an arch structure using finite element modeling. It makes assumptions about the structure's geometry and the material properties of stone. A shell element model with 6-inch elements is used. Two analyses are performed: (1) for self-weight, the weight multiplier is incrementally increased until failure occurs at 19.072 times the actual weight; (2) for displacement, a boundary condition allows downward movement at the central pier, causing failure in tension at 3.565 times the displacement. The analyses determine safety factors for self-weight and displacement-induced failure modes.

1. ANALYSIS OF ARCH STRUCTURE

3. SEQUENCE Assumptions Pertaining Geometry of Structure Assumptions Pertaining Material Properties Salient of Finite Element Model Analysis for Factor of Safety for Self Weight Analysis for Factor of Safety for Displacement Conclusion

4. Assumptions Pertaining Geometry of Structure 5’ 8’ 1.5’ 2’ Thick 10’ 2’ 8’ 3’ Thick 1’ 73.5’ 15’ 1.5’ 10’ 1.5’ 10’ 4’ Thick

5. Assumptions Pertaining material properties(stone) E = 30,000 N/mm2 Density = 2500 kg / m3 Poisson’s Ratio = 0.2 Compressive Strength = 30 N / mm2 Tensile Strength = 2 N / mm2

6. Salient of finite element model Element Type - Shell (Thick) Element Size - 6 inches Material - Stone

7. Salient of finite element model

8. Salient of finite element model

9. Analysis for safety factor for self weight

10. PROCEDURE Start from self weight multiplier zero Increase the multiplier step by step and by iterative approach find the factor of safety required for collapse Since self weight acts downward causing compression in the structure so it will fail in compression

11. Distribution of stress sigma zz(Self weight multiplier = 0)

12. Distribution of stress sigma zz(Self weight multiplier = 1)

13. Distribution of stress sigma zz(Self weight multiplier = 5)

14. Distribution of stress sigma zz(Self weight multiplier = 10)

15. Distribution of stress sigma zz(Self weight multiplier = 15)

16. Distribution of stress sigma zz(Self weight multiplier = 19)

17. Distribution of stress sigma zz(Self weight multiplier = 20)

18. Distribution of stress sigma zz(Self weight multiplier = 19.1)

19. Distribution of stress sigma zz(Self weight multiplier = 19.072) Max Compressive Force Develops Here

20. Analysis for fos for self weight 13 19.072

21. Analysis for safety factor for displacement

22. PROCEDURE Impose boundary condition on central pier i.e allow downward movement so as to cause differential settlement in the structure Start from self weight multiplier zero Increase the multiplier step by step and by iterative approach find the factor of safety required for collapse Since differential settlement will cause tension in central pier so it will fail in tension

23. Distribution of stress sigma zz(Self weight multiplier = 0)

24. Distribution of stress sigma zz(Self weight multiplier = 1)

25. Distribution of stress sigma zz(Self weight multiplier = 2)

26. Distribution of stress sigma zz(Self weight multiplier = 3)

27. Distribution of stress sigma zz(Self weight multiplier = 3.5)

28. Distribution of stress sigma zz(Self weight multiplier = 3.59)

29. Distribution of stress sigma zz(Self weight multiplier = 3.565) Max Tensile Force Develops Here

30. Analysis for fos for DISPLACEMENT 2 12.5 3.565

31. CONCLUSION

33. CONCLUSION SELF WEIGHT - 19.072 DISPLACEMENT START OF MECHANISM - 3.565 FAILURE - 12.5