ANNEX B SAMPLE COMPUTATION SHEET FOR ANALYTICAL DESIGN OF EXTERNAL REINFORCEMENT NOTATIONS: 1. A R Cross sectional area of circular ring 2. A U Cross sectional area of U beam of section considered 3. E Modulus of elasticity of steel 4. I R Moment of inertia of circular ring 5. I U Moment of inertia of U-beam at section considered 6. I UC Moment of inertia of U-beam at centre of element s 7. M U Bending Moment of U beam at section considered 8. I UC Bending Moment of U beam at at centre of element s due to reaction between circular ring and U beam, and unbalanced pressure 9. R Radius of main pipe 10. R 1 Radius of branch pipes at point M 11. R 2 Radius of centroidal axis of circular rings 12. R 3 Radius of curvature of inside of U beam at point considered 13. T Total vertical shear in U-beam at section considered 14. Y Reaction between inner circular ring and external U-beam girder. 15. b 1 Effective width of inner ring (equivalent flange) 16. b 2 Effective width of U-beam (equivalent flange) 17. c Distance from centroidal axis to extreme inner fiber of U beam 18. c Distance from centroidal axis to extreme outer fiber of U beam 19. e Distance from centroidal axis of extreme inner fiber of inner ring 20. e' Distance from centroidal axis of extreme outer fiber of inner ring 21. k i, k o Ratio of actual stress in inner or outer fiber, respectively, to stress computed by flexure formula for straight beam 22. m c Bending moment of U-beam at center of element s due to unit load at C. 23. p Internal pressure 24. q Constant for steel 25. μ Poissons ratio for steel 26. x Horizontal distance from centre line of circular ring 27. Angle of cross section of U beam with vertical 28. c Deflection of U beam at point C Note: positive moments produce tension of inner fiber + sign of tension - sign of compression
SAMPLE COMPUTATION SHEET FOR ANALYTICAL DESIGN OF
EXTERNALREINFORCEMENT
NOTATIONS:
1. AR Cross sectional area of circular ring2. AU Cross sectional
area of U beam of section considered3. E Modulus of elasticity of
steel4. IR Moment of inertia of circular ring5. IU Moment of
inertia of U-beam at section considered6. IUC Moment of inertia of
U-beam at centre of element s7. MU Bending Moment of U beam at
section considered8. IUC Bending Moment of U beam at at centre of
element s due to reaction
between circular ring and U beam, and unbalanced pressure9. R
Radius of main pipe10. R1 Radius of branch pipes at point M11. R2
Radius of centroidal axis of circular rings12. R3 Radius of
curvature of inside of U beam at point considered13. T Total
vertical shear in U-beam at section considered14. Y Reaction
between inner circular ring and external U-beam girder.15. b1
Effective width of inner ring (equivalent flange)16. b2 Effective
width of U-beam (equivalent flange)17. c Distance from centroidal
axis to extreme inner fiber of U beam18. c Distance from centroidal
axis to extreme outer fiber of U beam19. e Distance from centroidal
axis of extreme inner fiber of inner ring20. e' Distance from
centroidal axis of extreme outer fiber of inner ring21. ki, ko
Ratio of actual stress in inner or outer fiber, respectively, to
stress
computed by flexure formula for straight beam22. mc Bending
moment of U-beam at center of element s due to unit load at C.23. p
Internal pressure24. q Constant for steel25. Poissons ratio for
steel26. x Horizontal distance from centre line of circular ring27.
Angle of cross section of U beam with vertical28. c Deflection of U
beam at point C Note: positive moments produce tension of inner
fiber
