ANNEX B

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

+ sign of tension- sign of compression