Basic formulas highway engineering

A handy reference for use in analysis and design of Highway Engineering.

  1. 𝑦=2π‘₯2π‘›π‘Š(parabolic camber)
  2. 𝑆𝑆𝐷=𝑣𝑑+𝑣22𝑔(𝑓±𝑛) , 𝐼𝑆𝐷=2 ×𝑆𝑆𝐷
  3. 𝑂𝑆𝐷=𝑑1+𝑑2+𝑑3 , 𝑑1=𝑣𝑏𝑑, 𝑑2=2𝑠+𝑣𝑏𝑇 , 𝑑3=𝑣𝑇 , 𝑇=√4𝑠/π‘Ž
  4. 𝑣2𝑅𝑔=𝑒+𝑓,Β π‘Šπ‘’=𝑛𝑙22𝑅+𝑉9.5βˆšπ‘…
  5. 𝐿𝑠=𝑣3𝐢𝑅(comfort condition)
  6. 𝐿𝑠=𝑒𝑁(π‘Š+π‘Šπ‘’) (rotated about inner edge)
  7. 𝐿𝑠=2.7𝑉2𝑅for plain and rolling terrain, 𝐿𝑠=𝑉2𝑅 for steep and mountainous terrain.
  8. IRC recommends Spiral as transition curve.
  9. 𝑆=𝐿𝑠224𝑅
  10. π‘š=𝑅(1βˆ’cosπœƒ2),Β πœƒ=𝑆/𝑅(single lane, 𝐿>𝑆)
  11. π‘š=𝑅(1βˆ’cosπœƒ2)+π‘†βˆ’πΏ2sinπœƒ2 ,Β πœƒ=𝐿𝑅(Single lane, 𝐿<𝑆)
  12. Curve resistance =𝑇(1βˆ’cos𝛼)
  13. Grade compensation =30+𝑅𝑅or 75𝑅whichever is less
  14. 𝐿=𝑁𝑠2(√2β„Ž+√2𝐻)2 when 𝐿>𝑠(Summit curve for SSD),Β β„Ž=0.15Β π‘Žπ‘›π‘‘Β π»=1.2
  15. 𝐿=2π‘ βˆ’(√2β„Ž+√2𝐻)2𝑁when 𝐿<𝑠 (Summit curve for SSD),Β β„Ž=0.15Β π‘Žπ‘›π‘‘Β π»=1.2
  16. 𝐿=𝑁𝑠2(√2𝐻+√2𝐻)2 when 𝐿>𝑠(Summit curve for OSD), 𝐻=1.2
  17. 𝐿=2π‘ βˆ’(√2𝐻+√2𝐻)2𝑁, 𝐿<𝑠 (Summit curve for OSD), 𝐻=1.2
  18. 𝐿=𝑁𝑠22β„Ž+2𝑠tan𝛼when 𝐿>𝑠 (valley curve),Β β„Ž=0.75Β π‘Žπ‘›π‘‘Β π›Ό=1Β°
  19. 𝐿=2π‘ βˆ’2β„Ž+2𝑠tan𝛼𝑁, 𝐿<𝑠 (valley curve),Β β„Ž=0.75Β π‘Žπ‘›π‘‘Β π›Ό=1Β°
  20. 𝐿=2(𝑁𝑣3𝐢)12 (valley curve comfort condition)
  21. 𝐢=8075+𝑉
  22. πΉπ‘™π‘Žπ‘˜π‘–π‘›π‘’π‘ π‘ πΌπ‘›π‘‘π‘’π‘₯=π‘€π‘’π‘–π‘”β„Žπ‘‘Β π‘œπ‘“Β π‘“π‘™π‘Žπ‘˜π‘¦Β π‘π‘Žπ‘Ÿπ‘‘π‘–π‘π‘™π‘’π‘ Β π‘€β„Žπ‘–π‘β„ŽΒ π‘Žπ‘Ÿπ‘’Β π‘‘β„Žπ‘–π‘›π‘›π‘’π‘ŸΒ π‘‘β„Žπ‘Žπ‘›Β 0.6Β π‘‘π‘šπ‘‘π‘œπ‘‘π‘Žπ‘™Β π‘€π‘’π‘–π‘”β„Žπ‘‘Γ—100
  23. πΈπ‘™π‘œπ‘›π‘”π‘Žπ‘‘π‘–π‘œπ‘›πΌπ‘›π‘‘π‘’π‘₯=π‘€π‘’π‘–π‘”β„Žπ‘‘Β π‘œπ‘“Β π‘“π‘™π‘Žπ‘˜π‘¦Β π‘π‘Žπ‘Ÿπ‘‘π‘–π‘π‘™π‘’π‘ Β π‘€β„Žπ‘–π‘β„ŽΒ π‘Žπ‘Ÿπ‘’Β π‘™π‘œπ‘›π‘”π‘’π‘ŸΒ π‘‘β„Žπ‘Žπ‘›Β 1.8Β π‘‘π‘šπ‘‘π‘œπ‘‘π‘Žπ‘™Β π‘€π‘’π‘–π‘”β„Žπ‘‘Γ—100
  24. Angularity number=67βˆ’100(π‘ŠπΊ)𝐢, C is weight water in the cylinder, W is weight of aggregate packed in the cylinder.
  25. Penetration test unit is 1/10th mm. Weight used 100 grams. Temperature 25℃.
  26. πΊπ‘Ž=π‘Š1+π‘Š2+π‘Š3π‘Š1𝐺1+π‘Š2𝐺2+π‘Š3𝐺3 and 𝐺𝑑=π‘Šπ‘Ž+π‘Šπ‘π‘Šπ‘ŽπΊπ‘Ž+π‘Šπ‘πΊπ‘
  27. πΊπ‘š=π‘€π‘’π‘–π‘”β„Žπ‘‘π‘œπ‘“Β π‘šπ‘œπ‘’π‘™π‘‘π‘‰π‘œπ‘™π‘’π‘šπ‘’Β π‘œπ‘“Β π‘šπ‘œπ‘’π‘™π‘‘
  28. π‘£π‘Ž=πΊπ‘‘βˆ’πΊπ‘šπΊπ‘‘, 𝑣𝑏=π‘Šπ‘π‘Šπ‘šΓ—πΊπ‘šπΊπ‘Β and 𝑉𝑀𝐴=π‘£π‘Ž+𝑣𝑏
  29. 𝑉𝐹𝐡=𝑣𝑏𝑉𝑀𝐴
  30. Flow value units 1/4th mm
  31. 𝑁=365𝐴[(1+π‘Ÿ)π‘›βˆ’1𝑛]𝑉𝐷𝐹×𝐿𝐷𝐹 and 𝐴=𝑃(1+π‘Ÿ)π‘₯
  32. 𝐿𝐷𝐹=0.75Β π‘“π‘œπ‘Ÿπ‘‘π‘€π‘œΒ π‘™π‘Žπ‘›π‘’π‘ Β π‘Žπ‘›π‘‘Β 0.4Β π‘“π‘œπ‘ŸΒ π‘“π‘œπ‘’π‘ŸΒ π‘™π‘Žπ‘›π‘’Β (single carriageway)
  33. LDF=0.75 for two lanes and 0.60 for three lane and 0.45 for four lane (dual carriageway)
  34. 𝑉𝐷𝐹=(𝑃80)4, where P is in kN
  35. πΆπ΅π‘…π‘Žπ‘‘Β 2.5Β π‘šπ‘š=π‘π‘Ÿπ‘’π‘ π‘ π‘’π‘Ÿπ‘’Β π‘–π‘›Β π‘˜π‘”/π‘π‘š270=π‘™π‘œπ‘Žπ‘‘Β π‘–π‘›Β π‘˜π‘”1370
  36. πΆπ΅π‘…π‘Žπ‘‘Β 5Β π‘šπ‘š=π‘π‘Ÿπ‘’π‘ π‘ π‘’π‘Ÿπ‘’Β π‘–π‘›Β π‘˜π‘”/π‘π‘š2105=π‘™π‘œπ‘Žπ‘‘Β π‘–π‘›Β π‘˜π‘”2055
  37. πΈπ‘†π‘ŠπΏ: interpolate load for depth from line joining (π‘™π‘œπ‘”π‘ƒ,log𝑧2) and (π‘™π‘œπ‘”2𝑃,log2𝑠).
  38. Radius of relative stiffness 𝑙=[πΈβ„Ž312π‘˜(1βˆ’πœ‡2)]14
  39. π‘˜=𝑝(π‘˜π‘”π‘π‘š2)0.125Β π‘π‘šΒ (modulus of subgrade reaction)
  40. π‘˜=𝐸1.18Β π‘Ž(π‘ŽΒ is rigid plate radius)
  41. π‘˜=𝐸1.5Β π‘Ž(π‘ŽΒ is flexible plate radius)
  42. π‘˜1π‘Ž1=π‘˜2π‘Ž2
  43. π‘…π‘–π‘”π‘–π‘‘π‘–π‘‘π‘¦π‘“π‘Žπ‘π‘‘π‘œπ‘Ÿ=π‘π‘œπ‘›π‘‘π‘Žπ‘π‘‘Β π‘π‘Ÿπ‘’π‘ π‘ π‘’π‘Ÿπ‘’π‘‘π‘¦π‘Ÿπ‘’Β π‘π‘Ÿπ‘’π‘ π‘ π‘’π‘Ÿπ‘’Β (below 7Β π‘˜π‘”/π‘π‘š2 contact pressure is more)
  44. 𝐿𝛼𝑑=𝛿2 (expansion joint)
  45. 𝐿𝑐2π‘β„Žπ›Ύπ‘π‘“=π‘†π‘π‘β„Ž
  46. π‘β„Žπ›Ύπ‘π‘“=𝐴𝑠𝑑𝑆𝑠 (tie bar area of steel per meter)
  47. 𝐿2πœ‹βˆ…πœπ‘π‘‘=πœ‹βˆ…24𝑆𝑠(length of tie bar)
  48. 𝑃(π‘₯)=(πœ†π‘‘)π‘₯π‘’βˆ’πœ†π‘‘π‘₯! (Poisson distribution)
  49. 𝑃(β„Žβ‰₯𝑑)=π‘’βˆ’πœ†π‘‘
  50. π‘˜=π‘˜π‘—(1βˆ’π‘£π‘£π‘“) and 𝑣=𝑣𝑓(1βˆ’π‘˜π‘˜π‘—)
  51. π‘ž=π‘˜π‘£andΒ π‘˜=1000π‘ π‘π‘Žπ‘π‘–π‘›π‘”
  52. 𝑃𝐻𝐹=π‘π‘’π‘Žπ‘˜β„Žπ‘œπ‘’π‘ŸΒ π‘“π‘™π‘œπ‘€4 Γ—π‘π‘’π‘Žπ‘˜Β 15Β π‘šπ‘–π‘›Β π‘“π‘™π‘œπ‘€Β or 𝑃𝐻𝐹=30π‘‘β„ŽΒ β„Žπ‘œπ‘’π‘Ÿπ‘™π‘¦Β π‘£π‘œπ‘™π‘’π‘šπ‘’π΄π΄π·π‘‡
  53. π‘‡π‘–π‘šπ‘’π‘šπ‘’π‘Žπ‘›Β π‘ π‘π‘’π‘’π‘‘=𝑣1+𝑣2+β‹―+𝑣𝑛𝑛
  54. π‘†π‘π‘Žπ‘π‘’π‘šπ‘’π‘Žπ‘›Β π‘ π‘π‘’π‘’π‘‘=𝑑𝑑1+𝑑2+β‹―+𝑑𝑛𝑛
  55. π‘ž=π‘›π‘Ž+π‘›π‘¦π‘‘π‘Ž+𝑑𝑀, 𝑑̅=π‘‘π‘€βˆ’π‘›π‘¦π‘ž
  56. Safe speed limit is 85th percentile speed
  57. Geometric design is based on 98th percentile speed.
  58. Road side facilities are based on 30th highest hourly volume.
  59. 𝐢0=1.5𝐿+51βˆ’π‘Œ0
  60. 𝑄=280𝑀(1+𝑒𝑀)(1βˆ’π‘3)(1+𝑀𝑙)
  61. π‘‡π‘Ÿ=π‘‡π‘Ž+π‘‡π‘šβˆ’π‘‡π‘Ž3
  62. πΈπ‘™π‘’π‘£π‘Žπ‘‘π‘–π‘œπ‘›π‘π‘œπ‘Ÿπ‘Ÿπ‘’π‘π‘‘π‘–π‘œπ‘›=7 %Β π‘“π‘œπ‘ŸΒ 300Β π‘š
  63. π‘†π‘‘π‘Žπ‘›π‘‘π‘Žπ‘Ÿπ‘‘π‘‘π‘’π‘šπ‘π‘’π‘Ÿπ‘Žπ‘‘π‘’π‘Ÿπ‘’Β π‘œπ‘“Β π‘Žπ‘–π‘Ÿπ‘π‘œπ‘Ÿπ‘‘,𝑇𝑠=15βˆ’6.51000β„Ž
  64. Temperature correction =1%Β π‘π‘’π‘Ÿ1β„ƒπ‘Ÿπ‘–π‘ π‘’Β π‘œπ‘“Β π‘‡π‘ŸΒ π‘Žπ‘π‘œπ‘£π‘’Β π‘‡π‘ 
  65. Gradient correction =20%Β π‘π‘’π‘Ÿ1%Β π‘’π‘“π‘“π‘’π‘π‘‘π‘–π‘£π‘’π‘”π‘Ÿπ‘Žπ‘‘π‘–π‘’π‘›π‘‘.
  66. π‘‡π‘’π‘Ÿπ‘›π‘–π‘›π‘”π‘Ÿπ‘Žπ‘‘π‘–π‘’π‘ Β π‘…=𝑉2125𝑓
  67. π‘‡π‘’π‘Ÿπ‘›π‘–π‘›π‘”π‘Ÿπ‘Žπ‘‘π‘–π‘’π‘ Β π‘…=0.388π‘Š2𝑇2βˆ’π‘†Β where 𝑠=6+π‘‘π‘Ÿπ‘’π‘Žπ‘‘2
  68. Turning radius for subsonic aircraft is 120 m and for supersonic it is 180 m
  69. Grade compensation for BG is 0.04%, for MG is 0.03% and for NG is 0.02% per degree of curve.
  70. 𝐷=1720𝑅
  71. π‘‰π‘’π‘Ÿπ‘ π‘–π‘›π‘’π‘œπ‘“Β π‘π‘’π‘Ÿπ‘£π‘’=𝑐28𝑅
  72. πΈπ‘žπ‘’π‘–π‘™π‘–π‘π‘Ÿπ‘–π‘’π‘šπ‘π‘Žπ‘›π‘‘=𝑉2127𝑅×𝐺
  73. Theoretical cant =πΈπ‘žπ‘’π‘–π‘™π‘–π‘π‘Ÿπ‘–π‘’π‘šπ‘π‘Žπ‘›π‘‘+π‘π‘Žπ‘›π‘‘π‘‘π‘’π‘“π‘–π‘π‘–π‘’π‘›π‘π‘¦
  74. Widening of gauge in cm, 𝑑=13(𝐡+𝐿)2𝑅where B is wheel base in m, lap of flange in m, 𝐿=0.02βˆšβ„Ž2+π·β„ŽΒ , h is depth of wheel flange below rail top level, D dia of wheel in cm.
  75. 𝐿𝑠=3.28𝑣3𝑅(Transition curve)
  76. 𝑦=π‘₯36𝐿𝑅(Transition curve)
  77. Usually adopted transition curve for railways is cubic parabola.

Hello friends, my name is Bipin Kumar, I am the Writer and Founder of this blog and share all the information related to Civil Engineering, Civil practical Knowledge, Site Execution Knowledge, latest information about construction and more through this website.

Leave a Comment