Civil engg formulas

Strength of material
1. =
2.
3.
4.
5.
6.
7.
8.
9.
10. =
11.
12. and (Leaf spring)
13. (Helical spring)
14.
15.
16.
17.
18. (hinged and hinged)) , (fixed and free)
19. (Fixed and fixed) ,
20. where
Structural analysis
1. and (Point load)
2. and (udl)
3. and (uvl from left to right increase)
4. and (clockwise moment)
5. , and
6. (rectangular beam)
7. (two hinged arch)
8. H (cable with udl) and Length of cable
9. , right support sinks by
10. , right support sinks by
11.
12.
13. and
14. ,
15. Far end fixed, Transverse displacement, and
16. Far end hinged, Transverse displacement, and
RCC
1.
2. and
3.
4. ,
5. for T-beams.
6. for L-beams.
7. for isolated T-beams.
8. for isolated L-beams.
9. and
10. for
11.
12.
13.
14. when
15.
16.
17. (minimum tension reinforcement)
18. of for - and of for - .
(slabs)
19. (Beams) , (Beams)
20.
21. 7 for cantilever, 20 for SS and 26 for continuous beams.
If span is more than 10 m, multiply above values with 10/span for
SS and continuous beams.
22. , multiply value with 1.6 for deformed bars and 1.25
for bars in compression.
23. and (If confinement exists)
24. ,
25.
26. (minimum shear reinforcement)
27. for vertical stirrups.
28. and
29. for ss and for continuous slabs for Fe-250. For Fe-415
multiply above values with 0.8
30. , and
31. whichever is greater.
32. whichever is greater.
33.
34. , and
35.
36. , , Largest frustum of a
pyramid with side slopes 1 in 2, loaded area of column base
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Geotechnical Engineering
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. where is clay fraction (Activity)
11.
12. (non homogeneous)
13.
14. (absolute permeability)
15. (Permeability in unconfined aquifer)
16. (Permeability in confined aquifer)
17. (effective horizontal permeability in stratified
soils)
18. (effective vertical permeability in stratified soils)
19. (effective permeability)
20. (falling head permeability test)
21. (constant head permeability test)
22. (seepage discharge)
23.
24. where
formula)
25. (line load)
26. where (stress under centre
of strip load of width )
27. where
( strip eccentric point)
28. where (stress
under centre of circular load)
29. (for cohesion less soils)
30. (for cohesive soils)
31. where
32. (shear box test for cohesion less soils)
33. (if both top and bottom surfaces
contributes)
34. (if only bottom surface contribute)
35. (immediate settlement )
36. (settlement of footing based on plate
settlement)
37.
parameters)
38. is stress path equation where and
39.
40. (for normally consolidated soil)
41. (for over consolidated soil)
42.
43.
44.
45.
46. when
47. when
48.
49.
50.
51.
52.
53.
54.
55. s
rectangle)
56.
(Meyerhof)
and
57. (Skempton)
Limiting value of
58. (ENR) where
59. (Hiley)
where
with dolley and without dolley and
when
when
60. (Danish)
61. (clays)
62. (clays)
63. (sands)
64. or (Group)
65.
66.
67. and

68. and unsupported vertical cut
69.
70.
71. and
(Inclined backfill)
72. and
(Inclined backfill)
73.
(dilatancy)
74. (Quick sand condition)
Hydrology
1. A tropical cyclone is a zone of low pressure with anticlockwise
winds in the northern hemisphere.
2. Anticyclones cause clockwise wind circulations in the northern
hemisphere.
3. , and
4. (Normal ratio method)
5. (Thiessen-mean method)
6. (Isohyetal method)
7. and
8. 75% dependable annual rainfall is annual rainfall with probability
, i.e.
9. The chemical used as evaporation inhibitor is cetyl alcohol.
10. Evapotranspiration can be measured by Lysimeters.
11.
12. : It is the average rainfall above which the rainfall volume
is equal to the runoff volume.
13. :
14. and
15. (Dilution technique)
16. , (Equilibrium discharge) A in and D in h. in
17. and (Gumbels)
18.
19. , , and
,
20.
21. (recuperation test)

Fluid mechanics
1.
2. (continuity equation)
3. 0 (continuity equation)
4.
5. (Jet propulsion
moving with velocity)
6.
7. and
8. and
9.
10.
11.
12. (Turbulent)
13.
14. (Compound pipe)
15. and (Siphon)
16.
17.
18.
19. Blassius boundary layer thickness
20. Displacement thickness
21. Momentum thickness
22. and
23. Drag force ,
24. (Laminar sub layer)
25. and
26.
27. Q
28.
29. and
30.
31. and
32. and
33.
34.
35.
36.
37.
38.
39. Vorticity
40. Circulation
41.
42. ( is with plate)
43.
44.
45.
46. and
47.
48. + = (specific force pressure force momentum per
sec)
49. (sequent depths for rectangular channel)
50. (Energy loss in jump)

Irrigation Engineering
1.
2.
3.
4.
5.
6.
7.
8.
9. , and
10.
11.
12.
13.
14.
15. , is in meters
16.
17.
18.
19.
20.
21.
22.
23.
24. for Lined
Triangular section.
25. for Lined
Trapezoidal section.
26. Launching apron scour depth,
,
27. Length of launching apron
28. , where
29. , where
30. ,
31. , and
32. and
33. and
, and
,
34. Non-modular modules: Drowned pipe outlet, masonry
sluice and wooden shoots.
35. Semi modules or flexible modules: Pipe outlet, venturi
36.
foote module.
37. Flexibility , discharge in outlet and
discharge in channel, outlet index and
channel index. working head of outlet and
depth of water in channel.
38. Proportionality:
39. Setting
40. , hyper proportional outlet.
41. , sub proportional outlet.
42. Sensitivity,
43. Aqueduct: Canal over drainage with clear gap.
44. Syphon Aqueduct: Canal over drainage with syphonic
action.
45. Super passage: Drain over canal with clear gap.
46. Canal Syphon: Drain over canal with syphonic action.
47. Principal stress in dam
where and water
pressure of tail water and
48.
49. and
50.

Environmental Engineering
1. , where average of population
increase (Arithmetic increase method)
2. , where (Geometric increase
method)
3. , where average of incremental
increase
4. Carbonate hardness Total hardness or Alkalinity whichever is
lesser.
5. Non-carbonate hardness Total hardness carbonate hardness
6. Total hardness in mg/l in mg/l in
mg/l
7. Akalinity in mg/l in mg/l in
mg/l
8. Ammonia nitrogen and organic nitrogen is called Kjedahl nitrogen.
9. Colour: 5 Hazen units (max), PH: 6.5-8.5, Turbidity: 1 NTU (max),
TDS: 500 mg/l (max), Chloride: 250 mg/l (max), Sulphate: 200 mg/l
(max), Nitrate: 45 mg/l (max), fluoride : 1mg/l (max), Total
alkalinity: 200 mg/l (max), Total hardness: 200 mg/l (max),
Magnesium: 30 mg/l (max), Calcium: 75 mg/l (max), Zinc: 5 mg/l
(max), Iron: 0.3 mg/l (max), Free residual chlorine: 0.2 mg/l (min).
10. Toxic substances: Cadmium, Cyanide, lead, Mercury, Nickel,
Arsenic, chromium.
11. E-coli shall not be detectable in any 100 ml sample of drinking
water.
12. Standard sample of MPN: 10ml, 1 ml and 0.1 ml
13. MPN/100 ml, by Thomas
14.
15. Percentage particle removal: If
16. Chemical used in coagulation: Alum (Aluminium sulphate),
Copperas (Ferrous sulphate), Chlorinated copperas, Sodium
aluminates.
17. A 18 + 3 Ca
3Ca +2Al +6C +18
18. Alkalinity requirement as per of Alum
19. Permanent hardness due to alum as per
of Alum
20. Sludge production as per of Alum
21. release
22. where P is in Watts
23. PH range for alum: 6.5 to 8.3.
24. is most destructive disinfectant.
25. Quick lime required in softening Carbonate hardness in as
+
26. Soda required in softening Non-carbonate hardness in as
27.
28.
29. and
30.
where organic loading kg/ha-m/day
31. where
32. HRT =
33. Volumetric BOD loading = organic loading =
=
34. =
35.
36. Sludge volume index (SVI)
37. =
38. C =
39.
40.
41.
42. Primary pollutants: CO, , , hydrocarbons and particulate
matter are primary air pollutants.
43. Secondary pollutants: Ozone, PAN (Peroxy acetyl nitrate),
photochemical mog, Aerosols and mists.
: Sub adiabatic and stable.
: Super adiabatic and unstable
46. 20 where
47. =10
48. Addition of sound levels:
49. Averaging of Sound Pressure Levels:
50. 20

Transportation Engineering
1. (parabolic camber)
2. ,
3. , , , ,
4. ,
5. (comfort condition)
6. (rotated about inner edge)
7. for plain and rolling terrain, for steep and
mountainous terrain.
8. IRC recommends Spiral as transition curve.
9.
10. , (single lane, )
11. , (Single lane,
12. Curve resistance
13. Grade compensation or whichever is less
14. when (Summit curve for SSD),
15. when (Summit curve for SSD),
16. when (Summit curve for OSD),
17. , (Summit curve for OSD),
18. when (valley curve),
19. , (valley curve),
20. (valley curve comfort condition)
21.
22.
23.
24. Angularity number , 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. and
27.
28. , and
29.
30. Flow value units 1/4th
mm
31. and
32. (single
carriageway)
33. LDF=0.75 for two lanes and 0.60 for three lane and 0.45 for four
lane (dual carriageway)
34. , where P is in kN
35.
36.
37. interpolate load for depth from line joining
and .
38. Radius of relative stiffness
39. (modulus of subgrade reaction)
40. ( is rigid plate radius)
41. ( is flexible plate radius)
42.
43. (below contact
pressure is more)
44. (expansion joint)
45.
46. (tie bar area of steel per meter)
47. (length of tie bar)
48. (Poisson distribution)
49.
50. and
51. and
52. or
53.
54.
55. ,
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.
60.
61.
62.
63.
64. Temperature correction
65. Gradient correction
66.
67. where
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.
71.
72.
73. Theoretical cant
74. Widening of gauge in cm, where B is wheel base in
m, lap of flange in m, , h is depth of wheel
flange below rail top level, D dia of wheel in cm.
75. (Transition curve)
76. (Transition curve)
77. Usually adopted transition curve for railways is cubic parabola.

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