MP Sub Engineer Civil Formulas – Soil, Survey, BMC, RCC & Estimation | Complete Formula Sheet

MP Sub Engineer Civil
Complete Important Formulas
Soil + Survey + BMC + CT/RCC + Estimation

Last 5 Years Average Weightage (Technical 100 Qs)

Subject	Approx. Questions	Priority
Soil Mechanics + Foundation	12 – 20	Highest
Surveying	10 – 15	Highest
Building Materials + Construction	10 – 18	Highest
Concrete Technology + RCC	10 – 15	High
Estimation & Costing	8 – 13	High
Total from these 5	55 – 70	Most Important

1. Soil Mechanics – Complete Important Formulas

Basic Properties

1. Void Ratio (e) = V_v / V_s

2. Porosity (n) = (V_v / V) × 100   |   n = e/(1+e)

3. Degree of Saturation (S) = (V_w / V_v) × 100

4. Water Content (w) = (W_w / W_s) × 100

5. Specific Gravity (G) = γ_s / γ_w

6. Bulk Unit Weight γ = (G + S e)/(1 + e) × γ_w

7. Dry Unit Weight γ_d = G/(1 + e) × γ_w = γ/(1 + w)

8. Saturated Unit Weight γ_sat = (G + e)/(1 + e) × γ_w

9. Submerged Unit Weight γ' = (G – 1)/(1 + e) × γ_w

10. Fundamental Relation: S e = G w

11. Relative Density I_D = (e_max – e)/(e_max – e_min) × 100

12. Density Index I_d = (γ_d – γ_{d min})/(γ_{d max} – γ_{d min}) × 100

Index Properties & Classification

13. Liquidity Index I_L = (w – PL)/(LL – PL)

14. Consistency Index I_C = (LL – w)/(LL – PL)

15. Plasticity Index PI = LL – PL

16. Shrinkage Index = PL – SL

17. Activity = PI / (% clay fraction)

18. Coefficient of Uniformity C_u = D₆₀ / D₁₀

19. Coefficient of Curvature C_c = (D₃₀)² / (D₆₀ × D₁₀)

20. Group Index GI = 0.2a + 0.005ac + 0.01bd

Permeability

21. Darcy’s Law: Q = k i A   |   v = k i

22. Constant Head: k = (QL)/(A h t)

23. Falling Head: k = (2.303 a L / A t) log₁₀(h₁/h₂)

24. Hazen’s Formula: k = C D₁₀² (C ≈ 100–150)

Compaction

25. Dry Density γ_d = γ / (1 + w)

26. Zero Air Void Line: γ_d = (G γ_w)/(1 + w G)

27. Relative Compaction = (γ_{d field} / γ_{d max}) × 100

Consolidation

28. Compression Index C_c = (e₁ – e₂)/log(σ₂/σ₁)

29. Settlement S_c = [C_c H /(1 + e₀)] log₁₀[(σ₀ + Δσ)/σ₀]

30. Time Factor T_v = (C_v t)/d²

31. Coefficient of Consolidation C_v = (T_v d²)/t

32. Coefficient of Volume Compressibility m_v = a_v/(1 + e₀)

Shear Strength

33. Coulomb’s Equation: τ = c + σ tan φ

34. Unconfined Compressive Strength q_u = 2c (for φ=0)

35. Sensitivity = q_u undisturbed / q_u remoulded

Earth Pressure

36. Rankine Active: K_a = (1 – sinφ)/(1 + sinφ) = tan²(45° – φ/2)

37. Rankine Passive: K_p = (1 + sinφ)/(1 – sinφ) = tan²(45° + φ/2)

38. Active Pressure P_a = ½ γ H² K_a

39. Passive Pressure P_p = ½ γ H² K_p

Bearing Capacity

40. Terzaghi Ultimate: q_u = c N_c + γ D_f N_q + 0.5 γ B N_γ

41. Net Ultimate q_nu = q_u – γ D_f

42. Safe Bearing Capacity = q_nu / FOS + γ D_f

43. Plate Load Test: Settlement relation S_f/S_p = [(B_f(B_p+0.3))/(B_p(B_f+0.3))]²

2. Surveying – Complete Important Formulas

Chain Surveying & Corrections

1. True Length L = L' × (l / l')   (l = true length of chain, l' = incorrect)

2. Temperature Correction C_t = α (T_m – T₀) L

3. Pull Correction C_p = (P – P₀) L / (A E)

4. Sag Correction C_s = – (W² L)/(24 P²)

5. Slope Correction C_slope = – (h²)/(2L)

6. Absolute Error = Difference between true & measured

7. Relative Error = Absolute Error / True Value

Compass Surveying

8. Fore Bearing – Back Bearing = ± 180°

9. Included Angle = Difference of bearings of two lines

10. Declination: True Bearing = Magnetic Bearing ± Declination

Levelling

11. HI = RL of BS station + BS reading

12. RL = HI – FS (or IS)

13. Rise & Fall: New RL = Old RL + Rise – Fall

14. Check: Σ BS – Σ FS = Last RL – First RL

15. Curvature Correction C_c = –0.0785 D² (D in km)

16. Refraction Correction C_r = +0.0112 D²

17. Combined Correction = –0.0673 D²

Contouring & Area/Volume

18. Horizontal Equivalent = Contour Interval / tan(slope)

19. Trapezoidal Rule: A = (d/2)(y₁ + 2y₂ + … + 2y_n-1 + y_n)

20. Simpson’s Rule: A = (d/3)(y₁ + 4y₂ + 2y₃ + 4y₄ + … + y_n)

21. Volume by Trapezoidal: V = (d/2)(A₁ + 2A₂ + … + 2A_n-1 + A_n)

22. Volume by Prismoidal: V = (d/3)(A₁ + 4A_m + A₂)

Theodolite & Curves

23. Latitude = L cos θ   |   Departure = L sin θ

24. Radius of Curve R = 1720 / D (D = degree of curve for 30m chain)

25. Length of Curve L = (π R Δ)/180

26. Tangent Length T = R tan(Δ/2)

27. Chainage of T₁ = Chainage of Intersection – T

28. Chainage of T₂ = Chainage of T₁ + L

29. Mid Ordinate M = R (1 – cos(Δ/2))

30. External Distance E = R (sec(Δ/2) – 1)

31. Length of Long Chord = 2 R sin(Δ/2)

32. Apex Distance = R (sec(Δ/2) – 1)

3. Building Materials & Construction – Complete Formulas & Values

Cement

1. Specific Gravity of Cement ≈ 3.15

2. Standard Consistency = 25% – 35%

3. Initial Setting Time ≥ 30 min (OPC)

4. Final Setting Time ≤ 600 min (10 hrs)

5. Fineness (by sieve) ≤ 10% retained on 90 micron

6. Compressive Strength (28 days): 33/43/53 Grade

Aggregates & Concrete

7. Fineness Modulus = Σ Cumulative % retained / 100

8. Bulking of Sand = (V_moist – V_dry)/V_dry × 100

9. Water-Cement Ratio w/c = Weight of water / Weight of cement

10. Nominal Mixes (by volume):

• M10 → 1 : 3 : 6
• M15 → 1 : 2 : 4
• M20 → 1 : 1.5 : 3
• M25 → 1 : 1 : 2

11. Slump Values:

• Mass concrete / Roads → 25–50 mm
• Beams & Slabs → 50–100 mm
• Columns → 75–150 mm

12. Aggregate Impact Value ≤ 30% (for wearing surface)

13. Aggregate Crushing Value ≤ 30%

14. Los Angeles Abrasion Value ≤ 30% (for pavement)

Bricks & Masonry

15. Modular Brick Size = 190 × 90 × 90 mm

16. Brick with mortar = 200 × 100 × 100 mm

17. Number of modular bricks per m³ ≈ 500

18. Water Absorption of brick ≤ 20% (1st class)

19. Compressive Strength of 1st class brick ≥ 10.5 N/mm²

Timber & Others

20. Moisture Content of Timber = (W_wet – W_dry)/W_dry × 100

21. Seasoning reduces moisture to 10–12%

4. Concrete Technology + RCC – Complete Formulas

Working Stress Method (Most Asked)

1. Modular Ratio m = 280 / (3 σ_cbc)

2. Neutral Axis factor k = m / (m + σ_st/σ_cbc)

3. Lever Arm factor j = 1 – k/3

4. Moment of Resistance Factor Q = ½ σ_cbc k j

5. Moment of Resistance M = Q b d²

6. Area of Tension Steel A_st = M / (σ_st × j × d)

7. Percentage Steel p_t = (A_st /(b d)) × 100

8. Critical Neutral Axis depth n_c = (m σ_cbc /(m σ_cbc + σ_st)) × d

Shear & Bond

9. Nominal Shear Stress τ_v = V / (b d)

10. Development Length L_d = (φ σ_s) / (4 τ_bd)

11. Minimum Shear Reinforcement: A_sv / (b s_v) ≥ 0.4 / (0.87 f_y)

12. Maximum Spacing of Stirrups = 0.75 d (vertical) or 300 mm (whichever less)

Limit State Basics (IS 456)

13. Design Strength of Concrete = 0.67 f_ck / 1.5 = 0.446 f_ck

14. Design Strength of Steel = 0.87 f_y

15. Xu max / d = 0.53 (Fe250), 0.48 (Fe415), 0.46 (Fe500)

16. Limiting Moment of Resistance M_{u lim} = 0.149 f_ck b d² (for Fe415)

17. pt lim = 41.61 (f_ck/f_y) × (Xu max/d) (approx values used in exam)

Cover & Deflection

18. Nominal Cover (IS 456):

• Mild → 20 mm
• Moderate → 30 mm
• Severe → 45 mm
• Very Severe → 50 mm
• Extreme → 75 mm

19. Basic L/d ratio: Simply Supported = 20, Continuous = 26, Cantilever = 7

20. Effective Depth d = Overall depth D – Effective cover

5. Estimation & Costing – Complete Formulas

Types of Estimates & Areas

1. Plinth Area Estimate = Plinth Area × Plinth Area Rate

2. Cubic Content Estimate = Plinth Area × Height × Rate per m³

3. Carpet Area ≈ 50–65% of Plinth Area (residential)

4. Floor Area Ratio (FAR) = Total Floor Area / Plot Area

5. Built-up Area = Carpet Area + Wall Area + Wet Areas

Quantity of Materials

6. Number of Bricks = Volume of brickwork / Volume of 1 brick with mortar

7. Cement Bags (approx for 1 m³ concrete):

• 1:3:6 (M10) → 4.4 bags
• 1:2:4 (M15) → 6.4 bags
• 1:1.5:3 (M20) → 8.0 bags
• 1:1:2 (M25) → 10.2 bags

8. Dry Volume of Concrete = 1.54 × Wet Volume

9. Steel Weight = (D² / 162) × Length (m)   → kg

10. Thumb Rule Steel Quantity:

• Slab → 0.7% – 1.0% of concrete volume
• Beam → 1.0% – 2.0%
• Column → 1.0% – 5.0%
• Foundation → 0.5% – 0.8%

Valuation

11. Scrap Value = Original Cost – Total Depreciation

12. Salvage Value = Value at the end of utility period without being dismantled

13. Straight Line Depreciation = (C – S)/n

14. Constant Percentage Method: Annual Dep. = 1 – (S/C)^1/n

15. Sinking Fund A = S i / [(1+i)ⁿ – 1]

16. Year’s Purchase = 100 / Rate of Interest (%)

17. Capitalized Value = Net Annual Income × Year’s Purchase

18. Obsolescence = Loss in value due to change in fashion/design

Exam Tip: D²/162, Cement bags, Nominal mixes, Modular ratio, Se = Gw, Rankine Ka/Kp, Curve formulas (T, L, M, E) और Terzaghi bearing capacity सबसे ज्यादा पूछे जाते हैं। इन्हें रोज revise करें।

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MP Sub Engineer Civil – Complete Formula Sheet
Soil (43) + Survey (32) + BMC (21) + CT/RCC (20) + Estimation (18) = 134 Important Formulas
Practice daily for maximum score in Technical Section.