Civil Engineering Formulas and Handbook
Section 1) Surveying
Traverse Surveying
Correction For Sag $$ {C_s} = {{{w^2}{l^3}}\over {24.P^2}} $$ Note:-sag correction is subtractive
Where
w = weight of tape per meter
l= distance between supports
P = Applied Tension
Correction For Tension $$ {C_p} = {{(P-{P_0})l}\over AE} $$
Levelling
Reciprocal levelling
Section 2) Transportation Engineering
Stopping site distance
Stopping site distance (SSD in 'metres') of a vehicle is the sum of :
1) The distance travelled by the vehicle during the total reaction time known as lag distance and
$${\text{Lag distance}}=0.278Vt$$
2) The distance travelled by the vehicle after the application of the brakes, to a dead stop position which is known as braking distance.
$${\text{Braking distance}}={{V^2}\over {254(f\pm S \%)}}$$
$$\text{SSD = Lag distance + Braking distance}$$
$$SSD = 0.278Vt + {{V^2}\over {254(f\pm S \%)}}$$
Where S% is gradient '+' sign for ascending gradient & '-' sign for descending gradient
Overtaking Site Distance (OSD)
| Terrain Catogory | Over taking Sight Distance | Safe stopping sight for minimum design speed | Safe stopping sight for Rulling design speed |
|---|---|---|---|
| Plain Terrain | 475 | 120 | 170 |
| Rolling Terrain | 310 | 90 | 120 |
| Hilly Terrain | - | 50 | 60 |
| Steep | - | 40 | 50 |
Super Elevation (e)
| emax | Terrain Type |
|---|---|
| 0.07 | Plain and Rolling Terrain |
| 0.10 | Hilly Area |
| 0.04 | Urban roads with frequent intersections |
Ruling minimum radius of the curve
Radii for horizontal curves in meters
| Terrain Catogory | Absolute | Rulling |
|---|---|---|
| Plain Terrain | 250 | 370 |
| Rolling Terrain | 155 | 250 |
| Hilly Terrain | 50 | 80 |
| Steep | 30 | 50 |
Extra Widening (Ew)
Transition Curve
Length of transition curve (L)
(i) According to rate of change of centrifugal acceleration
(ii) According to rate of change of super elevation
(iii) According to empirical formula
To find out offset length at desired chainage 'x' the equation of cubical parabola
Set Back Distance (m)
1. For Single lane road
&
$${\alpha \over 2}={{180.s}\over {2\Pi R}}$$
Where, Lc = Length of Curve & s = SSD
(b) Lc < SSD
$$m=R\left({1-cos{\alpha \over 2}}\right) + {{S - L_c}\over 2} sin{\alpha \over 2}$$
&
$${\alpha \over 2}={{180.L_c}\over {2\Pi R}}$$
2. For two lane road
&
$${\alpha \over 2}={{180.s}\over {2\Pi (R-d)}}$$
Where, Lc = Length of Curve & s = SSD
(b) Lc < SSD
$$m=R-(R-d)\left({1-cos{\alpha \over 2}}\right) + {{S - L_c}\over 2} sin{\alpha \over 2}$$
&
$${\alpha \over 2}={{180.L_c}\over {2\Pi (R-d)}}$$
Grade Compensation
Vertical Curve
Summit curves (Crest curve with convexity upwards):
Valley Curves (Sag curve with Concavity Upward):
Summit curves (Crest curve with convexity upwards):
Section 3) Mechanics of Materials
1️⃣ Stress
2️⃣ Strain
$$\varepsilon = \frac{\Delta L}{L}$$
3️⃣ Hooke's Law
$$\sigma = E \times \varepsilon$$
4️⃣ Shear Stress
5️⃣ Bending Stress (Flexure Formula)
6️⃣ Torsional Shear Stress
7️⃣ Deflection of Simply Supported Beam (Center Load)
8️⃣ Euler's Buckling Load (Pinned-Pinned)
9️⃣ Moment of Inertia (Rectangle)
🔟 Torsion Equation
1️⃣1️⃣ Principal Stresses (2D)
1️⃣2️⃣ Maximum Shear Stress
1️⃣3️⃣ Strain Energy (Axial Load)
1️⃣4️⃣ Castigliano's Theorem (Deflection at point of load P)
1️⃣5️⃣ Shear Force (Beam Element)
$$\frac{dV}{dx} = -w(x)$$
1️⃣6️⃣ Bending Moment (Beam Element)
$$\frac{dM}{dx} = V(x)$$
1️⃣7️⃣ Relation between Moment and Slope
1️⃣8️⃣ Slenderness Ratio
1️⃣9️⃣ Radius of Gyration
Section 4) Hydraulics
The depth at partial flow can be evaluated from equation -
$$ d = ({D\over 2}-{D\over 2}.cos{\alpha\over 2}) $$Discharge when pipe is running partially full,
q =av
Proportionate discharge = $$ {q\over Q} = {{a.v}\over {A.v'}}$$
=$$ {q\over Q} =({\alpha\over 360^\circ}-{sin\alpha\over 2\pi}).{(1-{{{360^\circ}sin\alpha}\over {2 \pi \alpha}})}^{2\over 3}$$
for detailed derivation go to link
The broad-crested weir is a type of weir used in open channel flow measurements, which has a rectangular notch on top. The discharge over a broad-crested weir can be calculated using the following equation:
$$Q = CLH^{3/2}$$
where:
- Q is the discharge over the weir [m^3/s],
- C is the discharge coefficient, which depends on the shape and size of the weir,
- L is the width of the weir [m],
- H is the height of the water above the weir crest [m].
To calculate the value of C, you can use one of the following equations:
- For a rectangular weir:
$$C = 1.84 - 0.5\left(\frac{H}{L}\right)^{1.5} + 0.25\left(\frac{H}{L}\right)^3$$
For Trapezoidal weir:-
$$C = \frac{2}{3}\left(1 + \frac{2h}{b}\right)\left(1 - \frac{h}{H}\right)^{3/2}$$
where:
- V is the average velocity of flow [m/s],
- C is the Chezy coefficient, which is a dimensionless constant that depends on the roughness of the channel,
- R is the hydraulic radius, which is the cross-sectional area of flow divided by the wetted perimeter [m],
- S is the slope of the energy line, which is the change in energy per unit length of the channel [m/m].
The loss of head due to friction is an important concept in fluid mechanics and is often used in the design of pipelines and other fluid transport systems. The loss of head due to friction is given by the Darcy-Weisbach equation:
$$h_f = \frac{fLV^2}{2gd}$$
where:
- h_f is the loss of head due to friction [m],
- f is the Darcy-Weisbach friction factor, which depends on the Reynolds number and the roughness of the pipe,
- L is the length of the pipe [m],
- V is the average velocity of flow in the pipe [m/s],
- g is the acceleration due to gravity (approximately 9.81 m/s^2), and
- d is the diameter of the pipe [m].
where:
- V is the average velocity of flow [m/s],
- n is the Manning's roughness coefficient, which is a dimensionless constant that depends on the roughness of the channel,
- R is the hydraulic radius, which is the cross-sectional area of flow divided by the wetted perimeter [m],
- S is the slope of the energy line, which is the change in energy per unit length of the channel [m/m].
Section 5) Stresses in Structures
Equation of Pure torsion
$${T\over {I_p}}={\tau \over r}={{G \theta} \over L}$$
Where,
Ï„ --> Shear stress for example shear stress on wall of a tube subjected to torsion
Ó¨ --> Angle of twist
$$G = {E\over {2(1+\mu)}}$$
1) Circular tube subjected to torsion
$$\text{Polar Moment of Inertia }{I_p} = \text{Area of The section }\times{r^2}$$
$$(\pi D t)\times \left({D \over 2}\right)^2 = {{\pi {D^3} t}\over 4}$$
2) Thin Square tube subjected to torsion
Maximum shear stress Ï„ is given by
$$\tau = {T\over {2A.t}}$$
Normal Stress (Axial)
$$ \sigma = \frac{P}{A} $$
Where:
\( \sigma \) = Normal stress (N/mm² or MPa)
\( P \) = Axial load (N)
\( A \) = Cross-sectional area (mm²)
Shear Stress
$$ \tau = \frac{V}{A} $$
Where:
\( \tau \) = Shear stress (N/mm²)
\( V \) = Shear force (N)
\( A \) = Area resisting shear (mm²)
Bending Stress (Flexural Formula)
$$ \sigma = \frac{M y}{I} $$
Where:
\( M \) = Bending moment (Nmm)
\( y \) = Distance from neutral axis (mm)
\( I \) = Moment of inertia (mm⁴)
Torsional Shear Stress
$$ \tau = \frac{T r}{J} $$
Where:
\( T \) = Applied torque (Nmm)
\( r \) = Distance from center to outer fiber (mm)
\( J \) = Polar moment of inertia (mm⁴)
Combined Axial and Bending Stress
$$ \sigma_{max} = \frac{P}{A} \pm \frac{M y}{I} $$
Principal Stresses (2D State)
$$ \sigma_{1,2} = \frac{\sigma_x + \sigma_y}{2} \pm \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} $$
Where:
\( \sigma_x, \sigma_y \) = Normal stresses
\( \tau_{xy} \) = Shear stress
Maximum Shear Stress
$$ \tau_{max} = \frac{\sigma_1 - \sigma_2}{2} $$
Bearing Stress
$$ \sigma_b = \frac{P}{A_b} $$
Where:
\( A_b \) = Bearing area (mm²)
Hoop (Circumferential) Stress (Thin Cylindrical Pressure Vessel)
$$ \sigma_h = \frac{p d}{2 t} $$
Where:
\( p \) = Internal pressure (N/mm²)
\( d \) = Internal diameter (mm)
\( t \) = Thickness (mm)
Longitudinal Stress (Pressure Vessel)
$$ \sigma_l = \frac{p d}{4 t} $$
Section 6) Steel Design
1️⃣ Design Stress in Steel
2️⃣ Design Tensile Strength (Gross Section)
3️⃣ Design Tensile Strength (Net Section)
4️⃣ Slenderness Ratio
5️⃣ Plastic Section Modulus
6️⃣ Shear Strength (Web Area)
7️⃣ Bolt Shear Strength (Single Plane)
8️⃣ Weld Strength
9️⃣ Factored Load
$$P_u = \gamma_f \times P$$
🔟 Bending Moment — Shear Force Relation
$$\frac{dM}{dx} = V(x)$$
Section 7) Concrete Mix Design
Water-Cement Ratio (Abram’s Law)
$$ \frac{f_1}{f_2} = \left(\frac{w_2}{w_1}\right)^n $$
where:
\( f_1, f_2 \) = compressive strengths
\( w_1, w_2 \) = water-cement ratios
\( n \) = constant (usually between 5 to 7)
Volume of Concrete
$$ V = \frac{W + \frac{C}{\rho_c} + \frac{F}{\rho_f} + \frac{C.A}{\rho_{ca}} + \frac{F.A}{\rho_{fa}} + \frac{W}{\rho_w}}{1000} $$
Absolute Volume of Cement
$$ V_c = \frac{W_c}{\rho_c} $$
Absolute Volume of Fine Aggregate
$$ V_{fa} = \frac{W_{fa}}{\rho_{fa}} $$
Absolute Volume of Coarse Aggregate
$$ V_{ca} = \frac{W_{ca}}{\rho_{ca}} $$
Volume of Water
$$ V_w = \frac{W_w}{\rho_w} $$
Air Content (as percentage)
$$ \text{Air \%} = \frac{V_{air}}{V_{total}} \times 100 $$
Aggregate Proportioning by Weight
$$ \frac{W_{ca}}{W_{fa}} = \frac{V_{ca} \times \rho_{ca}}{V_{fa} \times \rho_{fa}} $$
Volume of Cementitious Materials
$$ V_m = \frac{W_c}{\rho_c} + \frac{W_{fa}}{\rho_{fa}} + \frac{W_{ca}}{\rho_{ca}} + \frac{W_w}{\rho_w} $$
Adjustment for Moisture Content
$$ W_{corrected} = W_{SSD} + (MC \times W_{SSD}) $$
Correction for Aggregate Water Absorption
$$ W_{adjusted} = W_{SSD} - (Absorption \times W_{SSD}) $$
Target Mean Strength
$$ f_{ck'} = f_{ck} + t \times s $$
where
\( f_{ck} \) = characteristic strength
\( t \) = tolerance factor (from IS 456 table)
\( s \) = standard deviation
Volume of Entrapped Air
$$ V_{air} = \text{as per IS 10262 recommendations (usually 1-2\%)} $$
Modulus of Elasticity of Concrete
$$ E_c = 5000 \sqrt{f_{ck}} $$
where:
\( E_c \) = modulus of elasticity (MPa)
\( f_{ck} \) = characteristic compressive strength (MPa)
Bulking of Sand (Approximate Correction)
$$ \text{Corrected Sand Volume} = \frac{\text{Specified Volume}}{1 + \frac{\text{Bulking Percentage}}{100}} $$
Mix Proportion by Volume
**For M20 concrete**
1 : 1.5 : 3 (Cement : Sand : Aggregate)
Water-cement ratio as per design requirements.
Fineness Modulus (FM)
$$ FM = \frac{\text{Cumulative \% retained on standard sieves}}{100} $$
Slump Test Value Range
- Very low workability: 0–25 mm
- Low workability: 25–50 mm
- Medium workability: 50–100 mm
- High workability: 100–175 mm
Degree of Workability — Compaction Factor
- Very low: 0.70
- Low: 0.85
- Medium: 0.92
- High: 0.95
Ultimate Creep Strain
$$ \epsilon_{cr} = \phi \times \epsilon_{e} $$
where:
\( \epsilon_{cr} \) = creep strain
\( \phi \) = creep coefficient
\( \epsilon_{e} \) = elastic strain
Maturity of Concrete (Nurse-Saul Equation)
$$ M = \sum (T_a - T_0) \times \Delta t $$
where:
\( T_a \) = average concrete temperature
\( T_0 \) = datum temperature (usually -11°C)
\( \Delta t \) = time interval (hours)
Specific Gravity
$$ G = \frac{\text{Weight of Aggregate in Air}}{\text{Weight of Equal Volume of Water}} $$
Water Absorption of Aggregate
$$ \text{Water Absorption (\%)} = \frac{W_{ssd} - W_{oven}}{W_{oven}} \times 100 $$
where:
\( W_{ssd} \) = saturated surface dry weight
\( W_{oven} \) = oven-dry weight
Segregation Index (SI)
$$ SI = \frac{\text{Difference of densities of top & bottom layers}}{\text{Average density}} $$
Compressive Strength Formula
$$ f_c = \frac{P}{A} $$
where:
\( P \) = failure load (N)
\( A \) = loaded area (mm²)
Cement Content per Bag
**1 bag cement = 50 kg = 0.035 m³**
Section 8) Geotechnical Engineering
Cohesive soils:- Soil consisting of the finer products of rock weathering. Cohesion is derived from large number of water films associated with the fine grained particles in the soil.
Total force of Attraction between two particle (f) =
$$f={{2 {\pi} rT}\over {1+tan \left({\theta}\over 2 \right) }}$$
where r => Radius of Particle
T => Surface Tension
Liquidity index:-The difference between natural moisture content and plastic limit expressed as percentage ratio of the plasticity index.
$$LI={{m-PL}\over {LL-PL}}\times 100$$
m => moisture content
$$\text{Plasticity Index}={\text{Liquid Limit }-\text{ Plastic Limit}} $$
1️⃣ Water Content
$$ w = \frac{W_w}{W_s} \times 100 $$
2️⃣ Specific Gravity of Soil Solids
$$ G = \frac{W_s}{W_s - W_w} $$
3️⃣ Void Ratio
$$ e = \frac{V_v}{V_s} $$
4️⃣ Porosity
$$ n = \frac{V_v}{V} \times 100 $$
5️⃣ Degree of Saturation
$$ S_r = \frac{V_w}{V_v} \times 100 $$
6️⃣ Dry Density
$$ \rho_d = \frac{W_s}{V} $$
7️⃣ Bulk Density
$$ \rho = \frac{W}{V} $$
8️⃣ Saturated Density
$$ \rho_{sat} = \frac{W_{sat}}{V} $$
9️⃣ Submerged Density
$$ \rho' = \rho_{sat} - \rho_w $$
🔟 Unit Weight Relationships
$$ \gamma_d = \frac{G \times \gamma_w}{1+e} $$
1️⃣1️⃣ Liquidity Index
$$ LI = \frac{w - PL}{LL - PL} \times 100 $$
1️⃣2️⃣ Plasticity Index
$$ PI = LL - PL $$
1️⃣3️⃣ Flow Index
$$ FI = \frac{w_1 - w_2}{\log(N_2/N_1)} $$
1️⃣4️⃣ Consistency Index
$$ CI = \frac{LL - w}{PI} $$
1️⃣5️⃣ Shear Strength (Coulomb’s Equation)
$$ \tau = c + \sigma \tan \phi $$
1️⃣6️⃣ Terzaghi’s Bearing Capacity Equation
$$ q_u = c N_c + \gamma D_f N_q + 0.5 \gamma B N_\gamma $$
1️⃣7️⃣ Settlement of Soil
$$ S = \frac{C_c}{1+e_0} \log \left( \frac{\sigma'_0 + \Delta \sigma}{\sigma'_0} \right) \times H $$
1️⃣8️⃣ Factor of Safety (Slope Stability)
$$ FOS = \frac{\text{Resisting forces}}{\text{Driving forces}} $$
Section 9) Sewerage and Sewage disposal
1️⃣ Chezy’s Formula
$$ V = C \sqrt{R S} $$Where:
= Velocity of flow (m/s)
= Chezy's coefficient
= Hydraulic radius (m)
= Slope of the energy line (m/m)
2️⃣ Manning’s Formula
$$ V = \frac{1}{n} R^{2/3} S^{1/2} $$
Where:
= Manning’s roughness coefficient
= Hydraulic radius (m)
= Slope of the channel (m/m)
3️⃣ Hydraulic Radius
$$ R = \frac{A}{P} $$
Where:
= Area of flow (m²)
= Wetted perimeter (m)
4️⃣ Discharge in Open Channel
$$ Q = A \times V $$
Where:
= Discharge (m³/s)
= Area of flow (m²)
= Velocity (m/s)
5️⃣ Population Forecast (Arithmetic Increase Method)
$$ P_n = P_0 + n \times I $$
Where:
= Population after decades
= Present population
= Average increase per decade
= Number of decades
6️⃣ Population Forecast (Geometric Increase Method)
$$ P_n = P_0 (1 + r)^n $$
Where:
= Population after decades
= Present population
= Number of decades
7️⃣ Sewage Flow Estimation
$$ Q = q \times P $$
Where:
= Sewage discharge (litres/day)
= Per capita sewage generation (litres/person/day)
$$ P_n = P_0 + n \times I $$
= Population
8️⃣ BOD First Order Reaction
$$ BOD_t = BOD_0 \left(1 - e^{-k t}\right) $$
Where:
= Ultimate BOD
= Time in days
9️⃣ Oxygen Demand for Nitrification
$$ O_2 = 4.57 \times NH_3 $$
🔟 Detention Time in Sedimentation Tank
$$ t = \frac{V}{Q} $$
Where:
Detention Time in Sedimentation Tank
$$ t = \frac{V}{Q} $$
Where:
\( t \) = Detention time (sec or hours)
\( V \) = Volume of tank (m³)
\( Q \) = Flow rate (m³/sec)
Surface Loading Rate (Overflow Rate)
$$ \text{SLR} = \frac{Q}{A} $$
Where:
\( Q \) = Flow rate (m³/day)
\( A \) = Surface area of tank (m²)
BOD (Biochemical Oxygen Demand) Removal
$$ BOD_t = BOD_0 \left(1 - e^{-k t}\right) $$
Where:
\( BOD_0 \) = Initial BOD (mg/L)
\( k \) = Reaction rate constant (day⁻¹)
\( t \) = Time (days)
BOD Loading on Aeration Tank
$$ \text{BOD Loading} = \frac{Q \times BOD}{V} $$
Where:
\( Q \) = Flow rate (m³/day)
\( BOD \) = Concentration (mg/L)
\( V \) = Volume of aeration tank (m³)
Food to Microorganism Ratio (F/M Ratio)
$$ F/M = \frac{Q \times S_0}{V \times X} $$
Where:
\( Q \) = Flow rate (m³/day)
\( S_0 \) = Influent BOD (mg/L)
\( V \) = Volume of aeration tank (m³)
\( X \) = MLSS (Mixed Liquor Suspended Solids) (mg/L)
Mean Cell Residence Time (MCRT)
$$ \theta_c = \frac{V \times X}{Q_w \times X_w + Q_e \times X_e} $$
Where:
\( Q_w \) = Waste sludge flow rate (m³/day)
\( X_w \) = Concentration of solids in waste sludge (mg/L)
\( Q_e \) = Effluent flow rate (m³/day)
\( X_e \) = Effluent solids concentration (mg/L)
Sludge Volume Index (SVI)
$$ SVI = \frac{\text{Settled Sludge Volume (mL/L)}}{\text{MLSS (mg/L)}} \times 1000 $$
Where:
SVI in mL/g
Air Requirement for Aeration
$$ Q_{air} = \frac{Q \times BOD \times Y}{C} $$
Where:
\( Q_{air} \) = Air required (m³/hr)
\( Y \) = Oxygen requirement per kg of BOD (kg O₂/kg BOD)
\( C \) = Oxygen transfer efficiency
Chlorine Dose
$$ \text{Dose (mg/L)} = \frac{\text{Chlorine applied (mg)}}{\text{Volume (L)}} $$
pH Definition
$$ pH = -\log[H^+] $$
Where:
\( [H^+] \) = Hydrogen ion concentration (mol/L)
Section 10) Water Supply and Purification
1️⃣ Population Forecasting (Arithmetic Increase Method)
$$ P_n = P_0 + n \times I $$
2️⃣ Per Capita Demand
$$ q = \frac{Q}{P} $$
3️⃣ Detention Time in Sedimentation Tank
$$ t = \frac{V}{Q} $$
4️⃣ Surface Loading Rate (Overflow Rate)
$$ SLR = \frac{Q}{A} $$
5️⃣ Filter Rate (for Rapid Sand Filter)
$$ FR = \frac{Q}{A} $$
6️⃣ Chlorine Dose
$$ C_d = C_r + D_c $$
7️⃣ Disinfection Contact Time (CT Concept)
$$ C \times T = \text{constant for effective disinfection} $$
8️⃣ Water Pipe Flow (Hazen-Williams Equation)
$$ V = 0.85 \times C \times R^{0.63} \times S^{0.54} $$
9️⃣ Loss of Head in Filter
$$ h_f = \frac{Q^2}{K} $$
🔟 Water Demand Formula (General)
$$ Q = q \times P $$
Section 11) Building Materials
| SR. No. | Items | Unit | Materials | ||
|---|---|---|---|---|---|
| Particulars | Quantity | Unit | |||
| 1 | Brick Work | 100 cu.m | Bricks | 50000 | Nos |
| Mortar | 30 | cu.m | |||
| 2 | Rubble stone Masonry | 100 cu.m | Stone | 125 | cu.m |
| Mortar | 42 | cu.m | |||
| 3 | 25 mm Cement Concrete 1:2:4 | 100 sq.m | Stone grit | 2.4 | cu.m |
| sand | 1.2 | cu.m | |||
| cement | 24 | Bags | |||
| 4 | 12 mm thick plastering | 100 sq.m | Mortar | 2 | cu.m |
| 5 | Pointing in brickwork | 100 sq.m | Mortar | 0.6 | cu.m |
| 6 | White washing one coat | 100 sq.m | Lime | 10 | Kg |
| 7 | Distempring | ||||
| i) First coat | 100 sq.m | Dry distemper | 6.5 | Kg | |
| ii) Second coat | 100 sq.m | Dry distemper | 5 | Kg | |
| 8 | Oil Painting one coat | 100 sq.m | Ready-made paint | 10 | Litres |
| 9 | Oil Painting one coat | 100 sq.m | Paint stiff | 10 | Kg |
| 10 | 20 mm thick Damp-proof course of 1:2:4 cement Mortar | 100 sq.m | Cement | 27 | Bags |
| Sand | 1.8 | Cu.m | |||
| Imperno | 27 | Kg | |||
| 11 | Painting with bitumen | ||||
| i) First coat | 100 sq.m | Bitumen | 150 | Kg | |
| ii) Second coat | 100 sq.m | Bitumen | 100 | Kg | |
| 12 | C.G.I. Sheet Roofing | 100 sq.m | C.G.I. sheets | 128 | Sq.m |
| 13 | A.C. Sheet Roofing | 100 sq.m | A.C. sheets | 115 | Sq.m |
| 14 | Panneled door shutter 40 mm thick | 100 sq.m | Timber | 4.5 | Cu.m |
| 15 | Battened door shutter 40 mm thick | 100 sq.m | Timber | 5 | Cu.m |
| 16 | Partialy Panneled and Glazed shutter 40 mm thick | 100 sq.m | Timber | 3 | Cu.m |
| 17 | Fully glazed shutter 40 mm thick | 100 sq.m | Timber | 2 | Cu.m |
Fineness Modulus (for Aggregates)
$$ \text{FM} = \frac{\text{Cumulative retained on standard sieves}}{100} $$
(Fineness modulus indicates average particle size.)
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