Mid Sectional Area Method Calculator

✖Length of Road Section is the total extent /stretch of the road.ⓘ Length of Road Section [L_section]			+10% -10%
✖Width of Formation Level or roadway is the sum of the width of the pavement or carriageway including the separators if any and the shoulders.ⓘ Width of Formation Level [B]			+10% -10%
✖Height of Bank at Start Portion of Embankment is the maximum distance between parallel sides of the c/s of the start portion of the embankment.ⓘ Height of Bank at Start Portion of Embankment [d₁]			+10% -10%
✖Height of Bank at End Portion of Embankment is the maximum distance between parallel sides of the c/s of the end portion of the embankment.ⓘ Height of Bank at End Portion of Embankment [d₂]			+10% -10%
✖Side Slope is the graded area immediately adjacent to the graded roadway shoulder. Side slopes are provided on embankments and fill to provide stability for earthworks.ⓘ Side Slope [S]			+10% -10%

✖Volume of Earthwork is measured in cubic meters without any allowance for an increase in bulk.ⓘ Mid Sectional Area Method [V_earthwork]

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Formula

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Mid Sectional Area Method

Formula

`"V"_{"earthwork "} = "L"_{"section"}*("B"*(("d"_{"1"}+"d"_{"2"})/2))+"L"_{"section"}*("S"*(("d"_{"1"}+"d"_{"2"})/2)^2)`

Example

`"358.556m³"="20000mm"*("10000mm"*(("1201mm"+"1600mm")/2))+"20000mm"*("2"*(("1201mm"+"1600mm")/2)^2)`

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Mid Sectional Area Method Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Earthwork = Length of Road Section*(Width of Formation Level*((Height of Bank at Start Portion of Embankment+Height of Bank at End Portion of Embankment)/2))+Length of Road Section*(Side Slope*((Height of Bank at Start Portion of Embankment+Height of Bank at End Portion of Embankment)/2)^2)
V_earthwork = L_section*(B*((d₁+d₂)/2))+L_section*(S*((d₁+d₂)/2)^2)
This formula uses 6 Variables

Variables Used

Volume of Earthwork - (Measured in Cubic Meter) - Volume of Earthwork is measured in cubic meters without any allowance for an increase in bulk.
Length of Road Section - (Measured in Meter) - Length of Road Section is the total extent /stretch of the road.
Width of Formation Level - (Measured in Meter) - Width of Formation Level or roadway is the sum of the width of the pavement or carriageway including the separators if any and the shoulders.
Height of Bank at Start Portion of Embankment - (Measured in Meter) - Height of Bank at Start Portion of Embankment is the maximum distance between parallel sides of the c/s of the start portion of the embankment.
Height of Bank at End Portion of Embankment - (Measured in Meter) - Height of Bank at End Portion of Embankment is the maximum distance between parallel sides of the c/s of the end portion of the embankment.
Side Slope - Side Slope is the graded area immediately adjacent to the graded roadway shoulder. Side slopes are provided on embankments and fill to provide stability for earthworks.

STEP 1: Convert Input(s) to Base Unit

Length of Road Section: 20000 Millimeter --> 20 Meter (Check conversion here)
Width of Formation Level: 10000 Millimeter --> 10 Meter (Check conversion here)
Height of Bank at Start Portion of Embankment: 1201 Millimeter --> 1.201 Meter (Check conversion here)
Height of Bank at End Portion of Embankment: 1600 Millimeter --> 1.6 Meter (Check conversion here)
Side Slope: 2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_earthwork = L_section*(B*((d₁+d₂)/2))+L_section*(S*((d₁+d₂)/2)^2) --> 20*(10*((1.201+1.6)/2))+20*(2*((1.201+1.6)/2)^2)

Evaluating ... ...

V_earthwork = 358.55601

STEP 3: Convert Result to Output's Unit

358.55601 Cubic Meter --> No Conversion Required

FINAL ANSWER

358.55601 ≈ 358.556 Cubic Meter <-- Volume of Earthwork

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Estimation and Costing » Quantity of Earthwork for Embankments » Mid Sectional Area Method

Credits

Created by Smriti Singh

MIT Academy of engineering, Pune (MITAOE), Alandi, Pune

Smriti Singh has created this Calculator and 25+ more calculators!

Verified by Ayush Singh

Gautam Buddha University (GBU), Greater Noida

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< 5 Quantity of Earthwork for Embankments Calculators

Mean Sectional Area Method

Go Volume of Earthwork = Length of Road Section*((Width of Formation Level*Height of Bank at Start Portion of Embankment)+(Side Slope*Height of Bank at Start Portion of Embankment^2)+(Width of Formation Level*Height of Bank at End Portion of Embankment)+(Side Slope*Height of Bank at End Portion of Embankment^2))/2

Mid Sectional Area Method

Go Volume of Earthwork = Length of Road Section*(Width of Formation Level*((Height of Bank at Start Portion of Embankment+Height of Bank at End Portion of Embankment)/2))+Length of Road Section*(Side Slope*((Height of Bank at Start Portion of Embankment+Height of Bank at End Portion of Embankment)/2)^2)

Prizmoidal Formula for Series of Cross-Section of Road

Go Volume of Earthwork = Distance between Consecutive Sections/3*(Area of First Section+Area of Last Section+4*(Odd Areas Sum)+2*(Even Areas Sum))

Trapezoidal Formula for Series of Cross-Section of Road

Go Volume of Earthwork = Distance between Consecutive Sections*(Area of First Section+Area of Last Section+2*(Remaining areas))/2

Sloping Surface Area of Embankment

Go Sloping Surface Area = Length of Road Section*Mean Height*sqrt((Side Slope)^2+1)

Mid Sectional Area Method Formula

How is the calculation of Earthwork in Road Longitudinal Section is done?

For the calculation of earthwork in a longitudinal section and cross-section of the ground are taken and the formation line is fixed. The formation line is fixed in consideration of flood level, gradient, height of bank, depth of cutting etc. But for estimating of earthwork this point of utilizing excavated earth from cutting in certain length in banking of the adjacent length may not be taken into account to avoid complicacy.

Explain Mid-Sectional Area Method steps.

The steps are as follows:
1. The mean depth is the average of depths of two consecutive sections.
2. The area of mid-sections is calculated by using mean depth.
3. The volume of the earthwork is calculated by multiplying the mid-section area by the distance between the two sections.

How to Calculate Mid Sectional Area Method?

Mid Sectional Area Method calculator uses Volume of Earthwork = Length of Road Section*(Width of Formation Level*((Height of Bank at Start Portion of Embankment+Height of Bank at End Portion of Embankment)/2))+Length of Road Section*(Side Slope*((Height of Bank at Start Portion of Embankment+Height of Bank at End Portion of Embankment)/2)^2) to calculate the Volume of Earthwork, The Mid Sectional Area Method formula is defined as calculating the volume of earthwork considering the other parameters such as height of the bank, length of a road section and side slope. Volume of Earthwork is denoted by V_earthwork symbol.

How to calculate Mid Sectional Area Method using this online calculator? To use this online calculator for Mid Sectional Area Method, enter Length of Road Section (L_section), Width of Formation Level (B), Height of Bank at Start Portion of Embankment (d₁), Height of Bank at End Portion of Embankment (d₂) & Side Slope (S) and hit the calculate button. Here is how the Mid Sectional Area Method calculation can be explained with given input values -> 358.4 = 20*(10*((1.201+1.6)/2))+20*(2*((1.201+1.6)/2)^2).

FAQ

What is Mid Sectional Area Method?

The Mid Sectional Area Method formula is defined as calculating the volume of earthwork considering the other parameters such as height of the bank, length of a road section and side slope and is represented as V_earthwork = L_section*(B*((d₁+d₂)/2))+L_section*(S*((d₁+d₂)/2)^2) or Volume of Earthwork = Length of Road Section*(Width of Formation Level*((Height of Bank at Start Portion of Embankment+Height of Bank at End Portion of Embankment)/2))+Length of Road Section*(Side Slope*((Height of Bank at Start Portion of Embankment+Height of Bank at End Portion of Embankment)/2)^2). Length of Road Section is the total extent /stretch of the road, Width of Formation Level or roadway is the sum of the width of the pavement or carriageway including the separators if any and the shoulders, Height of Bank at Start Portion of Embankment is the maximum distance between parallel sides of the c/s of the start portion of the embankment, Height of Bank at End Portion of Embankment is the maximum distance between parallel sides of the c/s of the end portion of the embankment & Side Slope is the graded area immediately adjacent to the graded roadway shoulder. Side slopes are provided on embankments and fill to provide stability for earthworks.

How to calculate Mid Sectional Area Method?

The Mid Sectional Area Method formula is defined as calculating the volume of earthwork considering the other parameters such as height of the bank, length of a road section and side slope is calculated using Volume of Earthwork = Length of Road Section*(Width of Formation Level*((Height of Bank at Start Portion of Embankment+Height of Bank at End Portion of Embankment)/2))+Length of Road Section*(Side Slope*((Height of Bank at Start Portion of Embankment+Height of Bank at End Portion of Embankment)/2)^2). To calculate Mid Sectional Area Method, you need Length of Road Section (L_section), Width of Formation Level (B), Height of Bank at Start Portion of Embankment (d₁), Height of Bank at End Portion of Embankment (d₂) & Side Slope (S). With our tool, you need to enter the respective value for Length of Road Section, Width of Formation Level, Height of Bank at Start Portion of Embankment, Height of Bank at End Portion of Embankment & Side Slope and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Volume of Earthwork?

In this formula, Volume of Earthwork uses Length of Road Section, Width of Formation Level, Height of Bank at Start Portion of Embankment, Height of Bank at End Portion of Embankment & Side Slope. We can use 3 other way(s) to calculate the same, which is/are as follows -

Volume of Earthwork = Length of Road Section*((Width of Formation Level*Height of Bank at Start Portion of Embankment)+(Side Slope*Height of Bank at Start Portion of Embankment^2)+(Width of Formation Level*Height of Bank at End Portion of Embankment)+(Side Slope*Height of Bank at End Portion of Embankment^2))/2
Volume of Earthwork = Distance between Consecutive Sections/3*(Area of First Section+Area of Last Section+4*(Odd Areas Sum)+2*(Even Areas Sum))
Volume of Earthwork = Distance between Consecutive Sections*(Area of First Section+Area of Last Section+2*(Remaining areas))/2

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