### How to calculate the length & volume of the segmental arch?

Let us now calculate the length & volume of the segmental arch as shown below.

Given data:

The span of the segmental arch = 3.5m.

Height of arch = h = 1m.

Width of the arch = 300mm.= 0.3m.

Thickness of the arch = 230mm = 0.23m.

First, we will calculate the length of the arch

The arch length is calculated by the formula

=[ ∅ × (2πr ÷ 360°)]

Here,

∅ = angle formed by the arch as shown below.

The given value of ∅ 120°  for the segmental arch.

r = Radius of the arch.

The formula for calculating the radius of the arch

= [ a2+ h2 ÷ 2h]

Here,

a = half of the arch span

= [3.5m. ÷ 2 ]

= 1.75m.

Putting the values of a & h in the above formula,

r = [ (1.75 2+ 12)÷ 2 × 1 ]

=[ (3.0625 + 1) ÷ 2]

=[ 4.0625 ÷ 2]

= 2.031m.

1.   The arch length

=[ ∅ × {(2πr) ÷ 360°}]

=[120° × {(2 × 3.142 × 2.031)÷ 360°}]

=[120° × {12.764 ÷ 360°}]

(By cancelling 120° & 360° with each other)

= [ 12.764 ÷ 3 ]

= 4.255m.

Now,

2. The volume of the segmental arch

= [length × breadth × thickness]

= [4.255m. × 0.3m. × 0.23m.]

=0.294 CUM.

### How to calculate the length & volume of a semi-circular arch?

Let us now calculate the length & volume of the semi-circular arch as shown below.

Given data:

The span of the semi-circular arch = 2m.

Height of arch = 1m.

Width of the arch = 300mm.= 0.3m.

Thickness of the arch = 230mm = 0.23m.

First, we will calculate the length of the arch

The arch length is calculated by the formula

=[ ∅ × (2πr ÷ 360°)]

Here,

∅ = angle formed by the arch as shown below.

For a semi-circular arch, the value of = 180°

r = Radius of the arch.

To calculate the volume of the arch, let us calculate the radius of the centerline as shown below.

= [{arch span + (half of the arch width on both sides.)}÷ 2 ]

= [{2m. + ( 2nos.×0.5 × 0.3m.)} ÷ 2]

= [{2m. + ( 0.3m.)} ÷ 2]

= [2.3m ÷ 2]

r  = 1.15m.

1.   The arch length

=[ ∅ × {(2πr) ÷ 360°}]

=[180° × {(2 × 3.142 × 1.15)÷ 360°}]

=[180° × {7.227÷ 360°}]

(By cancelling 180° & 360° with each other)

= [ 7.227 ÷ 2 ]

= 3.613m.

Now,

2. The volume of the semi-circular arch

= [length × breadth × thickness]

= [3.613m. × 0.3m. × 0.23m.]

=0.249 CUM.

### What will be the cost of M10 grade PCC ?/How to calculate the cost of concrete having a 1:3:6 mix ratio?

In this article, let us work out the cost of M10 grade PCC as shown in the below drawing.

All the calculation part of the material required for PCC is covered in the separate article. So, before proceeding further, you have to go through that article 👇

A.  Material cost:

The average ongoing market rate in India is considered for calculation purposes.

B.  Labor cost :

The labor rate for PCC ranges from INR 900/- to 1500/- per CUM.

Let us take the average rate of INR 1200/- for the calculation purpose.

Now, let us calculate the cost of the M10 grade PCC per CUM in the table format.

 Sl. no. Item. Qty. Rate. in INR. Unit. Cost in INR. 1. Cement 4.435 380/- Bags 1685.30 2. Sand 16.32 60/- Cu ft 979.20 3. Aggregate 32.63 48/- Cu ft. 1566.24 4. Curing Lump-sum 250.00 5. Miscellaneous Lump-sum 150.00 6. The material cost = 4630.74 7. Add 5% wastage = 231.54 8. Total material cost = 4862.28 9. Labour cost = 1200.00 10. The total cost of M10 grade PCC = 6062.28

Note:

1. The quantity of materials in the table is taken from the above-said article.

2. To get accurate results, insert the ongoing market rate of labor & materials in your country.

The cost of M10 grade PCC per cu ft.

= INR 6062.28/- ÷ 35.314

= INR 171.67/- per cu ft.

For contractor:

If the PCC work is handed over to any contractor, then you have to add 10% extra as profit.

The cost of M10 grade PCC done by a contractor

= INR 6062.28/- + 10% of INR 6062.28/-

= INR 6062.28/- + INR 606.22/-

= INR 6668.50/-

### Calculating the quantity of cement, sand, & aggregates in M10 (1:3:6) grade PCC./Rate analysis of PCC.

Let us consider M10 grade PCC as shown in the below drawing for the calculation purpose.

Given data:

The grade of PCC = M10.

Length of the PCC bed = 4m.

Breadth of the PCC  = 2.5m.

The thickness of the PCC = 100mm. = 0.01m.

The volume of the PCC bed

= length × breadth × thickness

= 4m. × 2.5m. × 0.01m.

= 1 CUM.

Here,

Cement:sand: aggregates = 1:3:6 (a:b:c)

M10 grade means 👉  1:3:6 ratio.

Wet volume of PCC = 1 cum.

Now, dry volume of PCC

= 1.54 × 1 cum = 1.54 cum.

1. Volume of  cement required

= [{its ratio  ÷ (total ratio)} × dry volume of PCC.]

=[{ a ÷ (a + b + c)} × dry volume of PCC.]

= [{1÷ ( 1 + 3 +6 )} × 1.54]

= [{ 1 ÷ 10 } × 1.54]

= [0.1 × 1.54]

=  0.154 cum.

As you know, 1 bag of cement = 0.03472 cum.

So, the number of cement bags required

= 0.154 cum. ÷ 0.03472 cum.

= 4.435 bags

Weight of cement

= 4.435 bags × 50 kgs.

(1 bag of cement = 50 kgs.)

221.77 kgs.

2. Volume of sand required

= [{its ratio  ÷ (total ratio)} × dry volume of PCC.]

=[{ b ÷ (a + b + c)} × dry volume of PCC.]

= [{3÷ ( 1 + 3 +6 )} × 1.54]

= [{3 ÷ 10 } × 1.54]

= [0.3 × 1.54]

=  0.462 cum.

=  16.32 cu ft.

3. Volume of aggregates required

= [{its ratio  ÷ (total ratio)} × dry volume of PCC.]

=[{ c ÷ (a + b + c)} × dry volume of PCC.]

= [{6÷ ( 1 + 3 +6 )} × 1.54]

= [{ 6 ÷ 10 } × 1.54]

= [0.6 × 1.54]

=  0.924 cum.

= 32.63 cu ft.

4. Volume of water required.

Let us consider the w/c ratio for M10 grade concrete as 0.5.

i.e. wt. of cement / wt. of water = 0.5

So, the weight. of water

= 0.5 × wt. of cement

=0.5 × 221.77 kgs

= 110.89 kgs

= 110.89 liters

( 1kg= 1 liter)

Note: This w/c ratio holds good if you use plasticizers. Practically for good workability, the water we add for the concrete is 133 liters.

#### Alternate method:

1. Volume of cement ( from above) = 0.154 cum.

2. Volume of sand

= [volume of cement × b]

=   [0.154 cum × 3]

= 0.462 cum.

3.  Volume of aggregates

= [volume of cement × c]

= [ 0.154 cum × 6]

= 0.924 cum.

Now, let us put these material quantities in a table format for easy reference.
 Materials in 1CUM of M10 grade PCC. Sl. No. Item Unit In cum. In cu ft. 1. Cement bags 4.435 bags - 2. Sand - 0.462 16.32 3. Aggregates - 0.924 32.63 4. Water litres 110.89 -

Note: To calculate the quantity of materials in M7.5 & M15 grade PCC, you have to replace the mix ratio in the above calculation.

### What should be the number of concrete cube samples for different concrete volumes?

According to IS 456 - 2000, the frequency of concrete cube samples for different concrete volumes is as follows.

Here,

1 sample 👉  3 nos. of concrete cube

or we say

1 sample 👉  3 specimen of a given concrete volume.

The same is given in a table format for your easy understanding as below.

 Frequency of concrete Sl. No. Vol. of concrete in cum. Samples in nos. Concrete cubes in nos. 1. 1 to 5 1 3 2. 6 to 15 2 6 3. 16 to 30 3 9 4. 31 to 50 4 12 5. 51 to 100 5 15 6. 101 to 150 6 18 7. 151 to 200 7 21 8. 201 to 250 8 24

### How to calculate the volume & weight of a concrete cube?

Let us go through the procedure to calculate the volume & weight of the standard concrete cubes used in the lab. testing.

Given data:

Dimension of the cube

= 150mm. × 150mm. × 150mm.

= 0.15m. × 0.15m. × 0.15m.

1. Volume of the cube is calculated  by the formula

= length × breadth × height

In any cube, all the 3 sides are equal

i.e. length = breadth = height = s

So, the volume of the concrete cube

= 0.15m. × 0.15m. × 0.15m.

= 0.003375 CUM.

2. The weight of the concrete cube

= density × volume.

As you know, the density of concrete =2400kg / CUM.

The weight of the concrete cube

= [2400 kg./ CUM × 0.003375 CUM]

= 8.1kg.

Note:

1. The density of RCC = 2500kg./CUM &

2. The density of PCC = 2400kg. / CUM.

The concrete cube does not contain a reinforcement. So, its density will be 2400 kg / CUM.

### The cost of fixing interlocking paver blocks./ Rate analysis of paver block flooring.

Let us calculate the cost of fixing an interlocking paver block for the below-given drawing.

Given data:

Flooring area = 20 ft. × 18 ft.

Sand bed thickness = 2" = 0.166 ft.

Cement mortar thickness = 3" = 0.25 ft.

Cement mortar depth = 4.5" = 0.375 ft.

A. Material calculation:

1. Paver blocks:

The number of paver blocks required = 1044 nos.

To observe the above-given calculation of paver blocks, go through the article👇

2. Sand:

The volume of the sand bed

= length × breadth × thickness

= 20 ft. × 18 ft. × (2 ÷ 12 ) ft.

= 60 cu ft.

3. Cement mortar:

= [(flooring periphery)  × depth × thickness]

= [(2nos. × 18 ft. + 2nos. × 20 ft.) × 0.375 ft. × 0.25 ft.]

= [( 36 ft. + 40 ft.) × 0.375 ft. × 0.25 ft.]

= [ 76 ft. × 0.375 ft. × 0.25 ft.]

= 7.125 cu ft.

Let us make the cement mortar in a 1:4 ratio.

Cement required /cu ft. of mortar =0.217 bags.

Sand required/ cu ft. of mortar   = 1.064 cu ft.

Note:  The above data is extracted from my article 👇

Calculating the quantity of materials in 1 cum. & 1cuft. of plastering mortar in different mix ratios.

Cement required for preparing the mortar

= total mortar vol. in cu ft.× cement / cu ft.

= 7.125 cu ft. × 0.217 bags

= 1.55 bags.

Sand required for mortar

= total mortar vol. in cu ft.× sand / cu ft.

= 7.125 cu ft. × 1.064 cu ft.

= 8.19 cu ft.

So, the total vol. of the sand required for paver installation

= [for sand bed + for cement mortar]

= [60 cu ft. + 8.19 cu ft.]

= 68.19 cu ft.

B. Labor calculation:

The labor rate for the paver fixing inclusive of mechanical floor compaction ranges from INR 10/- to INR 16/- per sq ft.

Let us consider the average rate of INR 13/- for the calculation purpose.

The total cost of the labor

= total area × rate / sq ft.

= 360 sq ft. × 13/-

= INR 4680/-

Now, let us calculate the cost of fixing the interlocking paver blocks in a table format.

 Sl. no. Item. Qty. Rate. in INR. Unit. Cost in INR. 1. Paver block 1044 16/- Nos. 16,704.00 2. Cement 1.55 400/- Bag 620.00 3. Sand 68.19 60/- Cu ft 4091.40 4. Curing Lump-sum 200.00 5. Miscellaneous Lump-sum 150.00 6. The material cost = 21,765.40 7. Add 5% wastage = 1,088.27 8. Total material cost = 22,853.67 9. Labour cost = 4680.00 10. The total cost of paver block flooring = 27,533.67

Note: To get accurate results, insert your regional market rate of materials & labor, in the above table.

Before fixing or selecting the paver blocks for installation, go through the articles👇

👀. Classification of paver blocks. / What are the different types of paver blocks?

1.  The cost of paver flooring / sq ft.

= [The total cost of paver installation ÷ total flooring area]

= [INR 27,533.67/-  ÷ 360 sq ft.]

= INR 76.48 / sq ft.

2. The cost of paver flooring / sq m.

= [the cost/ sq ft. × 10.764]

(As 1sq m. = 10.764 sq ft.)

= [ 76.48 × 10.764]

= INR 823.23 / sq m.

Thank you for going through this article. Have a good day 😄.

### How to calculate the coverage area of interlocking paver blocks?

The interlocking paver blocks are available in numerous varieties having their own pattern, model, & dimensions. Out of them, the 3 shapes of paver blocks that are widely used are,

1. I-shaped paver block.

2. Dumbbell-shaped paver block

3. Zig-zag patterned paver block.

The manufacturer provides the details & specifications of the paver blocks, to make our calculation work a lot easier. To understand what I said in a better way, go through the article 👇

How to calculate the number of interlocking paver blocks required for any given area?

But, when you purchase the locally manufactured paver blocks, you may need to calculate the coverage area of that particular shape.

So, let us go through the calculation procedure for the I-shaped paver block as shown below.

Area of I-shaped paver block

= [ external rectangular area - 2nos. of trapezoidal area.]

To understand the formula, you can observe the drawing as shown below.

Here, we will deduct the brown-colored trapezoidal portion from the total external rectangular area.

External area

= 160mm. × 200mm.

= 0.16m. × 0.2m.

= 0.032 sqm.

I have redrawn the trapezoidal part for your reference, as shown below.

Trapezoidal area

= [{(side AD + side BC) ÷ 2} × h]

Here, height h

= [(160mm - 120mm.) ÷ 2]

= [ 40mm ÷ 2]

= 20mm.

Trapezoidal area

=  [{(120mm.+ 80mm.) ÷ 2} × 20mm.]

=  [{200mm. ÷ 2} × 20mm.]

= [ 100mm.× 20mm.]

= 2000 sq. mm.

= 0.002 sq m.

Area of I- shaped paver block

= [ external rectangular area - (2nos. × trapezoidal area.)]

=[0.032 sq m. - (2nos. × 0.002 sq m.)]

=[0.032 sq m. - 0.004 sq m.]

= 0.028 sq m.

The no. of  I - shaped paver blocks required / sq m.

= [1 sq. m. area ÷ area of a paver block in sq m.]

= [1sq m. ÷ 0.028 sq m.]

= 35.71 nos.

The no. of  I - shaped paver blocks required / sq. ft.

= 35.71 nos. ÷ 10.764

= 3.32 nos.

For you 👇

Let us calculate the number of paver blocks required for 100 sq m. & 100 sq ft. area in a table format.

For 100 sq m.:

 Sl. No. Description. Area to be paved in sq m. Pavers required/sq m. in nos. Total No. of paver blocks 1. I-shaped paver block 100 35.71 3571 nos. 2. Add 5% wastage = 178.55 nos. 3. Total no. of I-shaped paver blocks required= 3749.55 nos.

For 100 sq ft.:

 Sl. No. Description. Area to be paved in sq ft. Pavers required/sq ft. in nos. Total No. of paver blocks 1. I-shaped paver block 100 3.32 332 nos. 2. Add 5% wastage = 16.60 nos. 3. Total no. of I-shaped paver blocks required= 348.6 nos.