How the formula of D²/162 derived for calculation of weight of reinforcement steel bar in Kg/meter

archdevil

Royal Member
How the formula of D²/162 derived for calculation of weight of reinforcement steel bar in Kg/meter

We know a formula to calculate the weight of bar. That is D²/162.
Where,
D= Diameter of bar in millimeter
L= Length of bar in meter
Now the question is what the 162 is.

Let's see.
To calculate the weight of something else we often use the following formula. To calculate the weight of reinforcement same formula can be used.

Weight= volume x unit weight [volume=area x length]

So,

Weight= area x length(L) x unit weight (γ) [area=πD²/4]

Therefore,

Weight (W)= πD²/4 x L x 7850

We know the unit weight of rod is 7850 kg/m³

But there are two conflicting unit in the above formula. Those are D is in millimeter (as we get the rod as millimeter, such as ø 16 mm, ø 20 mm etc.) and unit weight of rod is in m³ (kg/m³). If we estimate the rod in meter then L also is in meter unit in above formula.

So if we don't convert all three unit as same unit we can't use the above formula. We have to convert either D from millimeter to meter or L and γ from meter to millimeter.

Lets convert the D from millimeter to meter.

1 mm= 1/1000 meter

So,

D² (mm) = D²/(1000 x 1000), meter

If we implement this in the above formula, we'll find

W= D²/{4 x (1000 x 1000)} x L x 7850

= D²/162

Keep in mind that, in this formula D always should be in millimeter and L always should be in meter and to calculate weight per meter, value of L will be always 1 meter.

But what if you estimate the length of reinforcement is in foot?
In that case the formula for calculating the weight of reinforcement is = D²/533 (just convert meter into feet)


When the length of bar is in meter, below will be the weight of reinforcement steel bars in meter.
ø 10 mm bar = 0.617 kg/m
ø 12 mm bar = 0.888 kg/m
ø 16 mm bar = 1.580 kg/m
ø 20 mm bar = 2.469 kg/m
ø 25 mm bar = 3.858 kg/m

When the length of bar is in foot, below will be the weight of reinforcement steel bars in foot.
ø 10 mm bar = 0.188 kg/ft
ø 12 mm bar = 0.270 kg/ft
ø 16 mm bar = 0.480 kg/ft
ø 20 mm bar = 0.750 kg/ft
ø 25 mm bar = 1.172 kg/ft

Now do check working of formula, if you get same values stated above then you are doing calculation of reinforcement steel bars weight per meter or weight per foot correctly.
 
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