The beam which is supported at one end but free at the other end is known as a cantilever beam. Bar bending schedule of cantilever beam means simply to calculate the total quantity of steel rods or reinforcement required in the beam for safe load-bearing.
In the cantilever beam, tension force acted at the top and compression force acted at the bottom, unlike simply supported beam. So, we have to put more steel rods at the bottom of a cantilever beam.
You can read this article also Different Types of Beam- Why cantilever beams are made trapezoidal.
Now let us see the calculation step by step.
Bar Bending Schedule of Cantilever Beam
Given,
Top Horizontal Length of beam = 1800 mm
Bottom Horizontal length = 300 mm
Depth of beam at fixed support = 600 mm
Depth of beam at free support = 250 mm
Width of beam = 300 mm
Clear Cover = 25 mm
Diameter of top Main bars = 16 mm
Diameter of top Extra bars = 20 mm
Step-1, Calculate length and weight of Top main bars
Length of one top main bar (L) = (Support depth – Clear cover – Clear cover) + (Top horizontal Length – clear cover – clear cover) + (Free depth – clear cover – clear cover) – 2 x 90 Bend length
(L) = (600 – 25 – 25) + (1800 – 25 – 25) + (250 – 25 – 25) – 2 x 2 x 16= 1750 mm
(L) = 2436 mm
No of top bars = 3 Nos.
Therefore, total length of top main bars = L x 3 = 2436 x 3 = 7308 mm = 7.308 meter
Now,
Total weight of top steel rod required = d²/162.25 x length
Total weight of top steel rod required = 162/162.25 x 7.308 =11.53 kg
Step-2, Calculate length and weight of top Extra bars
Length of one top extra bar (L) = (Support depth – Clear cover – Clear cover) + Length toward free end – bend length
(L) = (600 – 25 – 25) + 1025 – 1 x 2d = 550 + 1025 – 2 x 20 = 1535 mm
No. of top extra bars = 2 Nos.
Therefore,
Total length of top extra bars = L x 2 = 1535 x 2 = 3070 mm = 3.07 meter
Now,
Total weight of top steel rod required = d²/162.25 x length
Total weight of top steel rod required = 202/162.25 x 3.07 = 7.568 kg
Step-3, Calculate length and weight of Bottom bars
Length of one bottom bar = (Vertical length of bar at support – clear cover) + (Bottom horizontal length – clear cover) + (Bottom inclined length – clear cover) + (Free vertical length – clear cover – clear cover) – bend length
Length of one bottom bar = (325 – 25) + (300 – 25) + (1540 – 25) + (250 – 25 – 25) – 2 x 2d
Length of one bottom bar = 2290 – 2 x 2 x 16 = 2226 mm
No. of bottom bars = 3 Nos.
Therefore,
Total length of bottom bars = L x 2 = 2226 x 3 = 6678 mm = 6.678 meter
Now,
Total weight of top steel rod required = d²/162.25 x length
Total weight of top steel rod required = 162/162.25 x 6.678 = 10.53 kg
Step-4 Calculate length and weight of Stirrups
This is most complicated parts of the cantilever beam.
Let’s see carefully how to calculate,
We have calculated previously the inclined length of cantilever beam = 1540.29 mm.
Now,
See, at the free end of the cantilever beam. The inclined length of the beam has divided into ten parts so, inclined length of each part will be equal to,
Li = (Bottom inclined length) / 10 = (1540.29)/10 = 154.03 mm
And, The horizontal length of each part will be = 1500/10 = 150 mm Hence, Vertical length of last free end part will be (Circled with red color),
Then, the height of first stirrups will be = 200 mm
Since, the spacing is same and on the same angle, as the horizontal length doubled, height will also be doubled and so on.
Similarly,
The height of 2nd stirrups will be = 200 + 1 x 35 = 235 mm
The height of 3rd stirrups will be = 200 + 2 x 35 = 270 mm
The height of 4th stirrups will be = 200 + 3 x 35 = 305 mm
The height of 5th stirrups will be = 200 + 4 x 35 = 340 mm
The height of 6th stirrups will be = 200 + 5 x 35 = 375 mm
The height of 7th stirrups will be = 200 + 6 x 35 = 410 mm
The height of 8th stirrups will be = 200 + 7 x 35 = 445 mm
The height of 9th stirrups will be = 200 + 8 x 35 = 480 mm
The height of 10th stirrups will be = 200 + 9 x 35 = 515 mm
The height of 11th stirrups will be = 200 + 10 x 35 = 550 mm
Now,
Cutting length of stirrups is given by,
L = Perimeter of stirrups + Hook length – Bend length
Let’s, start from first stirrups,
Cutting length of first stirrups = Perimeter of stirrups + Hook length – Bend length
Cutting length of first stirrups = {2 x (width of beam – 2 x Clear cover) + 2 x (Depth of beam at first stirrups)} + 2 x 10d – {(3 x 2d) – (2 x 3d)}
Hook length = 10d
Bend deduction = 2d for 90 and 3d for 135 (There are 3 bend having 90
Bend and 2 bend having 135 bend)
So,
Cutting length of first stirrups = 2 x (300 – 2 x 25) + 2 x 200 + 2 x 10 x 8 – (3 x 2 x 8) – (2 x 3 x 8) = 964 mm
Similarly,
Cutting length of 2nd stirrups = 2 x (300 – 2 x 25) + 2 x 235 + 2 x 10 x 8 – (3 x 2 x 8) – (2 x 3 x 8) = 1034 mm
Cutting length of 3rd stirrups = 2 x (300 – 2 x 25) + 2 x 270 + 2 x 10 x 8 – (3 x 2 x 8) – (2 x 3 x 8) = 1104 mm
Cutting length of 4th stirrups = 2 x (300 – 2 x 25) + 2 x 305 + 2 x 10 x 8 – (3 x 2 x 8) – (2 x 3 x 8) = 1174 mm
Cutting length of 5th stirrups = 2 x (300 – 2 x 25) + 2 x 340 + 2 x 10 x 8 – (3 x 2 x 8) – (2 x 3 x 8) = 1244 mm
Cutting length of 6th stirrups = 2 x (300 – 2 x 25) + 2 x 375 + 2 x 10 x 8 – (3 x 2 x 8) – (2 x 3 x 8) = 1314 mm
Cutting length of 7th stirrups = 2 x (300 – 2 x 25) + 2 x 410 + 2 x 10 x 8 – (3 x 2 x 8) – (2 x 3 x 8) = 1384 mm
Cutting length of 8th stirrups = 2 x (300 – 2 x 25) + 2 x 445 + 2 x 10 x 8 – (3 x 2 x 8) – (2 x 3 x 8) = 1454 mm
Cutting length of 9th stirrups = 2 x (300 – 2 x 25) + 2 x 480 + 2 x 10 x 8 – (3 x 2 x 8) – (2 x 3 x 8) = 1524 mm
Cutting length of 10th stirrups = 2 x (300 – 2 x 25) + 2 x 515 + 2 x 10 x 8 – (3 x 2 x 8) – (2 x 3 x 8) = 1594 mm
Cutting length of 11th stirrups = 2 x (300 – 2 x 25) + 2 x 550 + 2 x 10 x 8 – (3 x 2 x 8) – (2 x 3 x 8) = 1664 mm
Hence,
Total Cutting Length of Stirrups = 964 mm + 1034 mm + 1104 mm + 1174 mm
+ 1244 mm + 1314 mm + 1384 mm + 1454 mm + 1524 mm + 1594 mm + 1664 mm
Total Length of Stirrups required = 14454 mm = 14.454 meter
Now,
Total weight of top steel rod required = d²/162.25 x length
Total weight of top steel rod required = 82/162.25 x 14.454 = 5.701 kg
Final Step, calculate total length and weight
Total weight of steel rod required in the cantilever beam = Weight of Main top bars + Weight of top extra bars + Weight of bottom main bars + Weight of stirrups required.
Total weight of steel rod required in the cantilever beam = 11.53 kg + 7.568 kg + 10.53 kg + 5.701 kg
Total weight of steel rod required in the cantilever beam = 35.329 kg
I hope this article on “Bar Bending Schedule of Cantilever Beam” remains helpful for you.
Happy Learning – Civil Concept
Contributed by,
Civil Engineer – Ranjeet Sahani
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