## How to Calculate Beam Size Using Beam Design Formula

The beam is a structural element that transfers all the dead load, the live load of the slab to the column. We all know that calculating beam size is essential and indispensable while designing a house. In this post, you will get to know the method of how to calculate the beam size before designing a beam for 2 to 3 storey building design plans or multi-storey building design plans.

For designing the beam, it is essential to know how to calculate the beam size, load calculation and grade of concrete and grade of steel. You can design it with the help of beam design formula and concrete beam design calculator. Just brush the concepts once and start with the given process.

Apart from it, you can easily create a beam design from the concrete beam design calculator, available on various sites. Still, as a structural engineer, you must know the beam design formula and their design procedure and have a proper understanding of basic physics principles and engineering statics, as they are significant for designing and sizing beams. A structural engineer has complete knowledge and is fully equipped to choose the material, size and shape accordingly and check the loads acting on a beam, calculate the forces and stresses on the structure.

## WHAT IS A BEAM?

A Beam is an essential slanted or horizontal element of the structure. It is built to resist the load during the construction and structural design of the residential building, commercial and industrial buildings and supports all external and internal loads of walls, floors and slabs of the building; then the beam loads transfer through columns to the foundation of the structure.

## DIFFERENT TYPES OF BEAM –

Under the design basis, A structure is made from different kind of beams, few of them are here:

• CANTILEVER BEAM- In the structural design of the residential building, commercial building, the one end of a cantilever beam is free from any support whereas the other end remains fixed. Generally, we design the cantilever beams to support the covering or sunshade of a bigger span of the building. They are used for the maximum shear forces & moments developed at the support section, which is usually a reinforced concrete column.
• SIMPLY SUPPORTED BEAM- It is the type of beam which is loose to rotate because it’s one end is roller support, whereas the other end has pinned support. So it is supported from both the ends, and it is the most basic type of beam. You can quickly identify the simply supported beam in 2 to 3 storey building design plans or multi-storey building design plans.
• CONTINUOUS BEAM – The continuous beams usually have two or more than two supports, it has one end fixed, and the other end goes continue. The use of these continuous beams is mostly in multi-storeyed buildings of several bays in right-angle direction. You can easily calculate the dimension of the beam to beam design formula.
• OVERHANGING BEAM – It is also a type of beam used in the structural design of the residential building, the commercial building has two conditions. If one end of the beam expands beyond the support, then it is called overhanging beam, and if both ends of the beam expand beyond the support, then the beam is called a double overhanging beam.
• FIXED BEAM- Fixed-beam has strong support from both the ends due to which it opposes any rotation, on either column or wall.
• Lintel Beam- It is a type of beam usually used during constructions for openings like windows or door. It also acts as a guard for windows and doors during rain.
• COMPOSITE BEAM- A composite beam is a structural element provided horizontally or a horizontal structural element, with a combination of concrete and steel section, is called a composite beam or an encased beam.
• L BEAM- Beams are cast uniformly on one side of the slabs of the rib are called L- Beams. At the support section, hogging and torsional bending moments are maximum.

## HOW TO CALCULATE BEAM SIZE?

It helps to distribute all structure loads properly and prevent the structure from collapsing. You can calculate the minimum size of the beam from the below formula. We can always take the standard size of the concrete beam at least 230 mm x 230 mm (9” x 9”). The depth of the beam increases or decreases according to their span and applied load on the beam. The beam is an integral part of the structure.

The size of the beam depends on the span of the beam and the load on the beam. In multi-storey design plans, the size of the plinth beam, primary and secondary beams depend on the number of stories and loads acting on the beam. Here is some example with the formula which tells you how to calculate the size of the beam.

Effective depth =Span/Basic value
Total Depth = Effective depth + dia./2 + Clear Cover
Width = Depth/1.5 (width should not be less than 200 mm)

Note:
As per IS – 13920,

1. The width to depth ratio should be more than 0.3.
Width/Depth >0.3
2. Depth of beam shall not be exceeded ¼ of the clear span.

Example- For simply supported beam

Where,
Le = Effective length
D = Total depth of the beam
d = Effective depth of the beam
b = width of beam

Span of simply supported beam = 5 m
Then effective depth of beam = 5000 / 20
d = 250 mm
Total depth = effective depth + diameter of bar/2 + clear cover
Assume diameter of bar = 16 mm
D = 250 + 16/2 + 25
D = 283 mm ≈ 285 mm

And width = D/1.5
Width = 285 /1.5
b = 190 mm
So, we will take 200 mm for width

Then,
Width / Depth = 200/ 285 = 0.7 > 0.3, SAFE

Then,
we can check depth of beam = ¼ of span
= ¼ x 5000
= 1250 mm > 285 mm, SAFE

Example- For a cantilever beam

Span of cantilever beam = 2 m
Then effective depth of beam = 2000 / 7
d = 285 mm
Total depth = effective depth + diameter of bar/2 + clear cover
Assume diameter of bar = 16 mm
D = 285 + 16/2 + 25
D = 318 mm ≈ 320 mm

And width = D/1.5
Width = 320 /1.5
b = 213 mm
So, we will take 230 mm for width
Then,
Width / Depth = 230/ 320 = 0.71 > 0.3, SAFE

Then,
we can check depth of beam = ¼ of span
= ¼ x 2000
= 500 mm > 320 mm, SAFE

Example- For continuous beam

Span of continuous beam = 5 m
Then effective depth of beam = 5000 / 26
d = 192.3 mm ≈ 200 mm
Total depth = effective depth + diameter of bar/2 + clear cover
Assume diameter of bar = 16 mm
D = 200 + 16/2 + 25
D = 233 mm ≈ 235 mm

And width = D/1.5
Width = 235 /1.5
b = 156.67 mm
So, we will take 200 mm for width
Then,
Width / Depth = 200/ 235 = 0.85 > 0.3, SAFE

Then,
we can check depth of beam = ¼ of span
= ¼ x 5000
= 1250 mm > 235 mm, SAFE

Check for lateral stability or buckling:
(As per IS 456:2000, page no.39, clause 23.3)
For Simply Supported or Continuous Beam

Allowable L = 60 b
Allowable L= 250. b^2 / d
Take the least value of L
If beam span is less than L allowable, then the beam will be safe from lateral stability or buckling.

Where,
b = width of beam
d = effective depth of the beam

Example-

Allowable L = 60 b
Allowable L = 60 x 200
Allowable L = 12000 mm = 12 m
And
Allowable L = 250 b2 / d
Allowable L = 250 x 2002 / 285
Allowable L = 35087.7 mm = 35.087 m
Therefore,
Allowable L = 12 m
Here, Allowable L = 12 m > 5m, SAFE

For Cantilever Beam

Allowable L = 25 b
Allowable L= 100 b2 / d
Take the least value of L
If beam span is less than L allowable, then the beam will be safe from lateral stability or buckling.

Where,
b = width of beam
d = effective depth of the beam

Example-

Allowable L = 60 b
Allowable L = 60 x 230
Allowable L = 13800 mm = 13.8 m
And
Allowable L = 250 b2 / d
Allowable L = 250 x 2302 / 285
Allowable L = 46403.5mm = 46.4 m
Therefore,
Allowable L = 13.8 m
Here, Allowable L = 13.8 m > 2 m, SAFE

Thumb rule method:
You can also calculate the depth of the beam according to the method mention below
1 foot (span of the beam) = 1Inch (depth of beam)
If the span is of the beam is 16 feet, then the depth of the beam will be 16 inches.

Lintel Beam: it is an integral part of the structure which prevent door frame or window frame corners from cracks.
The minimum thickness of the lintel beam is 150 mm.

### This Post Has 14 Comments

1. Dipak barua

30cmx90cm beam size is ok or not. (width & depth ratio is ok ? )

1. As per Is 13920 width to depth ratio should be more than 0.3. You have taken beam width 30 cm and depth 90 cm, which fulfils the criteria. Furthermore, the size of the beam depends on span and type of load on beam. You can check span of the beam and type of load applied on beam for the size of beam.

2. Rahul Kumar

Hi
How do you calculate the dimensions of beam and no. of bars taking into account the slab load(DL &LL)

3. Engineer

Great thanks. Very nicely explained 🙂

4. S.majumdar

A 90 feet guard wall.of residential building how much tmt bar is needed for tie beam.

6. Engr wasiu

Informative article, I an electrical engineer, but find this beam theory an interesting.

7. John Gabriel

Where do we base the span of the beam, is it the clear span or the effective length (Le) ?

1. It is the clear span 🙂