Why depth of the beam is kept more than the width?/Why RCC beam depth is more than its width in construction?

 A. In Engineering terms:

The main function of the beam is to resist the moment formed by the load acting over them. When the beam resists the deflection, it creates a high moment over the beam.

So, the beams are designed to resist bending stresses with greater flexural rigidity.

Therefore, the most economical beam design is one, that provides greater flexural rigidity with a minimal sectional area.

The rigidity is defined as EI,

 Where, 

  E = flexural modulus or modulus of elasticity in bending. 

   I = The second moment of area or moment of inertia of the given cross-section.

In other words, the capability of the beam depends upon the moment of inertia, where MI is the index to the resistance i.e. created within the beam. The greater the MI, the more resistance to the moment is achieved in a beam.

For a given material, E is constant & the value of the moment of inertia (I) depends upon the sectional dimension of the beam.

i.e. I = [bd³ ➗ 12]

Here,

      b = sectional width of the beam.

      d = sectional depth of the beam.

As you can observe in the above formula, increasing the depth of the beam will be more effective & economical rather than increasing the width of the beam.

For eg:

 Let us consider 2 beams having the following dimensions.

1. Beam section-1

The breadth of the beam = b = 230mm.

Depth of the beam = d = 450mm.

 I =  [bd³ ➗ 12]

   = [ 230 x 450³ ➗ 12]

  I = 1.746 x 10⁹ mm⁴.

2. Beam section-2

 The breadth of the beam = b = 450mm.

Depth of the beam = d = 230mm.

I =  [bd³ ➗ 12]

   = [ 450 x 230³ ➗ 12]

  I = 0.456 x 10⁹ mm⁴.

From the above calculation, we can understand that beam -1 has a greater moment of inertia than beam-2 having the same sectional area.

So, designing a beam having a greater depth-to-width ratio is more economical.

B. In general terms:

Let us take a plastic measuring scale as shown below.

Usually, the thickness of the scale is 3 to 5mm. & width is about 28 to 32mm.

 Try to bend the scale having the width in the vertical position. Hardly you can bend the scale, & if you can, it will be very negligible.

Now, keep the width in the horizontal plane and try to bend the scale. You can deflect the scale until it gets broken down. 

Here, in both cases, the sectional area of the scale is the same. But by changing the orientation of the scale, we have created flexural rigidity within the scale.

 The scale resists the moments when the measurement along the vertical axis is greater than the horizontal axis.

As the loads in the beam act in a vertical direction, the same concept is applied to design a beam. So, to build an efficient beam, the depth of the beam is kept more than its width.

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

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