The load transfer from the slab to the beam can be determined using yield line theory.

But, the commonly adopted practice is

**1. For a one-way slab** **ðŸ‘‰** The load is split equally between the beams that support the longer span of the slab.

When Ly/Lx ≥ 2, the slab is considered a one-way slab.

Suppose if the total load of the slab is Wu, the load over the individual beam B1 = Wu/2

If the total load per unit area of the slab is W,

The load transferred to the individual beam B1

= [1/2 x area of slab x W]

= **[1/2 x Ly x Lx x W]**

**2. For a two-way slab** **ðŸ‘‰** The load is transferred to all 4 sides of the slab. Usually, the load of a triangular area is taken by the beam at the shorter side (Lx) & a load of the trapezoidal area is distributed to the longer side (Ly) of the slab.

When Ly/Lx < 2, the slab is considered a two-way slab.

**two-way slab**from the following drawing.

**1. Load transferred to the beam B1**

= [ trapezoidal area x total load per unit area of the slab (W)]

Here,

Area of trapezoid AEFD

= [average length x perpendicular width]

= [{(side AD + side EF) / 2 } x (length of DG)]

= [{(Ly + (Ly - Lx) /2} x (Lx / 2)]

= [{ 2Ly/2 - Lx/2} x (Lx / 2)]

= [Lx Ly /2 - Lx²/4]

= [1/2 ( Lx Ly - Lx²/2)]

Therefore,

The load transferred to the individual beam B1

=** [1/2 ( Lx Ly - Lx²/2) x W]**

**2. Load transferred to the beam B2**

**= **[ triangular area x total load per unit area of the slab (W)]

Here,

Area of triangle DFC

= [1/2 x base x height]

= [1/2 ✖ Lx ✖ Lx/2]

= **Lx²/4**

Therefore,

The load transferred to the individual beam B2

=** [ ****Lx²/4**** x W]**

**Note: **This method will be accurate only when the load over the slab will be uniformly distributed.

Now, my question to you is, "**what will be the load distribution pattern in a square-shaped slab?**"

In a square-shaped slab Lx = Ly

Ly /Lx = 1 < 2, the slab is considered a two-way slab.

Here, the load will be transferred equally to all 4 sides.

The load distributed over the beam-B1 = Load over the beam-B2

The load over the individual beam ( B1 or B2)

** = **[ triangular area x total load per unit area of the slab (W)]

= ** [ ****Lx²/4**** x W] or**** [ ****Ly²/4**** x W]**

**To go through all types of structural design articles,** **click here.**

**Thank you for going through these calculation steps❤. Have a good day ðŸ˜„.**

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