Given:
Half of the main steel is bent up near the support at a distance of x from the centre of slab bearing.

To find:
Value of x.

Solution:
Let's assume the total width of the slab be 2L, and the distance of x from the centre of the slab be 'a'.

- The reinforcement steel near the support is bent up to resist the negative bending moment.
- At the centre of the slab, there is no bending moment, so there is no need to provide any reinforcement.
- As we move towards the support, the bending moment increases, so we need to provide more reinforcement.
- Therefore, the reinforcement steel is bent up at a distance of a from the centre of the slab bearing.

Now, we can use the formula for the moment of inertia of a rectangular section to find the value of x.

Moment of inertia of a rectangular section:
Ixx = (b * h^3) / 12
where,
b = width of the slab
h = depth of the slab

- The maximum bending moment occurs at the support, which is equal to wL^2/8.
- Since half of the main steel is bent up, the remaining half resists the bending moment.
- Therefore, the effective depth of the slab is h/2.
- We can assume that the reinforcement steel is placed at a distance of a from the centre of the slab bearing, and the remaining distance is (L-a).
- The moment of inertia of the slab can be calculated as follows:

Ixx = (b * h^3) / 12 + (0.5 * Ast * (a - h/2)^2) + (0.5 * Ast * (L - a - h/2)^2)

where,
Ast = area of steel reinforcement

- Equating the bending moment to the moment of resistance, we get:

wL^2/8 = (f_y / y) * Ast * (d - a/2)

where,
f_y = yield strength of reinforcement steel
y = distance from the extreme compression fibre to the centroid of the reinforcement steel
d = effective depth of the slab

- Substituting for 'd' and 'y', we get:

wL^2/8 = (f_y / (h/2 + a/2)) * Ast * (h/2 - a/2)

- Simplifying the equation, we get:

Ast = (wL^2 * (h/2 + a/2)) / (8f_y * (h/2 - a/2))

- Substituting the value of Ast in the equation for Ixx, we get:

Ixx = (b * h^3) / 12 + (0.5 * (wL^2 * (h/2 + a/2)) / (8f_y * (h/2 - a/2))) * (a - h/2)^2 + (0.5 * (wL^2 * (h/2 + a/2)) / (8f_y * (h/2 - a/2))) * (L - a - h/2)^2

- Simplifying the equation, we get:

Ixx = (b * h^3) / 12 + (wL^4 * (h/2 + a/2)) / (128f_y * (h/