Introduction:
In order to determine the minimum overall depth of a continuous slab that satisfies the vertical deflection limit, several factors need to be considered. These factors include the material properties, loading conditions, and the deflection criteria specified for the slab.

Material properties:
The material properties of the slab, such as the modulus of elasticity (E) and the moment of inertia (I), will affect its deflection behavior. A higher modulus of elasticity and moment of inertia will result in a stiffer slab and lower deflections.

Loading conditions:
The loading conditions applied to the slab will play a significant role in determining its deflection. Different types of loads, such as dead loads (self-weight of the slab) and live loads (imposed loads), will have different effects on the deflection. It is important to consider the worst-case loading scenario that will result in the highest deflection.

Deflection criteria:
The specified vertical deflection limit for the slab will dictate the minimum overall depth required. This limit is usually expressed as a ratio of the deflection to the span length of the slab. For example, a common deflection limit is L/360, where L is the span length of the slab. This means that the maximum deflection should not exceed 1/360th of the span length.

Calculation of minimum overall depth:
To calculate the minimum overall depth of the slab, the deflection equation for a simply supported beam can be used. This equation relates the maximum deflection (δ) to the applied load (W), span length (L), material properties (E and I), and the slab depth (d):

δ = (W * L^3) / (48 * E * I)

Rearranging the equation to solve for the slab depth (d), we get:

d = ((W * L^3) / (48 * E * I))^(1/4)

By substituting the appropriate values for the applied load, span length, material properties, and the desired deflection limit, we can calculate the minimum overall depth of the slab.

Conclusion:
In conclusion, to determine the minimum overall depth of a continuous slab that satisfies the vertical deflection limit, it is necessary to consider the material properties, loading conditions, and the specified deflection criteria. By using the deflection equation and rearranging it to solve for the slab depth, the minimum overall depth can be calculated. It is important to ensure that the calculated depth satisfies the deflection limit to ensure the structural integrity and functionality of the slab.