Beam deflection calculation

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The mid-span deflection of a simply supported beam under various loads is as follows: For a uniformly distributed load, the deflection at the mid-span of the beam is given by the formula: Ymax = 5qL^4/(384EI). Here, Ymax represents the deflection at the mid-span of the beam in millimeters; q is the standard value of the uniformly distributed load in kN/m; E is the elastic modulus of steel, and for structural steel used in engineering, E = 2100000 N/mm^2. I is the moment of inertia of the steel section, which can be found in tables of steel sections in millimeters^4. For a concentrated load, the mid-span deflection of the beam is given by Ymax = 8pL^3/(384EI) = 1pl^3/(48EI). Here, Ymax is again the deflection at the mid-span of the beam in millimeters; p is the sum of the standard values of the concentrated loads in kN. E remains 2100000 N/mm^2, and I can be obtained from the tables of steel sections in millimeters^4. When two equal concentrated loads are arranged at equal intervals, the mid-span deflection of the beam is Ymax = 6.81pL^3/(384EI). Similarly, when three equal concentrated loads are arranged at equal intervals, Ymax = 6.33pL^3/(384EI). In the case of a cantilever beam subjected to a uniformly distributed load, or when the free end is subjected to a concentrated load, the deflection at the free end is given by the formulas: Ymax = qL^4/(8EI) and Ymax = pL^3/(3EI). Here, q is the standard value of the uniformly distributed load in kN/m, and p is the sum of the standard values of the concentrated loads in kN. You can use the deflection limit of 1/400, along with load conditions of 25 kN/m and other relevant load conditions, to determine the maximum upper load that can be applied