Here is the Scilab function for solving the support reactions, maximum shear, and maximum bending moment for a uniformly loaded simply supported beam with a variable load and span:

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function [RA, RB, Vmax, Mmax] = BeamAnalysis(W, L)
    // BeamAnalysis: Solve reactions, max shear, and max bending moment
    //
    // Inputs:
    //   W - Uniform load (kN/m)
    //   L - Span length (m)
    //
    // Outputs:
    //   RA - Reaction force at support A (kN)
    //   RB - Reaction force at support B (kN)
    //   Vmax - Maximum Shear Force (kN)
    //   Mmax - Maximum Bending Moment (kN·m)
    
    // Calculate support reactions (assuming uniform load)
    RA = W * L / 2; // Reaction at support A
    RB = RA;        // Reaction at support B (symmetric beam)
    
    // Maximum Shear Force
    Vmax = RA;      // Maximum shear is equal to the reaction force at A or B
    
    // Maximum Bending Moment
    Mmax = W * L^2 / 8; // Occurs at mid-span
    
    // Display results
    disp("Results:");
    disp("Reaction at Support A (RA): " + string(RA) + " kN");
    disp("Reaction at Support B (RB): " + string(RB) + " kN");
    disp("Maximum Shear Force (Vmax): " + string(Vmax) + " kN");
    disp("Maximum Bending Moment (Mmax): " + string(Mmax) + " kN·m");
endfunction

Explanation:

1. Reactions at Supports: The beam is symmetric with a uniform load $W$ distributed over the span $L$. Therefore, reactions at both supports are equal: $R_A = R_B = \frac{W \cdot L}{2}$

2. Maximum Shear Force: The maximum shear force occurs at the supports: $V_{\text{max}} = R_A = R_B$

3. Maximum Bending Moment: The maximum bending moment occurs at the midpoint of the span: $M_{\text{max}} = \frac{W \cdot L^2}{8}$

Usage:

To use this function in Scilab:

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// Example
W = 10; // Uniform load in kN/m
L = 6;  // Span in meters
[RA, RB, Vmax, Mmax] = BeamAnalysis(W, L);

This will compute and display the reactions, maximum shear force, and maximum bending moment for the given inputs.

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Follow-up Questions:

1. How does the function change if the load is triangular or non-uniform?
2. What if the beam has an overhang—how would you modify the calculations?
3. Can this function be extended to include distributed moments?
4. How does the bending moment distribution look graphically for this case?
5. What would change in this calculation if the supports were not pinned but fixed?

Tip:

When working with beam problems in Scilab, consider creating plots for shear force and bending moment diagrams for better visualization.