Beam Load Calculator

About the Beam Load Calculator

The Beam Load Calculator computes reactions, shear forces, and bending moments for a simply supported beam under point loads and uniformly distributed loads (UDLs). This tool is designed for structural engineers, civil engineering students, and educators analyzing beam behavior.

Simply Supported Beam: A beam supported by a pin at one end and a roller at the other, subjected to vertical loads.

Use this calculator to determine the forces and moments a beam must resist under specified loading conditions.

• Features:
  • Calculates reactions (\( R_A \), \( R_B \)), maximum shear force (\( V_{max} \)), and maximum bending moment (\( M_{max} \)).
  • Supports point loads (\( P \)) and UDLs (\( w \)).
  • Keypad includes digits (0–9) and decimal point (.).
  • Displays step-by-step calculations in LaTeX format.
  • Clear and backspace functionality, with a "Copy" button for results.
  • Uses MathJax for professional rendering of mathematical expressions.
• Practical Applications: Useful in structural design, beam analysis, and civil engineering education.
• How to Use:
  • Enter beam length (\( L \), in meters).
  • For point load: Enter magnitude (\( P \), kN) and position (\( a \), m from left support).
  • For UDL: Enter magnitude (\( w \), kN/m), start position (\( b \), m), and end position (\( c \), m).
  • Leave unused load fields empty (e.g., \( P \), \( a \) for UDL only).
  • Use the keypad to input digits and decimal points.
  • Click "Calculate" to compute reactions, shear, and moments.
  • Use "Clear" to reset or "⌫" to delete the last character.
  • Use "Copy" to copy the results and steps.
  • Share or embed the calculator using the action buttons.
• Helpful Tips:
  • Beam length (\( L \)) must be positive.
  • Point load position (\( a \)) must satisfy \( 0 \leq a \leq L \).
  • UDL positions (\( b \), \( c \)) must satisfy \( 0 \leq b \leq c \leq L \).
  • At least one load (point or UDL) must be specified.
  • Results assume linear elastic behavior and static equilibrium.
  • Consult structural engineering standards for detailed design.
• Examples:
  • Example 1: Point Load Only:
    • Inputs: \( L = 10 \) m, \( P = 20 \) kN, \( a = 4 \) m
    • Steps:
      • Reaction \( R_A \): \( R_A = \frac{P (L - a)}{L} = \frac{20 \times (10 - 4)}{10} = 12 \) kN
      • Reaction \( R_B \): \( R_B = \frac{P a}{L} = \frac{20 \times 4}{10} = 8 \) kN
      • Max shear: \( V_{max} = \max(R_A, R_B) = 12 \) kN
      • Max moment: \( M_{max} = \frac{P a (L - a)}{L} = \frac{20 \times 4 \times 6}{10} = 48 \) kN·m
    • Result: \( R_A = 12 \) kN, \( R_B = 8 \) kN, \( V_{max} = 12 \) kN, \( M_{max} = 48 \) kN·m
  • Example 2: UDL Only:
    • Inputs: \( L = 8 \) m, \( w = 5 \) kN/m, \( b = 0 \) m, \( c = 8 \) m
    • Steps: Similar calculations for full-span UDL.
    • Result: \( R_A = R_B = 20 \) kN, \( V_{max} = 20 \) kN, \( M_{max} = 40 \) kN·m
  • Example 3: Combined Loads:
    • Inputs: \( L = 12 \) m, \( P = 15 \) kN, \( a = 3 \) m, \( w = 4 \) kN/m, \( b = 4 \) m, \( c = 10 \) m
    • Steps: Combined equilibrium equations.
    • Result: Computed reactions, shear, and moment.

Analyze beam loads with this interactive calculator. Share or embed it on your site!