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Bending Moment Formula:
Where: M (Nm) = Bending Moment, V (N) = Shear Force, x (m) = Distance
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Bending moment is a measure of the bending effect that occurs when an external force is applied to a structural element. It's calculated as the integral of shear force along the length of the beam, representing the internal moment that resists external loads.
The calculator uses the bending moment formula:
Where:
Explanation: The calculator numerically integrates the shear force function between the specified limits to determine the bending moment at that section of the beam.
Details: Accurate bending moment calculation is crucial for structural design, ensuring beams and other structural elements can withstand applied loads without failure. It helps determine required material strength and cross-sectional dimensions.
Tips: Enter the shear force function as a mathematical expression, specify the integration limits (distance along the beam), and click calculate. Ensure the upper limit is greater than the lower limit.
Q1: What are common shear force functions?
A: Common functions include constants (uniform load), linear functions (triangular load), and more complex distributions depending on loading conditions.
Q2: How does bending moment relate to beam deflection?
A: Bending moment is directly related to beam curvature through the flexure formula M = EI/R, where E is modulus of elasticity, I is moment of inertia, and R is radius of curvature.
Q3: What are typical units for bending moment?
A: Bending moment is typically measured in Newton-meters (Nm) in SI units or pound-feet (lb-ft) in imperial units.
Q4: Where is maximum bending moment typically found?
A: Maximum bending moment typically occurs where shear force is zero or at supports/points of application of concentrated loads.
Q5: Can this calculator handle complex loading conditions?
A: This calculator provides basic integration capability. Complex loading conditions may require specialized structural analysis software.