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Beam Deflection Angle Formula:
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The beam deflection angle (θ) represents the angular displacement of a beam or structural element under load. It is calculated using the chord length and radius of curvature to determine how much a beam bends from its original position.
The calculator uses the deflection angle formula:
Where:
Explanation: This formula calculates the central angle subtended by a chord of length L in a circle of radius R, which corresponds to the deflection angle in beam analysis.
Details: Accurate deflection angle calculation is crucial for structural engineering, mechanical design, and civil engineering applications to ensure structural integrity, predict beam behavior under load, and prevent excessive deformation.
Tips: Enter the chord length (L) and radius of curvature (R) in meters. Both values must be positive numbers, and L must be less than or equal to 2R for valid results.
Q1: What is the physical significance of deflection angle?
A: The deflection angle indicates how much a structural element bends under applied loads, helping engineers assess stiffness and deformation limits.
Q2: When is this formula applicable?
A: This formula applies to circular arc segments and beams with constant curvature, commonly used in arch structures and curved beam analysis.
Q3: What are typical deflection angle limits?
A: Deflection limits vary by application and material, but generally range from 0.1° to 5° depending on structural requirements and safety factors.
Q4: How does radius affect deflection angle?
A: Larger radius results in smaller deflection angles for the same chord length, indicating gentler curvature and less bending.
Q5: Can this be used for large deflection analysis?
A: This formula is suitable for small to moderate deflections. For large deflections, non-linear analysis may be required.