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Angle of Deflection Formula:
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The angle of deflection (θ) represents the angular displacement of a beam or structural element under load. It's calculated by integrating the bending moment distribution along the length of the beam, divided by the product of the modulus of elasticity and moment of inertia.
The calculator uses the angle of deflection formula:
Where:
Explanation: This calculator simplifies the calculation for cases with constant bending moment along the beam length. For variable moments, the integral would need to be evaluated based on the specific moment distribution.
Details: Calculating deflection angles is crucial in structural engineering to ensure that beams and other structural elements don't deflect beyond acceptable limits, which could compromise structural integrity or functionality.
Tips: Enter bending moment in Nm, modulus of elasticity in Pa, moment of inertia in m⁴, and length in m. All values must be positive and non-zero.
Q1: What is the difference between deflection and angle of deflection?
A: Deflection refers to the linear displacement of a point on a beam, while angle of deflection refers to the angular rotation at that point.
Q2: When is this simplified formula not applicable?
A: This simplified formula works for constant bending moment. For variable moments (distributed loads, point loads), the integral must be evaluated based on the specific moment equation.
Q3: What are typical values for modulus of elasticity?
A: Steel: ~200 GPa, Aluminum: ~69 GPa, Concrete: ~20-30 GPa, Wood: ~8-12 GPa (varies by species and grade).
Q4: How does moment of inertia affect deflection?
A: Higher moment of inertia results in less deflection for the same loading conditions, as it represents the beam's resistance to bending.
Q5: Can this calculator handle composite beams?
A: For composite beams, equivalent stiffness properties would need to be calculated first before using this formula.