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Maximum Deflection Formula:
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The maximum deflection of a simply supported beam with a point load at midspan is calculated using the formula δ_max = Q l³ / (48 E I). This equation helps engineers determine how much a beam will bend under a specific load, which is crucial for structural design and safety.
The calculator uses the beam deflection formula:
Where:
Explanation: The formula calculates the maximum vertical displacement at the center of a simply supported beam when a concentrated load is applied at midspan.
Details: Accurate deflection calculation is essential for ensuring structural integrity, preventing excessive deformation, and meeting building code requirements for various types of beams and loading conditions.
Tips: Enter the point load in Newtons, beam length in meters, modulus of elasticity in Pascals, and moment of inertia in meters to the fourth power. All values must be positive numbers.
Q1: What is a simply supported beam?
A: A simply supported beam is a structural element that rests on two supports at its ends and is free to rotate at these supports.
Q2: When is this deflection formula applicable?
A: This formula applies specifically to simply supported beams with a single concentrated load applied at the midspan.
Q3: What are typical values for modulus of elasticity?
A: For steel, E ≈ 200 GPa; for aluminum, E ≈ 70 GPa; for wood, E varies from 8-14 GPa depending on species and grade.
Q4: How does beam length affect deflection?
A: Deflection increases with the cube of the beam length, meaning longer beams deflect significantly more under the same load.
Q5: What are acceptable deflection limits?
A: Building codes typically limit deflection to span/360 for live loads and span/240 for total loads, but specific requirements vary by application.