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Maximum Slope Formula:
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The maximum slope formula calculates the maximum angular deflection (slope) of a simply supported beam with a center point load. This is an important parameter in structural engineering for assessing beam performance under load.
The calculator uses the maximum slope formula:
Where:
Explanation: The formula calculates the maximum angular displacement at the supports of a simply supported beam with a center point load, considering the beam's material properties and geometry.
Details: Calculating maximum slope is crucial for structural design to ensure that beams meet serviceability requirements and don't experience excessive deformation under load, which could affect functionality and aesthetics.
Tips: Enter all values in the specified units. Load (P) in Newtons, Length (L) in meters, Modulus of Elasticity (E) in Pascals, and Moment of Inertia (I) in meters to the fourth power. All values must be positive.
Q1: What is a simply supported beam?
A: A simply supported beam is supported at both ends with one support allowing rotation and horizontal movement, and the other allowing only rotation.
Q2: What are typical values for modulus of elasticity?
A: Steel: ~200 GPa, Aluminum: ~69 GPa, Wood: ~10 GPa (varies by species and direction of grain).
Q3: How do I calculate moment of inertia?
A: Moment of inertia depends on the cross-sectional shape. For common shapes like rectangles or circles, standard formulas are available in engineering handbooks.
Q4: What is considered an acceptable slope for beams?
A: Acceptable slopes vary by application and building codes, but typically range from L/240 to L/360 for most structural applications.
Q5: Does this formula work for distributed loads?
A: No, this specific formula is for a center point load. Different formulas exist for distributed loads or loads at other positions.