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Slope at End for Point Load on Cantilever:
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The slope at the free end of a cantilever beam with a point load at the end is given by θ_end = P L² / (2 E I). This formula calculates the angular displacement at the free end of the beam when subjected to a concentrated load.
The calculator uses the beam deflection formula:
Where:
Explanation: The formula calculates the slope (angular displacement) at the free end of a cantilever beam subjected to a point load at its end.
Details: Calculating beam slope is crucial for structural analysis and design, ensuring that deflections and rotations remain within acceptable limits for safety and serviceability.
Tips: Enter all values in consistent SI units. Point load in Newtons (N), length in meters (m), modulus of elasticity in Pascals (Pa), and moment of inertia in meters to the fourth power (m⁴).
Q1: What is a cantilever beam?
A: A cantilever beam is a structural element fixed at one end and free at the other, commonly used in construction and engineering applications.
Q2: What are typical values for modulus of elasticity?
A: For steel: ~200 GPa, for aluminum: ~69 GPa, for wood: ~10 GPa (varies by species and grade).
Q3: How is moment of inertia calculated?
A: Moment of inertia depends on the cross-sectional shape. For a rectangle: I = (b h³)/12, where b is width and h is height.
Q4: What are acceptable slope limits?
A: Acceptable limits depend on the application, but typically slopes should be less than 1/360 to 1/240 of the span for visual comfort.
Q5: Does this formula work for distributed loads?
A: No, this specific formula is only for a point load at the free end. Different formulas exist for distributed loads.