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Beam Stiffness Formula:
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Beam stiffness (k) represents the resistance of a beam to deformation under applied loads. For a cantilever beam, it's calculated using the formula k = 3EI/L³, where E is the modulus of elasticity, I is the moment of inertia, and L is the length of the beam.
The calculator uses the beam stiffness formula:
Where:
Explanation: This formula calculates the stiffness of a cantilever beam, which is the force required to produce a unit deflection at the free end of the beam.
Details: Calculating beam stiffness is crucial in structural engineering for designing beams that can withstand expected loads without excessive deflection. It helps ensure structural integrity and safety in buildings, bridges, and other structures.
Tips: Enter the modulus of elasticity in Pascals (Pa), moment of inertia in meters to the fourth power (m⁴), and length in meters (m). All values must be positive numbers.
Q1: What is a cantilever beam?
A: A cantilever beam is a rigid structural element that extends horizontally and is supported at only one end.
Q2: How does beam length affect stiffness?
A: Stiffness decreases with the cube of the length (L³), meaning longer beams are significantly less stiff than shorter ones.
Q3: What is modulus of elasticity?
A: Modulus of elasticity (E) is a material property that measures its stiffness or resistance to elastic deformation under load.
Q4: What is moment of inertia?
A: Moment of inertia (I) is a geometric property that reflects how a cross-section's area is distributed relative to a specific axis, affecting its resistance to bending.
Q5: Is this formula specific to certain beam types?
A: Yes, this formula specifically applies to cantilever beams with a point load at the free end. Other beam configurations and loading conditions have different stiffness formulas.