Rectangular Beam Deflection Calculator

Maximum Deflection Equation:

\[ \delta_{max} = \frac{P L^3}{48 E I} \]

Point Load (P):

Beam Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Maximum Deflection (δ_max):

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1. What is the Maximum Deflection Equation?

The maximum deflection equation calculates the center deflection for a rectangular beam simply supported with a point load. This fundamental engineering formula helps determine how much a beam will bend under a specific load.

2. How Does the Calculator Work?

The calculator uses the deflection equation:

\[ \delta_{max} = \frac{P L^3}{48 E I} \]

Where:

\( \delta_{max} \) — Maximum deflection at center (m)
\( P \) — Point load applied (N)
\( L \) — Beam length (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: The equation shows that deflection is directly proportional to the load and cube of the length, and inversely proportional to the modulus of elasticity and moment of inertia.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for structural design, ensuring beams can withstand loads without excessive bending that could compromise structural integrity or functionality.

4. Using the Calculator

Tips: Enter 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.

5. Frequently Asked Questions (FAQ)

Q1: What types of beams does this equation apply to?
A: This equation applies to simply supported rectangular beams with a single point load at the center.

Q2: How does beam material affect deflection?
A: Materials with higher modulus of elasticity (stiffer materials) will deflect less under the same load compared to more flexible materials.

Q3: What is the significance of moment of inertia?
A: Moment of inertia represents the beam's resistance to bending. Larger moments of inertia result in less deflection for the same load.

Q4: Are there limitations to this equation?
A: This equation assumes linear elastic material behavior, small deflections, and ideal simply supported conditions without considering shear deformation.

Q5: How does load position affect deflection?
A: Maximum deflection occurs when the load is applied at the center. Off-center loads will produce different deflection patterns and require different equations.