Calculate Beam Deflection Load At Any Point

Beam Deflection Equation:

\[ \delta(x) = \frac{P b x}{6 E I L} (L^2 - x^2 - b^2) \]

Point Load (P):

Distance from Support (b):

Deflection Point (x):

Beam Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Deflection at x (δ(x)):

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1. What is Beam Deflection?

Beam deflection refers to the displacement of a beam under load. This calculator determines the deflection at any point along a simply supported beam with a point load applied at a specific distance from one support.

2. How Does the Calculator Work?

The calculator uses the beam deflection equation:

\[ \delta(x) = \frac{P b x}{6 E I L} (L^2 - x^2 - b^2) \]

Where:

\( \delta(x) \) — Deflection at point x (m)
\( P \) — Point load (N)
\( b \) — Distance from support to load point (m)
\( x \) — Distance from support to deflection point (m)
\( L \) — Beam length (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: This equation calculates the vertical displacement at any point x along a simply supported beam with a single point load applied at distance b from the left support.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is essential in structural engineering to ensure that beams don't deflect excessively under load, which could lead to structural failure or serviceability issues.

4. Using the Calculator

Tips: Enter all values in consistent units (meters for distances, Newtons for force, Pascals for modulus, and m⁴ for moment of inertia). All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

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

Q2: What are typical deflection limits?
A: Deflection limits vary by application but are often limited to L/360 for live loads and L/240 for total loads in building design.

Q3: How does material affect deflection?
A: Materials with higher modulus of elasticity (E) will deflect less under the same load. Steel has higher E than wood or concrete.

Q4: What if the load is at the center?
A: When b = L/2, the equation simplifies to the standard center point load deflection formula.

Q5: Are there limitations to this equation?
A: This equation assumes linear elastic material behavior, small deflections, and applies only to simply supported beams with a single point load.