Calculating Deflection Of A Beam

Intermediate Point Load Deflection Formula:

\[ \delta = \frac{P a^2 (L - a)^2}{3 E I L} \]

Load (P):

Distance from Support (a):

Beam Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Deflection (δ):

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1. What is Beam Deflection?

Beam deflection refers to the displacement of a beam under load. The intermediate point load deflection formula calculates how much a beam will bend when a force is applied at a point between its supports.

2. How Does the Calculator Work?

The calculator uses the intermediate point load deflection formula:

\[ \delta = \frac{P a^2 (L - a)^2}{3 E I L} \]

Where:

\( \delta \) — Deflection (m)
\( P \) — Applied load (N)
\( a \) — Distance from support to load point (m)
\( L \) — Total beam length (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: This formula calculates the maximum deflection of a simply supported beam with a single point load applied at distance 'a' from one support.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial in structural engineering to ensure that beams will not deflect excessively under load, which could lead to structural failure or serviceability issues.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure the distance 'a' is less than the beam length 'L'. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

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

Q2: What is the modulus of elasticity (E)?
A: The modulus of elasticity is a material property that measures its stiffness. Common values are around 200 GPa for steel and 10-30 GPa for wood.

Q3: How do I calculate moment of inertia (I)?
A: Moment of inertia depends on the cross-sectional shape. For common shapes like rectangles or I-beams, standard formulas or tables are available.

Q4: What are typical deflection limits?
A: Building codes often limit deflection to L/360 for live loads and L/240 for total loads, where L is the span length.

Q5: Does this formula account for beam self-weight?
A: No, this formula only considers the applied point load. For self-weight calculations, additional formulas are needed.