Fixed Beam Deflection Calculator

Fixed Beam Deflection Formula:

\[ \delta_F = \frac{F a^3 b^3}{3 L^3 E I} \]

Force (F):

Distance a:

Distance b:

Beam Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Deflection (δ_F):

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1. What is Fixed Beam Deflection?

Fixed beam deflection refers to the displacement of a beam under load when both ends are fixed (cannot rotate or translate). The formula calculates the maximum deflection at the point where the load is applied.

2. How Does the Calculator Work?

The calculator uses the fixed beam deflection formula:

\[ \delta_F = \frac{F a^3 b^3}{3 L^3 E I} \]

Where:

\( \delta_F \) — Deflection at the point of load application (m)
\( F \) — Applied force (N)
\( a \) — Distance from left support to the load (m)
\( b \) — Distance from right support to the load (m)
\( L \) — Total length of the beam (m)
\( E \) — Modulus of elasticity of the material (Pa)
\( I \) — Moment of inertia of the beam cross-section (m⁴)

Explanation: This formula calculates the deflection of a fixed-fixed beam with a single point load applied at a distance 'a' from the left support and 'b' from the right support.

3. Importance of Deflection Calculation

Details: Deflection calculations are crucial in structural engineering to ensure that beams and structures can withstand applied loads without excessive deformation that could compromise structural integrity or functionality.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure that a + b = L for accurate results. All input values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between fixed and simply supported beams?
A: Fixed beams have both ends restrained against rotation and translation, while simply supported beams have ends free to rotate but restrained against vertical movement.

Q2: How does beam material affect deflection?
A: Materials with higher modulus of elasticity (E) will have less deflection under the same load, as they are stiffer.

Q3: What is moment of inertia and why is it important?
A: Moment of inertia (I) measures a beam's resistance to bending. Higher I values mean less deflection for the same load.

Q4: Can this formula be used for distributed loads?
A: No, this specific formula is for point loads only. Different formulas exist for distributed loads.

Q5: What are typical deflection limits in structural design?
A: Deflection limits vary by application but are typically L/360 for floors and L/240 for roofs under live loads, where L is the span length.