Beam Deflection And Stress Calculator

Beam Equations:

\[ \delta = \frac{5 w L^4}{384 E I} \] \[ \sigma = \frac{w L^2 c}{8 I} \]

Distributed Load (w):

N/m

Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Distance to Extreme Fiber (c):

Deflection (δ):

Stress (σ):

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1. What is Beam Deflection and Stress Calculation?

Beam deflection and stress calculations are fundamental in structural engineering to determine how a beam will deform under load and whether it will withstand the applied forces without failure. These calculations help ensure structural integrity and safety.

2. How Does the Calculator Work?

The calculator uses the standard beam equations:

\[ \delta = \frac{5 w L^4}{384 E I} \] \[ \sigma = \frac{w L^2 c}{8 I} \]

Where:

\( \delta \) — Deflection (m)
\( \sigma \) — Stress (Pa)
\( w \) — Distributed load (N/m)
\( L \) — Length of beam (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)
\( c \) — Distance to extreme fiber (m)

Explanation: These equations calculate the maximum deflection and bending stress for a simply supported beam with uniformly distributed load.

3. Importance of Beam Analysis

Details: Proper beam analysis is crucial for structural design, ensuring that beams can support intended loads without excessive deflection or stress that could lead to failure.

4. Using the Calculator

Tips: Enter all values in consistent units (meters for length, Pascals for modulus and stress, N/m for load). All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What types of beams do these equations apply to?
A: These equations are for simply supported beams with uniformly distributed loads.

Q2: What is the significance of the distance to extreme fiber (c)?
A: The distance from the neutral axis to the outermost fiber determines the maximum bending stress in the beam.

Q3: How does modulus of elasticity affect deflection?
A: Higher modulus materials (like steel) deflect less than lower modulus materials (like wood) under the same load.

Q4: What are typical acceptable deflection limits?
A: Deflection is typically limited to L/360 for live loads and L/240 for total loads in building design.

Q5: Can this calculator be used for other beam configurations?
A: No, these specific equations are only valid for simply supported beams with uniformly distributed loads.