How does the beam configuration affect deflection?

The beam configuration defines boundary conditions. Simply supported beams are free to rotate at the ends. Cantilever beams are fixed at one end and free at the other, resulting in higher deflections.

What is the flexure formula for bending stress?

The maximum normal bending stress is calculated using σ = M_max · c / I.

Engineering DisclaimerEngineering calculations are provided for preliminary design and educational/reference purposes only. Users must verify all results according to applicable engineering standards, supplier data, manufacturing requirements, and professional engineering judgment.

Roark's Formulas

Structural Analysis

Beam Deflection Calculator

Calculate maximum deflection and bending stress for simply supported, cantilever, fixed-fixed, and fixed-pinned beams under common load configurations. Based on Roark's Formulas for Stress and Strain.

Workspace Mode:

Unsaved Configuration

Flexural Analysis Outputs

Max Deflection

4.5000mm

Max Moment

15.00kN·m

Max Shear Force

5.00kN

Max Bending Stress

30.00MPa

Calculation Summary

Input Parameters

Configuration	Simply Supported Beam
Load Type	Point Load
Span Length	6m
Young's Modulus	200GPa
Moment of Inertia	5010⁶ mm⁴
Extreme Fiber distance	100mm
Load Value	10kN

Calculated Results

Max Deflection	4.5000mm KEY
Max Bending Moment	15.00kN·m
Max Shear Force	5.00kN
Extreme Fiber Stress	30.00MPa KEY
Reaction Left	5.00kN
Reaction Right	5.00kN

Safety Notes

Bending stress results should be verified against the material yield limit including appropriate design factors of safety.

Mathematical Models & Equations

Euler-Bernoulli Elastic Equations (Simply Supported Beam)

Max Deflection (δ_max) = F * L³ / (48 * E * I)  [at center]
Max Bending Moment (M_max) = F * L / 4  [at center]
Max Shear Force (V_max) = F / 2  [at supports]
Reactions R_left = R_right = F / 2
Max Bending Stress (σ_max) = M_max * c / I

Verification Calculation Log

1Identify Configuration & Design Parameters:
- •Beam configuration: simply supported
- •Load type: point load
- •Span length (L) = 6.00 m
- •Young's Modulus (E) = 200.00 GPa
- •Moment of Inertia (I) = 50.00 10⁶ mm⁴
- •Distance to extreme fiber (c) = 100.00 mm
- •Applied load value = 10.00 kN
2Calculate Maximum Deflection (δ_max):
- •Conversions to base SI units (N, mm):
- •L = 6000 mm, E = 200000 MPa, I = 50000000 mm⁴
- •Point Load (F) = 10000 N
- •Equation: δ_max = F * L³ / (48 * E * I)
- •Substitution: δ_max = (10000 * 6000³) / (48 * 200000 * 50000000)
- •Result: δ_max = 4.5000 mm
3Calculate Maximum Bending Moment (M_max) & Bending Stress (σ_max):
- •Bending Moment: M_max = F * L / 4 = (10.00 * 6.00) / 4
- •Resulting M_max = 15.00 kN·m
- •Bending Stress equation: σ_max = M_max * c / I
- •Substitution: σ_max = (15.00 kN·m * 100.0 mm) / 50.00 * 10⁶ mm⁴
- •Result: σ_max = 30.00 MPa
4Calculate Reactions and Shear Forces:
- •Max Shear Force (V_max) = 5.00 kN
- •Vertical Reaction R_left = 5.00 kN
- •Vertical Reaction R_right = 5.00 kN

Engineering Application Notes

Young's modulus and cross-sectional geometries govern standard beam stiffness. Solid cross sections and hollow profiles require correct Inertia formulas (I = pi*d^4/64 for round shafts, I = b*h^3/12 for rectangular sections) prior to entering values here. Stress checks should verify tension and compression limits.

Standard Citations & References

AISC Steel Construction Manual - Flexural Sizing Procedures.
Shigley's Mechanical Engineering Design, Chapter 4 - Deflection and Stiffness.
Roark's Formulas for Stress and Strain - Bending of Beams.

Beam Deflection Calculator

Flexural Analysis Outputs

Calculation Summary

Mathematical Models & Equations

Verification Calculation Log

Engineering Application Notes

Standard Citations & References

Related Calculators

Applicable Standards

Related Formulas

Engineering Data

Related Engineering Articles

Beam Deflection & Bending Analysis Report — Calculation Report

Beam Deflection & Bending Analysis Report

Design Inputs

Calculated Results

Verification Steps

Flexural Analysis Outputs

Calculation Summary

Mathematical Models & Equations

Verification Calculation Log

Engineering Application Notes

Standard Citations & References

Related Calculators

Applicable Standards

Related Formulas

Engineering Data

Related Engineering Articles

Beam Deflection & Bending Analysis Report — Calculation Report

Beam Deflection & Bending Analysis Report

Design Inputs

Calculated Results

Verification Steps

Maximum Deflection (δ):	4.5000 mm
Max Bending Moment (M):	15.00 kN·m
Max Shear Force (V):	5.00 kN
Extreme Bending Stress (σ):	30.00 MPa
Left Reaction (R1):	5.00 kN
Right Reaction (R2):	5.00 kN