Understand the engineering model
What is Beam Deflection?
Materials and structural fundamentals connect applied loads, section geometry, deformation, strain, stiffness, temperature change, stress, and ideal elastic response under explicit assumptions.
Give a bounded set of clearly named textbook load cases instead of asking visitors to guess a coefficient.
The relationship
Write the model before substituting values
Uses the named Euler–Bernoulli closed forms: PL³/(48EI), 5wL⁴/(384EI), PL³/(3EI), or wL⁴/(8EI), with corresponding slopes and reactions.
See the calculation
From measurement to engineering result
1Load, geometry, material2Elastic or section model3Stress, strain, or response
Worked context
Read the output with its units
A simply supported 2 m beam with 1 kN at centre, E=200 GPa and I=8×10⁶ mm⁴ deflects about 0.104 mm.
Interpret with care
Important model boundary
Ideal small-deflection Euler–Bernoulli behavior, constant EI, ideal supports, and the selected load case are assumed. Shear deformation, dynamics, stability, connections, composite action, and design-code limits are excluded.
A calculated value does not certify a component, material, installation, operating envelope, code requirement, or safety decision. Check measurements, signs, standards, uncertainty, and professional approval where consequences matter.
Browse Engineering & science for connected physical relationships.
Quick guide
How to use this calculator
- Choose the physical relationship and solve direction that match the known measurements rather than forcing unlike quantities into one formula.
- Enter every unit, sign, reference direction, geometry, material property, fluid property, temperature basis, coefficient, and idealization explicitly. The calculator normalizes compatible quantities internally and exposes intermediate values.
- Use reconciliation and companion outputs to catch entry mistakes, then retain the stated model boundary. A theoretical result is not a design approval, material certificate, equipment rating, or safety determination.
Calculation method
How the beam deflection calculator works
Give a bounded set of clearly named textbook load cases instead of asking visitors to guess a coefficient.
Uses the named Euler–Bernoulli closed forms: PL³/(48EI), 5wL⁴/(384EI), PL³/(3EI), or wL⁴/(8EI), with corresponding slopes and reactions.
Worked example
Beam Deflection example
A simply supported 2 m beam with 1 kN at centre, E=200 GPa and I=8×10⁶ mm⁴ deflects about 0.104 mm.
Uses the named Euler–Bernoulli closed forms: PL³/(48EI), 5wL⁴/(384EI), PL³/(3EI), or wL⁴/(8EI), with corresponding slopes and reactions.
Supported inputs
Precision and limits
Engineering-model boundary
Ideal small-deflection Euler–Bernoulli behavior, constant EI, ideal supports, and the selected load case are assumed. Shear deformation, dynamics, stability, connections, composite action, and design-code limits are excluded.
Units and precision
Calculations normalize compatible inputs to SI, retain working precision, and round only for display. Very small and large nonzero values use scientific notation; displayed digits cannot create accuracy beyond the entered measurements and properties.
Decision boundary
This page solves the declared idealized relationship only. Verify applicable material data, operating conditions, geometry, loads, coefficients, standards, codes, manufacturer requirements, uncertainty, and professional approval before consequential use.
Category ownership
Generic mechanics, materials, fluid, aerodynamic, wave, and thermodynamic relationships live here. Trade-specific pipe, HVAC, motor, electrical, construction, automotive, radiation, statistical, chemical, and astronomical workflows remain with their established categories.
Privacy
Entered values and results stay in this browser and are not sent to analytics or third parties.
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