UDL, Simply Supported
δmax = 5wL⁴ / 384EILoading page content...
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Professional beam deflection calculator with multiple support types, cross-sections, and materials. Calculate maximum deflection, bending stress, and safety factors for structural engineering.
E=200GPa, σy=250MPa
Enter values above to see results.
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Structural Serviceability Guide
Apply fast screening checks for stiffness, deflection limits, and constructability before detailed structural analysis.
Primary Equation
δ ∝ wL⁴ / EI
Core Inputs
Load, Span, E, I
Use Stage
Concept + DD
Check Focus
Serviceability
Reviewed by: CalculatorApp Engineering Editorial Team
Beam deflection quantifies how much a member bends under applied loads. Engineers use deflection checks to protect finishes, maintain drainage and alignment, and ensure comfort in occupied structures. In many projects, deflection governs member depth even when strength demand is acceptable.
UDL, Simply Supported
δmax = 5wL⁴ / 384EIPoint Load Midspan
δmax = PL³ / 48EICantilever Tip Load
δmax = PL³ / 3EIFlexural Stiffness
k ∝ EI / L³| System Type | Deflection Trend | Typical Application |
|---|---|---|
| Simply supported | Moderate-high | Residential/secondary framing |
| Fixed-ended | Lower | Moment frames/continuous members |
| Cantilever | Higher | Canopies/balconies/sign arms |
| Continuous spans | Lower in many cases | Commercial floor systems |
1678: Hooke formalizes elastic proportionality concepts.
1744: Euler introduces foundational beam-column stability methods.
1826: Navier publishes elastic beam theory developments.
1880s: Industrial steel beams standardize practical deflection checks.
1950s: Matrix structural analysis accelerates multi-span evaluation.
1990s+: Digital FEM workflows make advanced serviceability analysis routine.
Human loading and structural response studies.
Global guidance relevant to fall and impact safety.
Construction and occupational safety references.
Clinical and engineering-adjacent evidence context.
Myth: Strength checks alone are enough.
Fact: Serviceability checks are required to prevent functional failures.
Myth: Material change always solves deflection.
Fact: Section geometry and span control often dominate.
Myth: Cantilevers are only a strength problem.
Fact: Cantilevers are frequently governed by tip deflection and vibration.
Myth: Hand checks are obsolete.
Fact: Hand checks remain essential for validating software output.
Beam deflection is vertical or lateral displacement of a structural member under load. It affects serviceability, alignment, and user comfort.
Even when stress is safe, excessive deflection can crack finishes, misalign doors, and cause vibration complaints.
Deflection is highly sensitive to span, often scaling with L³ to L⁴ depending on load case and boundary conditions.
Yes. A larger elastic modulus E increases stiffness and reduces deflection for the same geometry and loading.
Moment of inertia I grows strongly with depth. Increasing depth is usually the most effective way to reduce deflection.
Fixed, pinned, and cantilever supports produce different bending shapes and peak deflections.
Building codes and design standards define span-to-deflection limits for floors, roofs, and facades.
No. It is suitable for screening and preliminary checks. Final design should be done by licensed engineers.
Use code-prescribed load combinations and appropriate factors for serviceability and strength checks.
For long spans and light structures, vibration and resonance checks may control design beyond static deflection.
Use FEA for irregular geometry, complex loading, discontinuities, and mixed boundary conditions.
Use project- and code-specific criteria. Typical practice includes conservative assumptions and peer review.
Run cross-checks with stress, flow, and thermal calculators to improve early-stage decision quality.
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