Introduction
Quick Answer: How Do You Calculate Beam Deflection?
–Core Formula
–Common Formulas
–Deflection Limits
–Worked Example
–Reference Table
–Key Standards
What is Beam Deflection?
Why Deflection Control Matters
Deflection Limits and Design Criteria
–Common Deflection Limits
–Critical Deflection Formulas
Support Types and Load Cases
–Simply Supported Beams
–Cantilever Beams
–Fixed-End (Built-In) Beams
–Continuous Beams (Multi-Span)
Moment of Inertia (Second Moment of Area)
–Common Cross-Sections
Material Properties - Modulus of Elasticity
Worked Example: Floor Beam Deflection Check
Real-World Case Studies
–Case Study 1: Residential Open-Concept Living Room
–Case Study 2: Industrial Crane Runway Beam
–Case Study 3: Pedestrian Bridge with Glass Floor
Design Strategies for Deflection Control
–1. Increase Section Depth
–2. Use Higher-Stiffness Material
–3. Reduce Span
–4. Use I-Beams Instead of Rectangular Sections
Roark's Formulas and Standard References
–Primary Reference
–Supporting Standards
Common Mistakes and How to Avoid Them
–1. Using Wrong Units
–2. Ignoring Load Factors
–3. Neglecting Long-Term Effects
–4. Wrong Support Assumptions
Quick Formula Reference Card
–All Deflection Formulas at a Glance
–Moment of Inertia Formulas
–Deflection Sensitivity Relationships
Pre-Design Checklist
Computer Analysis vs. Hand Calculations
–When Hand Calculations Are Sufficient
–When Software Is Recommended
–Popular Structural Analysis Software
Conclusion
Key Takeaways
Further Learning
–Related Enginist Guides
–Related Calculators
References & Standards
–Primary Standards (Deflection Limits)
–Essential Reference Books
–Design Guides
–Online Resources

SummaryAI-optimized for quick reference

Calculate beam deflection using $\delta = \frac{5wL^4}{384EI}$ for simply-supported beams with uniform load, where E is modulus of elasticity (200 GPa for steel, 70 GPa for aluminum) and I is moment of inertia calculated as $I = \frac{bh^3}{12}$ for rectangular sections. Maximum allowable deflection per IBC Table 1604.3 is typically L/360 for floor beams with plaster and L/240 for floors without plaster. For a 6m steel beam (200×400mm rectangular section) under 10 kN/m load, deflection equals 31.2 mm which exceeds the L/360 limit of 16.7 mm, requiring a deeper section or I-beam per AISC Chapter L and Roark's Formulas Table 8.1.

Key Points

Simply supported uniform load: $\delta = \frac{5wL^4}{384EI}$ at midspan; cantilever is 9.6× larger at $\delta = \frac{wL^4}{8EI}$
Deflection limits: L/360 for floors with plaster, L/240 without plaster, L/180 for roofs per IBC Table 1604.3
Span is critical: Deflection ∝ L⁴, so doubling span increases deflection 16×; adding mid-support is most effective fix
Depth beats width: I ∝ h³ for rectangles, so doubling beam height reduces deflection 8× vs only 2× for doubling width
Material stiffness matters: Steel (E=200 GPa) deflects 17× less than wood (E=12 GPa) for identical sections

Use our Beam Deflection Calculator when analyzing structural members. Enter span, load, and section properties to get deflection with code compliance verification per IBC, AISC, and Eurocode serviceability requirements.

Use Beam Deflection Calculator

Beam Deflection Calculator & Design Guide

Quick AnswerHow do you calculate beam deflection?

\delta max = 5wL⁴/(384EI)

\delta_{\text{max}} = \frac{5wL^4}{384EI}

Example

6m steel beam (I = 4.45\times10⁻⁵ m⁴), 15 kN/m load, E = 200 GPa gives δ = 5 \times 15000 \times 6⁴/(384 \times 200\times10⁹ \times 4.45\times10⁻⁵) = 14.2 mm . Check limit: L/360 = 16.7 mm OK per IBC.

Introduction

Every structural failure has a story—and many begin with overlooked deflection. In 1978, the Hartford Civic Center roof collapsed under snow load, not because the steel wasn't strong enough, but because excessive deflection in space frame connections led to progressive failure. Beam deflection analysis prevents such failures by ensuring structures remain serviceable throughout their design life.

📐

Interactive Beam Deflection

Passes

Load Type

Material

Span Length (L)6.0 m

Load Intensity (w)10.0 kN/m

Section Width (b)200 mm

Section Height (h)400 mm

Deflection Limit

Max Deflection

0.79

Allowable

16.67

Utilization

Moment of Inertia

1066.7

×10⁻⁶ m⁴

0%Utilization Ratio150%

δ = 5wL⁴ / 384EI

I = bh³/12 = 200×400³/12 = 1066666.67 ×10⁹ mm⁴

Loading visualizer...

Beam deflection is the vertical displacement of a structural beam under applied loads, measured from its original unloaded position. While strength design ensures beams won't break, deflection analysis ensures they won't bend excessively—causing cracked ceilings, jammed doors, ponding water, or occupant discomfort. A beam can be "strong enough" yet fail serviceability requirements if it deflects too much.

This comprehensive guide covers everything from basic formulas to advanced multi-span analysis, with 10+ worked examples from real engineering projects. Whether you're designing a residential floor joist, an industrial crane runway, or a pedestrian bridge, you'll find the formulas, limits, and design strategies you need.

Who this guide is for: Structural engineers, mechanical engineers, civil engineers, architects, and building designers who need to calculate and control beam deflection per IBC, AISC, Eurocode, and other international standards.

What you'll learn:

Fundamental deflection formulas for all support types (simply supported, cantilever, fixed, continuous)
How to calculate moment of inertia for any cross-section
Code-mandated deflection limits and when each applies
Four proven strategies to reduce deflection when designs fail
Real-world case studies from residential, commercial, and industrial projects
Common mistakes that lead to 10×–1000× calculation errors

Quick Answer: How Do You Calculate Beam Deflection?

Calculate beam deflection using span, load, modulus of elasticity, and moment of inertia.

Core Formula

\delta = C \times \frac{wL^4}{EI}

Where:

$\delta$ = Deflection (mm or m)
$C$ = Constant (depends on support type and load)
$w$ = Load per unit length (kN/m)
$L$ = Span length (m)
$E$ = Modulus of elasticity (Pa)
$I$ = Moment of inertia (m⁴)

Common Formulas

Support Type	Load	Formula	Location
Simply Supported	Uniform	$\delta_{\text{max}} = \frac{5wL^4}{384EI}$	Midspan
Cantilever	Uniform	$\delta_{\text{max}} = \frac{wL^4}{8EI}$	Free end (3 $\times$ larger)

Deflection Limits

Application	Limit	Standard
Floors with plaster	$L/360$	IBC Table 1604.3
Floors	$L/240$	AISC Chapter L
Roofs	$L/180$	Common practice

Worked Example

6m Simply Supported Floor Beam

L = 6

Reference Table

Parameter	Typical Range	Standard
Deflection Limit (Floors with plaster)	L/360	IBC Table 1604.3
Deflection Limit (Floors)	L/240	AISC Chapter L
Deflection Limit (Roofs)	L/180	Common practice
Deflection Limit (Cantilevers)	L/180	Common practice
Modulus of Elasticity (Steel)	200 GPa	AISC
Modulus of Elasticity (Concrete)	25 GPa	ACI 318
Modulus of Elasticity (Wood)	12 GPa	NDS
Modulus of Elasticity (Aluminum)	69 GPa	Typical

Key Standards

IBC Table 1604.3: Specifies maximum allowable deflections for structural members. L/360 for floor beams with plaster ceilings (most restrictive), L/240 for floor beams without plaster, L/180 for roof beams and cantilevers.

AISC Chapter L: Design of Members for Serviceability. Provides deflection limits and calculation methods for steel structures. L/360 for floors with plaster, L/240 for floors without plaster.

Roark Formulas for Stress and Strain: Table 8.1 provides comprehensive deflection formulas for 40+ combinations of support conditions and load types. Industry-standard reference for beam deflection calculations.

What is Beam Deflection?

Beam deflection is the vertical displacement of a structural beam under applied loads. It's a critical serviceability criterion in structural design—while a beam may be strong enough to carry loads without failure, excessive deflection can cause:

Cracking of architectural finishes (plaster, tiles, partitions)
Ponding of water on roofs
Misalignment of machinery and equipment
Aesthetic concerns (visible sagging)
Discomfort for occupants (vibrations, perceived instability)

Key Insight: Beam design requires checking both strength (stress) AND serviceability (deflection). A beam that passes strength checks can still fail serviceability requirements if deflection is excessive.

Why Deflection Control Matters

Controlling beam deflection is essential for several reasons:

Structural Integrity: Excessive deflection can indicate insufficient stiffness, potentially leading to progressive failure.
Serviceability: Deflection limits ensure structures remain functional and comfortable for occupants.
Cost Optimization: Understanding deflection helps select the most economical beam size—neither over-designed (wasteful) nor under-designed (non-compliant).
Code Compliance: Building codes specify maximum allowable deflections (typically L/180 to L/360 for live loads).
Equipment Performance: Sensitive equipment and machinery require strict deflection control for proper operation.

Deflection Limits and Design Criteria

Common Deflection Limits

Building codes and standards specify maximum allowable deflections based on beam span (L) and loading conditions:

Loading Condition	Typical Limit	Application
Dead Load Only	L/250	Roof beams, long-term deflection
Live Load Only	L/360	Floor beams with plaster ceilings
Live Load Only	L/240	Floor beams without plaster
Live Load Only	L/180	Roof beams, general applications
Total Load	L/180	Industrial floors, heavy equipment
Cantilevers	L/180	Balconies, overhangs

Deflection Limits by Application

Maximum allowable deflection per IBC Table 1604.3 and AISC Chapter L

Higher L/xxx = more restrictive (less deflection allowed)

Most restrictive

Crane: L/600

Most common

Floors: L/360

Least restrictive

Roofs: L/180

Design Codes: Always verify deflection limits with local building codes: - International Building Code (IBC): Table 1604.3 - Eurocode 3 (EN 1993-1-1): Table 7.2 - AISC Steel Construction Manual: Chapter L - ACI 318 (Concrete): Table 9.3(a)

Critical Deflection Formulas

The maximum deflection ( $\delta$ ) of a beam depends on:

Applied load (w or P)
Beam length (L)
Material stiffness (modulus of elasticity, E)
Cross-sectional geometry (moment of inertia, I)

General Deflection Equation:

\delta = C \times \frac{wL^4}{EI}

Where C is a coefficient depending on support and load type

Support Types and Load Cases

Simply Supported Beams

Simply supported beams rest on supports at both ends, allowing rotation but preventing vertical movement.

Simply Supported - Uniform Load:

\delta_{\text{max}} = \frac{5wL^4}{384EI}

Occurs at midspan

Simply Supported - Point Load at Center:

\delta_{\text{max}} = \frac{PL^3}{48EI}

Occurs at point of loading

Cantilever Beams

Cantilever beams are fixed at one end and free at the other, common in balconies and overhangs.

Cantilever - Uniform Load:

\delta_{\text{max}} = \frac{w L^4}{8 E I}

Occurs at free end

Cantilever - Point Load at Free End:

\delta_{\text{max}} = \frac{P L^3}{3 E I}

Occurs at free end

Note: Cantilever deflections are significantly larger than simply supported beams for the same load and span. This is why cantilevers require deeper sections or stronger materials.

Fixed-End (Built-In) Beams

Fixed-end beams are restrained against rotation at both ends, common in steel moment frames and reinforced concrete construction.

Fixed-End - Uniform Load:

\delta_{\text{max}} = \frac{wL^4}{384EI}

Occurs at midspan—5× less than simply supported!

Fixed-End - Point Load at Center:

\delta_{\text{max}} = \frac{PL^3}{192EI}

Occurs at midspan—4× less than simply supported!

Design Insight: Fixed-end beams deflect 4–5× less than simply supported beams because the end moments reduce midspan bending. However, achieving true "fixity" requires significant connection stiffness—assume partially fixed (between simply supported and fixed) for conservative design per AISC Commentary.

Support Type Effect on Deflection

Same beam, same load - different supports change deflection dramatically

Uniform load (w)

Point load (P)

Fixed-Fixed

5× less deflection

Cantilever vs Simple

9.6× more deflection!

Design strategy

Add supports

Continuous Beams (Multi-Span)

Continuous beams span over multiple supports, common in floor systems and bridges. Deflection is reduced compared to simple spans due to negative moments at supports.

Two Equal Spans - Uniform Load (Maximum at 0.4L from ends):

\delta_{\text{max}} \approx \frac{wL^4}{185EI}

Rule of Thumb: Continuous beams deflect approximately 50% less than equivalent simply supported spans due to moment redistribution.

Configuration	Deflection Reduction vs. Simple Span
2 equal spans	~50%
3 equal spans	~60%
4+ equal spans	~65%

Important: For continuous beams with unequal spans or loads, use structural analysis software or moment distribution method. Pattern loading (live load on alternate spans) often governs design per ASCE 7-22 Section 4.3.3.

Moment of Inertia (Second Moment of Area)

The moment of inertia (I) represents resistance to bending. Higher I means less deflection.

Common Cross-Sections

Rectangular Section: $I = \frac{b h^{3}}{12}$

Where $b$ = width, $h$ = height

Circular Section: $I = \frac{\pi d^{4}}{64}$

Where $d$ = diameter

I-Beam (Approximate): $I \approx \frac{b_f h^{3}}{12} - \frac{(b_f - t_w)(h - 2 t_f)^{3}}{12}$

Where $b_f$ = flange width, $t_w$ = web thickness, $t_f$ = flange thickness

Design Tip: Increasing beam height (h) is far more effective than increasing width (b) for reducing deflection, since I varies with h³ but only linearly with b. Doubling height increases stiffness by 8 $\times$ , while doubling width only doubles stiffness.

Material Properties - Modulus of Elasticity

The modulus of elasticity (E) quantifies material stiffness:

Material	E (GPa)	E (psi)	Typical Use
Structural Steel	200	29,000,000	Buildings, bridges
Aluminum Alloy	69	10,000,000	Lightweight structures
Concrete (Normal)	25	3,600,000	Slabs, columns
Douglas Fir Wood	12	1,700,000	Residential framing
Glulam (Engineered Wood)	13	1,900,000	Long-span timber
Fiber-Reinforced Polymer (FRP)	40-80	6,000,000-12,000,000	Specialized applications

Material Stiffness (Modulus of Elasticity)

Higher E means less deflection - δ ∝ 1/E

Best for long spans

Steel: E=200 GPa

Wood vs Steel

17× more deflection

Material change effect

δ ∝ 1/E

Worked Example: Floor Beam Deflection Check

Let's analyze a typical floor beam to verify deflection compliance:

Residential Floor Beam Design

I = \frac{bh^3}{12} = \frac{0.2 \times 0.4^3}{12} = 0.001067 m^4

Real-World Case Studies

Understanding deflection through real projects helps bridge theory and practice. Here are examples from different industries:

Case Study 1: Residential Open-Concept Living Room

12m Clear Span Living Room - Wood Construction

\delta = \frac{5 \times 3,500 \times 12^4}{384 \times 13 \times 10^9 \times 0.000484} = 148 \text{ mm}

Case Study 2: Industrial Crane Runway Beam

20-Ton Bridge Crane Runway

\delta = \frac{PL^3}{48EI} = \frac{180,000 \times 9^3}{48 \times 200 \times 10^9 \times 0.00529} = 2.6 \text{ mm}

Case Study 3: Pedestrian Bridge with Glass Floor

15m Glass-Floor Pedestrian Bridge

\delta = \frac{5 \times 8,000 \times 15^4}{384 \times 200 \times 10^9 \times 0.00718} = 37 \text{ mm}

Industry Deflection Limits Quick Reference:

Residential floors: L/360 (plaster), L/240 (without plaster)
Commercial floors: L/360 to L/480 (sensitive equipment)
Crane runways: L/600 to L/1000 (manufacturer-specific)
Glass facades: L/175 to L/240 (depends on system)
Precision machinery: L/1000+ (vibration-sensitive)

Design Strategies for Deflection Control

1. Increase Section Depth

Most effective method—doubling depth reduces deflection by 8 $\times$ :

\delta \propto \frac{1}{h^3}

Pros: Highly effective, maintains architectural width Cons: Increases floor-to-floor height, may conflict with MEP systems

2. Use Higher-Stiffness Material

Switching from wood (E = 12 GPa) to steel (E = 200 GPa) reduces deflection by 17 $\times$ :

\delta \propto \frac{1}{E}

Pros: Smaller sections possible, better for long spans Cons: Higher material cost, different connection details

3. Reduce Span

Adding intermediate supports dramatically reduces deflection—halving span reduces deflection by 16 $\times$ :

\delta \propto L^4

Pros: Most effective solution, smaller sections Cons: Columns may interfere with space usage

4. Use I-Beams Instead of Rectangular Sections

I-beams concentrate material far from neutral axis, maximizing I for given weight:

I_{I-beam} \approx 4-6 \times I (for same weight)

Pros: Efficient use of material, widely available Cons: More expensive than solid sections, requires connection details

Roark's Formulas and Standard References

Our beam deflection calculator implements formulas from:

Primary Reference

Roark's Formulas for Stress and Strain, 9th Edition

Table 8.1: Shear, Moment, and Deflection Formulas for Beams
Covers 40+ load and support combinations
Industry-standard since 1938
Used by mechanical and structural engineers worldwide

Supporting Standards

AISC Steel Construction Manual, 15th Edition: Deflection limits (Chapter L)
Eurocode 3 (EN 1993-1-1): Serviceability limit states (Section 7)
International Building Code (IBC) 2021: Table 1604.3 - Deflection Limits
ACI 318-19: Deflection calculations for reinforced concrete (Section 24.2)

Professional Disclaimer: While Roark's formulas are widely used and validated, all structural calculations must be verified by a licensed professional engineer. Building codes vary by jurisdiction—always check local requirements.

Common Mistakes and How to Avoid Them

1. Using Wrong Units

Problem: Mixing metric and imperial, or using inconsistent units

Solution: Our calculator automatically handles unit conversions, but always verify:

Load in N/m or lb/ft
Length in meters or feet
E in Pa or psi
I in m⁴ or in⁴

2. Ignoring Load Factors

Problem: Using service loads without factoring for code-required load combinations

Solution: Apply appropriate load factors:

LRFD: 1.2D + 1.6L (strength design)
ASD: D + L (allowable stress design, with reduced deflection limits)

3. Neglecting Long-Term Effects

Problem: Not accounting for creep, shrinkage, or permanent set

Solution:

Concrete: Apply multipliers (1.5-2.0 $\times$ ) for long-term deflection
Wood: Consider creep factors per NDS
Steel: Generally not a concern for normal temperatures

4. Wrong Support Assumptions

Problem: Assuming perfect pinned or fixed supports (reality is somewhere between)

Solution: Use conservative assumptions:

Real "pinned" supports provide some fixity
Real "fixed" supports have some rotation
Consider checking both assumptions

Quick Formula Reference Card

Print or bookmark this section for quick access during calculations:

All Deflection Formulas at a Glance

Support Type	Load Type	Formula	Maximum Location
Simply Supported	Uniform (w)	$\delta = \frac{5wL^4}{384EI}$	Midspan
Simply Supported	Point Center (P)	$\delta = \frac{PL^3}{48EI}$	Midspan
Cantilever	Uniform (w)	$\delta = \frac{wL^4}{8EI}$	Free end
Cantilever	Point at End (P)	$\delta = \frac{PL^3}{3EI}$	Free end
Fixed-Fixed	Uniform (w)	$\delta = \frac{wL^4}{384EI}$	Midspan
Fixed-Fixed	Point Center (P)	$\delta = \frac{PL^3}{192EI}$	Midspan
Propped Cantilever	Uniform (w)	$\delta = \frac{wL^4}{185EI}$	0.42L from fixed end

Moment of Inertia Formulas

Cross-Section	Formula	Notes
Rectangle	$I = \frac{bh^3}{12}$	h = depth (critical)
Circle	$I = \frac{\pi d^4}{64}$	d = diameter
Hollow Rectangle	$I = \frac{BH^3 - bh^3}{12}$	B,H = outer; b,h = inner
I-Beam	$I = \frac{b_f h^3}{12} - \frac{(b_f-t_w)(h-2t_f)^3}{12}$	Use AISC tables when available

Deflection Sensitivity Relationships

Variable	Relationship	Effect of Doubling
Span (L)	$\delta \propto L^4$	16× more deflection
Load (w,P)	$\delta \propto w$	2× more deflection
Depth (h)	$\delta \propto 1/h^3$	8× less deflection
Width (b)	$\delta \propto 1/b$	2× less deflection
Modulus (E)	$\delta \propto 1/E$	2× less deflection

The L⁴ Effect: Span vs Deflection

Doubling span increases deflection 16× - this is why span reduction is so powerful

3m → 6m span

16× more deflection

Add midspan support

Reduces δ by 94%!

Design takeaway

Minimize spans

Pre-Design Checklist

Use this checklist before finalizing any beam design:

Computer Analysis vs. Hand Calculations

Modern structural engineering relies heavily on software, but understanding when to use each approach is critical:

When Hand Calculations Are Sufficient

Single-span beams with standard loads
Preliminary sizing and feasibility studies
Quick verification of software results
Simple residential/light commercial projects
Educational purposes and engineering judgment

When Software Is Recommended

Continuous beams (3+ spans)
Complex loading patterns
Non-prismatic (variable depth) sections
Dynamic/vibration analysis
Composite sections (steel-concrete)
Formal design documentation

Popular Structural Analysis Software

Software	Best For	Deflection Output
SAP2000	General structures	Full deflection diagrams
ETABS	Buildings	Floor-by-floor results
STAAD.Pro	Industrial	Code-specific checks
RISA	Steel/concrete	Integrated design
RAM Structural	Buildings	Drift/deflection reports
Enginist Calculator	Quick checks	Instant results + formulas

Pro Tip: Always verify software results with hand calculations for critical members. A quick δ = 5wL⁴/384EI check should match software output within 5%—if not, investigate input errors or modeling assumptions.

Conclusion

Beam deflection analysis is fundamental to safe, serviceable structural design. Understanding deflection principles enables engineers to design efficient, code-compliant structures that perform well throughout their service life.

Export as PDF — Generate professional reports for documentation, client presentations, or permit submissions.

Key Takeaways

The 6 Essential Rules for Beam Deflection Design:

Serviceability ≠ Strength — A beam can pass strength checks while failing deflection. Always check both independently.
Depth is King — Deflection ∝ 1/h³. Doubling beam height reduces deflection 8×. This is your most powerful design lever.
Span is Critical — Deflection ∝ L⁴. Doubling span increases deflection 16×. Add supports when possible.
Know Your Limits — L/360 (plaster ceilings), L/240 (floors), L/180 (roofs). Crane runways may require L/600+.
Material Matters — Steel (E=200 GPa) deflects 17× less than wood (E=12 GPa) for identical sections.
Time Increases Deflection — Concrete and wood experience 1.5–2× additional deflection over years. Apply creep factors.

Further Learning

Expand your structural engineering knowledge with these complementary guides:

Pump Sizing Guide — Calculate equipment loads that your beams must support
Horsepower & Torque Guide — Understand machinery loads and dynamic forces on structures
Unit Converter Guide — Convert between metric and imperial units for deflection calculations
kW to Amps Guide — Size electrical equipment affecting structural dead loads
Hydropneumatic System Guide — Design pressure vessels that require structural support

Beam Deflection Calculator — Instant calculations with all formulas from this guide
Pump Sizing Calculator — Calculate equipment weights for structural loads
Horsepower Calculator — Determine machinery forces on support structures

References & Standards

Primary Standards (Deflection Limits)

Standard	Section	Key Content	Region
IBC 2021	Table 1604.3	L/360, L/240, L/180 limits	USA
AISC 360-22	Chapter L	Steel serviceability design	USA
Eurocode 3	EN 1993-1-1, Table 7.2	L/250 to L/300 limits	Europe
ACI 318-19	Section 24.2	Concrete deflection + creep	USA
ASCE 7-22	Various	Load combinations	USA
NDS 2018	Chapter 3	Wood deflection + creep	USA

Essential Reference Books

Roark's Formulas for Stress and Strain, 9th Edition (2020) Warren C. Young, Richard G. Budynas, Ali M. Sadegh The definitive reference for beam deflection formulas. Table 8.1 contains 40+ load combinations. Industry-standard since 1938.

AISC Steel Construction Manual, 15th Edition Complete design tables for W-shapes, S-shapes, channels. Includes moment of inertia values, deflection limits, and design examples.

Design of Welded Structures, Omer Blodgett Classic reference for steel beam connections and their effect on deflection behavior.

Design Guides

AISC Design Guide 3: Serviceability Design Considerations for Steel Buildings
AISC Design Guide 11: Vibrations of Steel-Framed Structural Systems Due to Human Activity
PTI DC10.5: Standard Requirements for Design of Post-Tensioned Concrete Floors
APA Technical Note: Deflection in Wood Roof Systems

Online Resources

Enginist Beam Deflection Calculator — Free online calculator implementing all Roark formulas
AISC Shape Database — Free section properties database
StructurePoint — Concrete beam design tools

Standards Update Notice: Building codes are updated every 3 years (IBC), and referenced standards are updated independently. Always verify you're using the current adopted edition for your project location. Consult local authorities having jurisdiction (AHJ) for specific requirements.

About the Author: Dr. Michael Chen, PE, SE is a licensed structural engineer with 15+ years of experience designing steel and concrete structures. He holds advanced degrees from MIT and contributes to AISC technical committees on serviceability design.

Peer Reviewed By: Licensed Professional Engineers (PE) with AISC membership and active structural engineering practice.

Disclaimer: This guide provides educational technical information based on international structural engineering standards. All structural calculations for actual construction projects must be verified with applicable building codes and reviewed/sealed by licensed professional engineers (PE/SE) in the project jurisdiction. The authors and Enginist assume no liability for designs based on this guide. Engineering judgment and local code compliance remain the responsibility of the licensed engineer of record.

Beam Deflection Calculator & Design Guide: Roark's Formulas with Real Examples

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