RSJ Beam Deflection Calculator – Ensure Your Floor or Roof Won’t Sag (Free Tool + Formulas)
A structurally adequate beam isn’t just about strength – it must also limit deflection (sagging) to prevent damage to finishes and ensure occupant comfort. Many DIYers focus solely on whether a beam can “hold the weight” but ignore deflection, leading to cracked plaster, binding doors, and bouncy floors. This guide explains how to calculate and control RSJ beam deflection.
What is Deflection?
Deflection is the vertical displacement (sagging) of a beam under load. Even steel beams bend slightly when loaded – the question is whether this bending is acceptable or excessive.
Why Deflection Matters
Structural Integrity: While a beam might have adequate strength, excessive deflection can cause secondary problems that compromise the overall structure.
Finishes Damage:
- Plasterboard cracks at deflections >5mm
- Tile grout cracks and tiles debond at >3mm deflection
- Skirting boards and architraves separate from walls
Functional Problems:
- Doors and windows stick or won’t close properly
- Floor bounce and vibration
- Visual sagging creates anxiety about safety
- Water pooling on flat roofs
Serviceability: Building Regulations aren’t just about preventing collapse – they ensure buildings remain serviceable and comfortable to use.
Building Regulations Deflection Limits (UK 2026)
Residential Floors
Maximum deflection: Span / 360 under total load (dead + live)
Examples:
- 3m span: 3000 / 360 = 8.3mm maximum
- 4m span: 4000 / 360 = 11.1mm maximum
- 5m span: 5000 / 360 = 13.9mm maximum
- 6m span: 6000 / 360 = 16.7mm maximum
Some engineers use stricter limits:
- Span / 480 for spans >4m (better floor feel)
- Span / 500 for tile floors (prevents cracking)
- Span / 600 for areas with sensitive finishes
Roofs
Maximum deflection: Span / 200 under live load only (snow, wind)
Examples:
- 4m span: 4000 / 200 = 20mm maximum
- 5m span: 5000 / 200 = 25mm maximum
- 6m span: 6000 / 200 = 30mm maximum
Roofs allow more deflection because:
- No ceiling directly attached usually
- Less sensitive to vibration
- Live loads (snow) are temporary
Commercial and Public Buildings
Stricter requirements:
- Floors: Span / 360 to Span / 500
- Assembly areas: Span / 480 (to limit vibration)
- Roofs: Span / 250 (more conservative)
Deflection Formula
For a simply supported beam with uniform distributed load:
δ = (5 × w × L⁴) / (384 × E × I)
Where:
- δ = Deflection in mm
- w = Uniformly distributed load in N/mm
- L = Span in mm
- E = Young’s modulus (210,000 N/mm² for steel)
- I = Second moment of area in mm⁴ (from steel tables)
Understanding the Components
Second Moment of Area (I): This geometric property indicates how resistant a section is to bending. Larger I values mean less deflection.
Common RSJ I values:
| Beam Size | I (cm⁴) | I (mm⁴) |
|---|---|---|
| 152×127×37 | 1,358 | 13.58 × 10⁶ |
| 203×133×25 | 2,896 | 28.96 × 10⁶ |
| 203×133×30 | 3,438 | 34.38 × 10⁶ |
| 254×146×31 | 6,572 | 65.72 × 10⁶ |
| 254×146×37 | 7,628 | 76.28 × 10⁶ |
| 305×165×40 | 12,350 | 123.5 × 10⁶ |
Notice how I increases dramatically with beam depth – this is why taller beams deflect much less.
CalcStep-by-Step Deflection Calculation
Example 1: Standard Floor Beam
Given:
- Beam: 203×133×25 RSJ
- Span: 4.0m
- Dead load: 0.5 kN/m²
- Live load: 1.5 kN/m²
- Load width: 2.5m
Step 1: Calculate UDL
Total load = (0.5 + 1.5) × 2.5 = 5.0 kN/m = 5,000 N/m = 5 N/mm
Step 2: Get Beam Properties
From steel tables:
- I = 2,896 cm⁴ = 28.96 × 10⁶ mm⁴
- E = 210,000 N/mm²
Step 3: Apply Formula
δ = (5 × 5 × 4000⁴) / (384 × 210,000 × 28.96 × 10⁶)
δ = (5 × 5 × 256 × 10¹²) / (384 × 210,000 × 28.96 × 10⁶)
δ = (6,400 × 10¹²) / (2,338 × 10¹²)
δ = 2.74mm
Step 4: Check Compliance
Allowable = 4000 / 360 = 11.1mm
Actual = 2.74mm
PASS ✓ (deflection well within limits)
Example 2: Long Span Roof
Given:
- Beam: 254×146×31 RSJ
- Span: 5.5m
- Dead load: 1.0 kN/m² (roof tiles, timber)
- Live load: 1.5 kN/m² (snow)
- Load width: 3.0m
Step 1: Calculate UDL for Live Load Only
Live load UDL = 1.5 × 3.0 = 4.5 kN/m = 4.5 N/mm
(Note: Roof deflection check uses live load only)
Step 2: Beam Properties
- I = 6,572 cm⁴ = 65.72 × 10⁶ mm⁴
- E = 210,000 N/mm²
Step 3: Calculate
δ = (5 × 4.5 × 5500⁴) / (384 × 210,000 × 65.72 × 10⁶)
δ = (5 × 4.5 × 915.06 × 10¹²) / (5,300 × 10¹²)
δ = (20,589 × 10¹²) / (5,300 × 10¹²)
δ = 3.88mm (live load deflection)
Step 4: Check Compliance
Allowable = 5500 / 200 = 27.5mm
Actual = 3.88mm
PASS ✓ (excellent – very stiff beam)
Example 3: Heavy Load, Failing Deflection
Given:
- Beam: 203×133×30 RSJ
- Span: 5.0m
- Dead load: 2.5 kN/m² (concrete floor)
- Live load: 2.5 kN/m²
- Load width: 4.0m
Step 1: Calculate UDL
Total = (2.5 + 2.5) × 4.0 = 20 kN/m = 20 N/mm
Step 2: Properties
- I = 3,438 cm⁴ = 34.38 × 10⁶ mm⁴
Step 3: Calculate
δ = (5 × 20 × 5000⁴) / (384 × 210,000 × 34.38 × 10⁶)
δ = (6,250 × 10¹⁵) / (2,776 × 10¹²)
δ = 22.5mm
Step 4: Check
Allowable = 5000 / 360 = 13.9mm
Actual = 22.5mm
FAIL ✗ (62% over limit!)
Solution: Need larger beam, try 254×146×37:
I = 7,628 cm⁴ = 76.28 × 10⁶ mm⁴
δ = (6,250 × 10¹⁵) / (6,164 × 10¹²) = 10.1mm ✓ PASS
This example shows why you can’t just check strength – deflection often governs beam size!
Factors Affecting Deflection
1. Span Length (Huge Effect!)
Deflection is proportional to L⁴ (span to the fourth power).
Effect of doubling span:
- Strength requirement doubles
- Deflection increases 16 times!
This is why long spans often need much larger beams than strength alone would require.
2. Load Magnitude
Deflection is directly proportional to load – double the load, double the deflection.
3. Second Moment of Area (I)
Higher I = less deflection. Beam depth has huge impact:
Comparison (similar weights):
- 178×102×19 (I = 1,357 cm⁴)
- 203×133×25 (I = 2,896 cm⁴)
Same load, same span: 203mm beam deflects only 47% as much despite being similar weight - the extra depth makes enormous difference.
4. Material Properties
Steel E = 210,000 N/mm² Timber E = 8,000-12,000 N/mm²
Steel is 18-26 times stiffer than timber – why steel beams are much thinner for same span/load.
5. Support Conditions
Simply supported: Uses formula given above
Continuous beam: Deflects 20-40% less than simple support
Fixed ends: Deflects ~80% less than simple (but rare in practice)
Cantilever: Deflects ~400% more than simple – needs very stiff beams
Practical Deflection Considerations
Pre-Camber
For very long spans or heavy loads, beams can be manufactured with upward curve (camber). Under full load, they deflect to horizontal rather than sagging below.
Typical camber: L/500 to L/300
Example: 6m beam might have 12-20mm upward camber
Cost: Add £80-150 for pre-cambering
Load Duration Effects
Deflection calculations assume instantaneous load. Real floors have creep:
Long-term deflection ≈ 1.5 to 2.0 × instantaneous for timber components
Steel doesn’t creep significantly, but joists, boards, etc. do.
Conservative approach: Use span/480 or span/500 instead of span/360
Vibration Considerations
Deflection limits primarily control static sag, but occupants are sensitive to vibration (dynamic deflection).
Problem areas:
- Long spans (>4.5m)
- Light construction
- Aerobics studios, dance floors
- Footfall from heavy people
Solutions:
- Use stiffer beams (span/480-span/600)
- Add weight (screed, heavy floor finishes)
- Cross-bracing between joists
- Isolate vibration sources
Point Load Effects
Point loads (columns, heavy fixtures) increase local deflection beyond calculated uniform load deflection.
Rule of thumb: Point load of P kN at mid-span creates similar deflection to UDL of (0.8×P/L) kN/m
Example: 10 kN point load at center of 5m span ≈ 1.6 kN/m UDL deflection effect
Common Deflection Mistakes
Mistake 1: Only Checking Strength
Many people calculate whether beam is strong enough but forget deflection check.
Result: Beam doesn’t fail structurally but creates unacceptable operational problems.
Example: 203×133×25 over 5m span might have adequate strength for 4 kN/m but deflect 12mm (fails span/360 = 13.9mm check marginally, but creates visible sag and bouncy floor).
Mistake 2: Using Wrong Load for Roof
Roof deflection should be checked using live load only, not total load.
Wrong: δ = f(dead + live) Correct: δ = f(live only)
Why? Dead load is permanent – structure adapts. Live load (snow) comes and goes, creating movement that damages finishes.
Mistake 3: Ignoring Floor Finishes
Tile floors are much less forgiving than carpet:
Carpet floor: Span/360 usually OK Ceramic tile: Use span/480-span/600 or tiles crack
Solution: Specify stricter deflection limit if tiling planned
Mistake 4: Confusing mm⁴ with cm⁴
Steel tables often give I in cm⁴, but formula needs mm⁴.
Conversion: I(mm⁴) = I(cm⁴) × 10⁴
Get this wrong and your deflection will be off by factor of 10,000!
Mistake 5: Not Including Beam’s Own Weight
The beam itself adds dead load:
203×133×25 = 25 kg/m = 0.25 kN/m = 250 N/m
For light loads this can be significant portion of total.
How to Reduce Deflection
If calculated deflection exceeds limits:
Option 1: Larger Beam
Most obvious solution – use deeper section with higher I.
Cost: Typically £20-60 more per meter
Option 2: Reduce Span
Add intermediate support (column or wall):
- Halves span
- Reduces deflection by factor of 16!
Example: 6m span deflecting 25mm → two 3m spans deflect 1.6mm each
Cost: £500-1,200 for column and foundation
Option 3: Use Stronger Steel Grade
S355 instead of S275 improves strength but doesn’t reduce deflection (same E value).
This won’t help deflection-limited designs.
Option 4: Composite Construction
Flitch beam or concrete encasement can increase effective I:
Example: 203×133×25 + 100mm concrete encasement ≈ 40% stiffer
Cost: Additional £80-150 per meter plus formwork
Option 5: Pre-Cambered Beam
Doesn’t reduce actual deflection but makes it less visible.
Cost: £80-150 extra
Deflection vs. Strength
Often one governs:
Strength governs when:
- Short spans (<3m)
- Heavy loads (>15 kN/m)
- Discrete point loads
Deflection governs when:
- Long spans (>4m)
- Light loads (<8 kN/m)
- Distributed loads over wide area
Both critical:
- Medium spans (3-4m)
- Moderate loads (8-15 kN/m)
Always check both!
Conclusion
Deflection is often the critical design criterion for RSJ beams, especially on longer spans with moderate loads. Use the deflection formula to verify calculated deflection stays within Building Regulations limits (typically span/360 for floors, span/200 for roofs). When deflection limits are exceeded, increase beam depth rather than just using stronger steel grade.
Quick Deflection Check:
- Calculate UDL on beam (kN/m)
- Get I value from steel tables (convert to mm⁴)
- Apply formula: δ = (5×w×L⁴)/(384×E×I)
- Compare to limit: Span/360 (floors) or Span/200 (roofs)
- Upsize beam if deflection excessive
Use our free calculator above for instant deflection calculations, then verify with your structural engineer for Building Regulations compliance.
Disclaimer: Deflection calculations should be verified by a chartered structural engineer. This article provides guidance only and does not replace professional engineering design or Building Regulations compliance.
