Introduction
Hypothetical case study – illustrative example, not a real project. No real building, client, or construction is described here. What follows is a fully worked planning scenario showing how the pieces of a deflection check fit together: estimating loads, selecting properties, running the calculation, checking both limits, and cross-checking units. Every number is computed live in the text so you can follow – or reproduce – each step.
To run your own scenario alongside this one, use the Beam Deflection Calculator: enter the span, loads, and beam properties below and confirm you get the same results. The methods used here are detailed in the estimating guide and the formula-explained guide.
The Scenario (Hypothetical)
A homeowner is planning an open-concept renovation – hypothetical, for illustration – and wants to remove a load-bearing wall beneath a 20-ft clear span, replacing it with a single steel beam carrying the floor above. The floor joists frame into the proposed beam location with an 8-ft tributary width. The floor above is residential living space with a tiled finish. The planning question: does a W12x26 steel beam deflect within L/360 (live) and L/240 (total)?
This is a planning exercise only. In reality, removing a load-bearing wall requires a licensed structural engineer for the beam design, temporary shoring, connections, and the load path down to the foundation – see the DIY vs pro guide for why.
Step 1: Establish the Inputs
Span: 20 ft clear between supports = 240 in (6.096 m). Simply supported – the beam will sit on bearing posts at each end, so no fixity is claimed (a conservative, honest default per the pro tips guide).
Beam properties: W12x26 wide-flange, I = 245 in^4 (published section property); steel E = 29,000,000 psi (200 GPa). Self-weight: 26 lb/ft.
Loads via tributary area (tributary width 8 ft, residential living area):
- Live load: 40 psf x 8 ft = 320 lb/ft
- Dead load: joists + subfloor 6 psf + tile finish 8 psf + ceiling 4 psf = 18 psf; 18 x 8 = 144 lb/ft, plus beam self-weight 26 lb/ft = 170 lb/ft
- Total: 320 + 170 = 490 lb/ft
Two load cases, as required: live-load case w = 320 lb/ft against L/360; total-load case w = 490 lb/ft against L/240.
Step 2: Run the Calculation (Imperial)
Convert to consistent units: w_live = 320 / 12 = 26.67 lb/in; w_total = 490 / 12 = 40.83 lb/in; L = 240 in.
Simply supported, uniform load: deflection = 5 x w x L^4 / (384 x E x I).
Live-load deflection = 5 x 26.67 x 240^4 / (384 x 29,000,000 x 245) = 0.162 in.
Total-load deflection = 5 x 40.83 x 240^4 / (384 x 29,000,000 x 245) = 0.248 in.
Step 3: Check Against the Limits
| Check | Calculated deflection | Limit | Result |
|---|---|---|---|
| Live load vs. L/360 | 0.162 in | 240 / 360 = 0.667 in | Passes – uses 24% of the allowance |
| Total load vs. L/240 | 0.248 in | 240 / 240 = 1.0 in | Passes – uses 25% of the allowance |
Both checks pass with wide margin. Note the utilization: the beam uses only about a quarter of each deflection allowance, which is typical for steel at moderate spans – steel’s high E makes deflection easy to satisfy here, and strength or connection design would likely govern the real selection.
Step 4: Cross-Check in Metric
w_live = 320 lb/ft = 4.67 kN/m; w_total = 490 lb/ft = 7.15 kN/m; L = 6.096 m; E = 200 GPa; I = 245 in^4 = 1.02 x 10^-4 m^4.
Live: 5 x 4670 x 6.096^4 / (384 x 200 x 10^9 x 1.02 x 10^-4) = 4.12 mm. Check: 0.162 x 25.4 = 4.11 mm – agreement.
Total: 5 x 7150 x 6.096^4 / (384 x 200 x 10^9 x 1.02 x 10^-4) = 6.30 mm. Check: 0.248 x 25.4 = 6.30 mm – agreement.
Limits: 6100 / 360 = 16.9 mm; 6100 / 240 = 25.4 mm. Both pass in metric exactly as in imperial, as they must – the cross-check confirms no unit slipped anywhere in the chain.
Step 5: What the Numbers Do Not Tell You
A real engineer picking this beam would also verify, at minimum:
- Bending strength and shear – deflection passing says nothing about strength.
- Bearing and connections – the beam’s reactions (about 4,900 lb per end under total load) need posts, bearing plates, and connections designed for them.
- Lateral bracing – the compression flange needs restraint; an unbraced 20-ft beam has buckling considerations no deflection formula sees.
- The load path below – those 4,900-lb reactions land on posts, which land on footings, which land on soil. Every step needs its own check.
- Temporary shoring during wall removal – a construction sequencing question, not a beam question.
- Long-term behavior and vibration – floor vibration under footfall is a separate serviceability check from static deflection.
This list is exactly why the scenario is labeled hypothetical and illustrative: the deflection check is one chapter of a design, not the design. The complete guide covers the deflection chapter; the engineer writes the rest.
Lessons From the Exercise
- Splitting the loads changed the story’s precision, not its outcome – but on a beam with heavier live load relative to dead, the L/360 check is the one that bites. Always run both.
- Self-weight mattered modestly here (26 of 490 lb/ft, about 5%) – on longer or heavier sections it would matter more. Including it is free accuracy.
- The metric cross-check caught nothing because nothing was wrong – which is precisely its value. It is a two-minute audit that fails loudly the one time you need it.
- Conservative assumptions compound safely: simply supported (not fixed), full code live load, tile-heavy dead load – each choice leans safe, and the beam still passed comfortably. That is what margin looks like.
Related Guides
- Complete Guide – limits, terminology, and the standard worked example.
- Estimating Guide – the tributary-area load buildup used here.
- Formula Explained – the uniform-load formula derived and audited.
- Pro Tips – judgment habits behind the assumptions above.
- Checklist – the step sequence this study follows.
Frequently Asked Questions
Is this case study a real project?
No. It is explicitly a hypothetical, illustrative example with computed planning numbers – not a real building, client, or construction project, and not a design recommendation.
Can I copy these numbers for my own 20-ft span?
No – the loads depend on your tributary width, occupancy, and finishes, and the beam choice depends on strength, connections, and code checks beyond deflection. Work your own inputs; use this study as a method template, not a data source.
Why check both live and total load?
Because codes impose both limits independently (commonly L/360 live, L/240 total), and a beam can fail either one. The live-load check guards feel and finishes; the total check guards overall movement.
What does “uses 24% of the allowance” mean?
Utilization: calculated deflection divided by the limit. Low utilization means comfortable margin; utilization near 100% means the beam just barely complies and any input optimism becomes a problem.
Why did the study assume simply supported ends?
Because ordinary bearing supports behave much closer to pinned than fixed, and claiming fixity would cut the calculated deflection to one-fifth – an unsafe optimism unless connections are detailed as moment-resisting by an engineer.
What would change with a wood beam instead?
Everything about stiffness: wood’s E is roughly one-eighteenth of steel’s, so the same span and load needs a far larger I – deeper sections, engineered lumber, or reduced span. The material guide compares the properties.
Get Your Number
Follow the same five steps with your own span, tributary width, loads, and beam: establish inputs, calculate both load cases, check both limits, cross-check units, and list what the numbers do not cover. The Beam Deflection Calculator handles the arithmetic – your job is honest inputs and a documented assumption list to hand your engineer.
Disclaimer: This case study is a hypothetical illustrative example, not a real project and not a design recommendation. Calculator results are planning estimates based on the inputs you enter, not structural design calculations. Verify deflection limits against your local building code and consult a licensed structural engineer for any structural design decisions.
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