Design a simply-supported timber beam under a uniformly distributed load. Adjust the width, depth, span, load and species to see the bending, shear and deflection checks update in real time, and find a safe section while watching which check governs the design.
Parameters
Beam width b
mm
Beam depth h
mm
Vertical dimension of the beam — the strongest lever on bending and deflection
Span L
m
Distance between the supports
Distributed load w
kN/m
Load per unit length from the floor or roof
Species / grade
Sets allowable bending f_b, allowable shear f_v and Young's modulus E
Results
—
Max bending stress σ (MPa)
—
Bending ratio σ/f_b
—
Max shear stress τ (MPa)
—
Shear ratio τ/f_v
—
Max deflection δ (mm)
—
Overall verdict
—
Timber beam model — load & deflection animation
A simply-supported timber beam deflecting under a uniformly distributed load. The arrow row above is the load, the curve below is the deflected shape. The beam colour shows the governing check ratio (green → orange → red).
Maximum bending stress σ, maximum shear stress τ and maximum deflection δ. M: maximum bending moment, V: maximum shear force, Z: section modulus, I: second moment of area, b: beam width, h: beam depth, E: Young's modulus.
The design passes only when the bending, shear and deflection check ratios are all 1 or below. If even one exceeds 1, the beam section must be revised.
What is the Timber Beam Design Simulator?
🙋
When I look up at the ceiling of a wood house I see thick "beams" running across. How do engineers decide how big those beams have to be?
🎓
Good question. Timber beam design is basically the job of making one section pass three checks. The first is bending stress — when the load bows the beam, the top fibres compress and the bottom fibres stretch, and that stress must stay below the wood's allowable value. The second is shear stress — the beam must not slice apart near the supports. The third is deflection — how far the beam sags. Raise the load w on the left and you will see all three check ratios climb together.
🙋
Three checks? I heard that for a steel beam you mainly just check bending. Is wood different?
🎓
That is the most interesting thing about timber beams. Wood's modulus of elasticity — the number that says how hard it is to bend — is only about a twentieth of steel's. So you can have plenty of margin on bending stress and still have the beam sag far too much. In practice, timber beam design is decided by deflection surprisingly often. Keep the default settings and stretch the span L to about 6 m: you will see the deflection ratio reach 1 before the bending ratio does.
🙋
I see. So when deflection is the tight one, how should I change the beam — make it wider, or taller?
🎓
Overwhelmingly "make it taller" — increase the depth h. Deflection is inversely proportional to the second moment of area I, and I scales with the cube of h. So making h just 1.26 times larger roughly halves the deflection. Width b only enters linearly, so for the same amount of timber a tall narrow beam beats a flat wide one by a long way. Look at the "deflection vs beam depth" chart below and you will see the steep curve as h grows. That is exactly why ceiling beams are tall and thin rather than flat.
🙋
When does shear actually become a problem? I do not hear about it much.
🎓
Wood is very weak in shear along the grain. For cedar the allowable shear stress is only 0.6 MPa — less than a tenth of its bending value. So for short, stocky beams — short span but a big load — shear can govern before bending does. Try shortening the span L to about 1.5 m and raising the load w: you will see the shear ratio overtake the bending ratio. On long-span beams shear is almost always comfortable, and it becomes a contest between deflection and bending.
🙋
When I switch the species from "cedar" to "glulam" the numbers change a lot. Can it really differ that much, if it is all wood?
🎓
It really does. Ungraded cedar carries its knots and scatter straight into its strength, so its allowable bending is a modest 6.5 MPa. Glulam, on the other hand, is made by selecting thin laminations, spreading the defects around and bonding them — so it is strong and consistent: 13.5 MPa, more than double cedar. Its modulus is higher too, so deflection is smaller. Long-span beams and exposed feature beams often use glulam. But remember, real design also adds reductions for moisture content and how long the load is applied. Not being able to count on the full strength for long-duration loads is a quirk unique to timber.
Frequently Asked Questions
Wood has a modulus of elasticity E about 20 times lower than steel (around 7 GPa for cedar versus 205 GPa for steel), so it deflects far more under the same load. Even when the bending and shear stresses sit comfortably below the allowable values, the deflection often exceeds a serviceability limit such as span/300 — and so deflection becomes the case that decides the beam section. This tool shows the bending, shear and deflection check ratios side by side so you can see at a glance which one governs.
The section modulus Z=bh²/6 scales with the square of the depth h, and the second moment of area I=bh³/12 scales with the cube of h. Width b only enters linearly. So increasing the depth h is by far the more efficient move for both bending stress and deflection. Because deflection is inversely proportional to I, making h 1.26 times larger roughly halves the deflection. For the same amount of timber, a tall narrow section is far stronger than a flat wide one. Note, however, that a very deep section risks lateral-torsional buckling and needs separate lateral bracing.
Wood is weak in shear parallel to the grain (horizontal shear): the allowable shear stress is only about 0.6 MPa for cedar and 0.9 MPa for Douglas fir — less than a tenth of the bending value. For a rectangular section the shear stress peaks at the neutral axis and is τ=1.5V/(bh). For short, heavily loaded beams, or beams with a concentrated load near a support, shear can govern before bending does. In this tool, shorten the span and raise the load and you will see the shear check ratio overtake the bending ratio.
Even within 'wood', strength varies widely with species and grade. The presets in this tool use 6.5 MPa allowable bending for ungraded cedar, 10.6 MPa for Douglas fir E120 and 13.5 MPa for glulam. Glulam is made by selecting and bonding small laminations, which disperses defects such as knots and gives a higher, more consistent strength than ungraded sawn timber. In real design, reduction factors for moisture content and load duration (long-term versus short-term) also apply — so you cannot count on the full strength for sustained loads.
Real-World Applications
Floor and roof beams of wood houses: In a timber post-and-beam house, the floor beams that carry the floor and the roof beams that carry the roof are exactly the "simply-supported beam under a uniform load" this tool handles. Floor beams carry the imposed load of people and furniture plus the weight of the floor itself; roof beams carry roofing and snow load. The designer finds the distributed load from the span and tributary width, then picks a section (such as 105×300 or 120×360) that passes the bending, shear and deflection checks.
Long-span glulam beams: For buildings that want a large column-free space — gymnasiums, shops, halls — ungraded sawn timber falls short on both strength and deflection, so large glulam sections are used. Because glulam stacks laminations, the section depth can be made freely large, keeping deflection within L/300 even over long spans. Curved glulam can even form arched roofs.
Renovation and reinforcement checks: When a renovation removes a partition wall from an old wood house, the load that the wall used to carry shifts onto a beam, and the deflection can become excessive. A quick estimate like this tool tells you whether the existing beam section can carry the new span and load; if not, options such as adding a beam, sistering, or steel-plate reinforcement are considered.
Preliminary structural sizing and teaching: Before running detailed structural software or a finite-element analysis, a hand calculation with beam theory like this tool gives a first estimate of the beam section. For students and junior designers it is a useful teaching aid — feeling how the three check ratios move when the load goes up, and what changes when the species changes. Conversely, if analysis software output differs from this estimate by an order of magnitude, it is a sanity check pointing to an input or support-condition mistake.
Common Misconceptions and Pitfalls
The most common one is "if the bending stress is within the allowable value, the beam is fine". A timber beam is checked independently for bending, shear and deflection, and the design is decided by the tightest of the three. Because wood has a low modulus of elasticity, the deflection very often hits its limit while the bending stress still has plenty of margin. Choosing a section that ignores deflection invites serviceability problems such as floor squeak, doors that no longer fit and wavy ceilings. This tool lists the three check ratios together precisely to prevent this "mistaking the governing case" error.
Next, the misconception that the allowable stress of wood is a single fixed number. The preset values here are typical representative figures, but the real allowable stress varies strongly with load duration. Wood creeps — its strength drops gradually under a sustained load — so structural codes allow only a small fraction of the base strength for long-term loads (self-weight, permanent imposed load) and a larger fraction for short-term loads (earthquake, storm). For the same beam, the allowable stress can differ by nearly a factor of two between long-term and short-term, so the single f_b and f_v in this tool are estimate-grade values only. Higher moisture content also lowers strength.
Finally, the oversimplification that "a deeper beam is always better, and the more depth the safer". It is true that both bending and deflection improve as the depth h grows, but a slender beam whose depth is extreme compared with its width can twist sideways and topple under load — lateral-torsional buckling. This tool addresses section strength and deflection assuming no lateral-torsional buckling occurs; a real slender beam needs separate design that restrains the top edge sideways (lateral bracing) with purlins, joists or bracing members. Remember: when you raise the depth, plan the lateral bracing along with it.
How to Use
Select timber species (e.g., Spruce-Pine-Fir, Southern Pine) to populate allowable bending stress f_b and shear stress f_v values.
Enter beam width (b, mm), depth (h, mm), span length (L, mm), and uniform load (w, kN/m) using the input sliders or numeric fields.
Review the output: maximum bending stress σ and ratio σ/f_b, maximum shear stress τ and ratio τ/f_v, deflection δ (mm), and pass/fail verdict based on stress ratios <1.0 and typical L/360 deflection limits.
Worked Example
Design a Southern Pine beam (f_b=12 MPa, f_v=1.2 MPa) spanning 4 m with width b=100 mm and depth h=200 mm under uniform load w=8 kN/m. Maximum bending moment M=32 kN·m; section modulus S=bh²/6=667,000 mm³; bending stress σ=M/S=47.9 MPa. Bending ratio 47.9/12=3.99 (FAIL). Reduce load to w=2 kN/m: σ=11.97 MPa, ratio=0.998 (PASS). Shear stress τ=3V/(2bh)=0.3 MPa (PASS). Deflection δ=5wL⁴/(384EI) with E=11 GPa and I=bh⁴/12≈667 mm⁴: δ=6.2 mm (L/645, acceptable).
Practical Notes
Increase beam depth h rather than width b for significantly better bending resistance (strength varies with h³ vs b linearly).
Softwoods like Spruce have lower allowable stresses (f_b≈8–10 MPa) than hardwoods; check species grade and moisture content (<12% reduces adjustment factors).
Deflection often governs design before stress: a 5 m span may require depth ≈L/15 to stay within L/360 limits under typical floor loads (2.5 kN/m).
Account for load duration factor (permanent vs. short-term): short-term loads increase allowable stresses by 1.15–1.6× for design.