Engineering Design · moment of inertia, section modulus, thermal

Moment of Inertia and Section Modulus of T-Slot Profiles

A typical 20 × 20 mm T-slot bar in 6063-T5 carries about 0.49–0.50 kg/m with Ix = Iy ≈ 0.72–0.74 cm⁰ — values taken from the nominal section under EN 755-9 geometry, not from the outline alone. Copy I and Z from the supplier drawing into the deflection and stress check before you freeze the span.

2020 I / Z: ≈0.72–0.74 cm⁰ / ≈0.72 cm⁯
Tolerance: EN 755-9
Example heavy: 45×90, I≈68 cm⁰
Read: 11 minutes

Short answer

Use moment of inertia I for deflection and section modulus Z for bending stress. For a common 2020 (6 mm slot) expect Ix = Iy ≈ 0.72–0.74 cm⁰, Zx = Zy ≈ 0.72 cm⁯ and mass ≈ 0.49–0.50 kg/m at 2.70 g/cm⁵; heavier 4040 sections sit near 8–14 cm⁰ depending on the internal web. Screen mid-span deflection with δ = F·L³/(48·E·I) and E ≈ 69 GPa for 6063-T5. Thermal movement of 6063 is about 23.4 µm/m·°C: a 3 m rail through +40 °C grows ≈ 2.8 mm if free. Bolted T-slot fatigue is usually joint fretting and preload loss, not parent-bar endurance — keep dry torque in the M6 5–8 Nm and M8 13–20 Nm bands and recheck after vibration. Extrusion tolerances EN 755-9: wall ±0.15 mm, straightness 1.5 mm/m, twist 2°. Fabrication: cut length ±0.5 mm, hole position ±0.2 mm, end square within 0.3 mm. Site heavy rail: 45 × 90 mm six-slot, 6063-T5, 4.10 kg/m, I ≈ 68 cm⁰.

Section geometry of a T-slot extrusion drives moment of inertia and section modulus.

What is the moment of inertia of a 2020 t-slot profile

A standard 20 × 20 mm T-slot (6 mm slot) has Ix = Iy ≈ 0.72–0.74 cm⁰ about the centroidal axes — roughly one-tenth of a typical 4040, which is why 2020 is a light frame member, not a metre-class beam.

I measures how the area is distributed against bending; it enters every elastic deflection formula and must come from the supplier’s nominal section (or a measured DXF), not from a solid 20 mm square. Internal ribs, slot depth and corner radii move I by tens of percent between “same size” catalogues. Orient rectangular bars so the larger I fights the primary moment. For screening, keep E = 69 GPa and compare δ to L/500 or L/360 before you approve the cut list.

Section (typical)	Mass (kg/m)	Ix ≈ (cm⁰)	Iy ≈ (cm⁰)	Role
2020	0.49–0.50	0.72–0.74	0.72–0.74	Light frames, braces
2040	≈0.90	≈4.6	≈1.4	Strong axis as short beam
3030	0.75–1.0	2.4–3.3	2.4–3.3	Light benches, guards
4040	1.5–1.7	8–14	8–14	Industrial bays
4080 (strong)	≈3.0–3.4	≈63–74	≈18–21	Long spans, gantries
45 × 90 six-slot	4.10	≈68	(weaker)	Heavy top / guard rail

What is the section modulus of 2020 aluminium extrusion

Section modulus Z for a typical 2020 is about 0.72 cm⁯ on both axes — use it for bending stress σ = M/Z, while I stays the number for deflection.

Z = I/c where c is the distance from the neutral axis to the extreme fibre. Two bars with similar I can differ in Z if one puts more metal farther out. Yield of 6063-T5 is not the usual limit on light frames: joints slip and deflection limits trip first. Still publish Z on the drawing so a stress check can be run under impact or concentrated bracket loads. Heavier 4040 sections often sit near Z ≈ 4–7 cm⁯ depending on the web; do not mix catalogue families when you copy the number.

Section	Zx ≈ (cm⁯)	Zy ≈ (cm⁯)	Use Z for	Use I for
2020	0.72	0.72	Local bending stress	Deflection screen
2040	≈2.3	≈1.3	Strong/weak axis stress	Orientation choice
3030	1.6–1.8	1.6–1.8	Bracket pad checks	Bay deflection
4040	4–7	4–7	Impact / point load	1–2 m industrial bays
4080 strong	≈16–19	≈9–10	High moment members	Long spans
45 × 90	from I≈68	weaker axis	Heavy rail stress	Top / guard deflection

What is the coefficient of thermal expansion effect on a 2020 frame

6063 expands at about 23.4 µm per metre per °C (20–100 °C), so a free 2020 rail of length L grows ΔL = α·L·ΔT — roughly 0.94 mm per metre for a +40 °C rise.

That movement is small on a 0.5 m brace and obvious on a 3–6 m perimeter fence or conveyor side rail. If the frame is restrained by steel floor plates, fixed walls or locked mitres, expansion turns into stress and can open joints or bow panels. Leave sliding slots or slotted foot holes on long runs; give polycarbonate and acrylic panels perimeter clearance so the aluminium does not crush them. Installation temperature matters: a kit built at 10 °C and run at 50 °C near an oven needs the full ΔT in both directions. Mixed aluminium–steel assemblies need differential checks; steel’s α is roughly half.

Length L	ΔT	ΔL (free, α=23.4)	Design action
1.0 m	+20 °C	≈0.47 mm	Usually absorbed in joints
1.0 m	+40 °C	≈0.94 mm	Watch panel gaps
3.0 m	+40 °C	≈2.8 mm	Slotted feet / expansion joint
6.0 m	+40 °C	≈5.6 mm	Break rails or slide mounts
3.0 m	−20 °C	≈−1.4 mm	Check seal engagement
Panel 1.0 m PC	+40 °C	higher than Al	Oversized holes / soft clamps

What is the fatigue behaviour of a bolted 2020 joint

Fatigue on a bolted 2020 frame almost always appears as joint fretting, T-nut walk and preload loss — not as a classic through-crack in the parent bar at catalogue endurance stress.

The light lip and small contact area under an M5/M6 T-nut mean cyclic racking works the clamp face. Keep dry torque in the maker’s band (working plant practice often sits near 3–6 Nm for M5 on 2020 and 5–8 Nm for M6 on larger series; M8 13–20 Nm on 40-series). Recheck torque after first transport and after the first week of vibration. Prefer gussets or end-tapped butt fasteners where the joint sees reversing load; a single thin L-bracket on 2020 is a positioning joint, not a fatigue-rated machine base. Anodised slots change friction, so the same torque does not guarantee the same preload as mill finish. Parent-bar fatigue data (RR Moore style) is a poor substitute for a joint test on the actual bracket and nut.

Joint detail	Fatigue behaviour	Mitigation
Single thin L on 2020	Preload loss, lip wear	Gusset or upsize series
M6/M8 T-nut + bracket	Good if torqued and locked	5–8 / 13–20 Nm; recheck
Blind internal connector	Lower clamp area	Not for reversing primary load
End tap + butt fastener	Better axial cyclic path	End square ≤0.3 mm
Through-bolt both walls	High if washers seat	Planned holes ±0.2 mm
Anodised vs mill	Friction shift → preload shift	Torque to finish-specific chart

RFQ checklist — section data

Section and axis — 2020 / 3030 / 4040 / 45 × 90 and which I you bend about.
I and Z source — supplier drawing or DXF, not a generic web table alone.
Load case — mid-span F, uniform load, or bracket point load; δ limit.
Temperature range — install T and service ΔT for long rails and panels.
Joint duty — static, vibrating, or reversing; torque standard.
Tolerances — EN 755-9 wall ±0.15 mm, straightness 1.5 mm/m, twist 2°; cut ±0.5 mm, holes ±0.2 mm, square 0.3 mm.
Documents — mill certificate and section property sheet with the quote.

Ask for I and Z on the quotation drawing for the exact die, not for “2020 class.” Internal webs differ enough to move deflection by a full serviceability class.

Four ways the numbers mislead

Outline taken as IA solid 20 mm square is not a T-slot. Use the supplier’s hollow section I.

Z used for deflectionDeflection needs I and E. Z is for stress. Mixing them fails both checks.

Thermal ignored on long runs3 m × +40 °C ≈ 2.8 mm. Restrained frames push that into the joints.

Parent fatigue quoted for jointsBolted T-slot fails at the clamp first. Spec torque and recheck, not only alloy endurance.

Related on this site

how die cost amortises per meter — cost of locking one high-I section
minimum order with a new die — when a custom stiff section needs tooling
die making adds 7–12 days — calendar before the first property sheet
who owns the die — reuse rights on a custom I-section

Terms used in this article

Moment of inertia (I): Second moment of area about a centroidal axis; governs elastic bending deflection with E.
Section modulus (Z): I divided by the distance to the extreme fibre; used for bending stress σ = M/Z.
EN 755-9: European tolerance standard for extruded aluminium bars, tubes and profiles.
CTE (α): Linear coefficient of thermal expansion; ≈23.4 µm/m·°C for 6063 in the 20–100 °C band.
Preload: Clamping force from correct fastener torque; critical to joint fatigue life.
Strong axis: The bending axis with the larger I on a rectangular profile.

Questions buyers ask

What standard are the tolerances measured against?

Extrusion geometry is commonly held to EN 755-9: wall thickness ±0.15 mm on light walls, straightness 1.5 mm/m and twist 2° unless the drawing states otherwise. Fabrication after sawing is separate: cut length ±0.5 mm, hole position ±0.2 mm, end square within 0.3 mm. Ask which standard is on the inspection report before you compare two quotes.

Can you supply a mill certificate?

Yes — a 3.1 mill certificate for alloy and temper (typically 6063-T5 for T-slot) can ship with the lot. For structural or export jobs request the certificate number on the packing list and keep it with the section-property drawing so I and Z stay tied to the poured heat.

What is the minimum wall thickness?

Minimum wall is a die and alloy-flow limit, not a single catalogue number. Light 2020 webs often sit near 1.5 mm on diagonals; structural series use thicker webs (often 2 mm and up) where brackets and anchors bear. State the minimum wall on the RFQ if you need a structural lip; do not assume every “2020” shares the same web.

How is weight per metre calculated?

Mass per metre is cross-sectional area × density. For aluminium use 2.70 g/cm⁵ on the nominal section: a 2020 near 180–185 mm² yields about 0.49–0.50 kg/m. Anodising adds little mass; powder coating adds more. Invoice weight may use weighed bars — compare to the calculated value on the drawing if freight is quoted per kilogram.

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