Why A 10 Mm Polycarbonate Panel Is Not Four Times Stiffer Than A 5 Mm One
The question expressed as “Why a 10 mm Polycarbonate Panel Is Not Four Times Stiffer Than a 5 mm One” can be answered through the flexural rigidity relationship for solid polycarbonate (PC) sheet. Bending stiffness is not a direct function of thickness in the way that mass per unit area or tensile cross-section is. For a flat, solid, homogeneous sheet, flexural rigidity per unit width is D = Et3 / [12(1 − ν2)], where E is tensile modulus, t is thickness, and ν is Poisson’s ratio. Doubling thickness from 5 mm to 10 mm therefore increases the cubic thickness term by a factor of 23 = 8, not 4.
Under identical boundary conditions, the load-deflection stiffness of a simply supported rectangular plate under transverse pressure also scales with D. For a beam specimen in three-point flexure, the second moment of area for a solid rectangle is I = bt3 / 12. The cubic term is not an empirical curve fit; it results from integration of tensile and compressive stresses through the thickness. Scaling thickness by a factor of 2 increases the cross-sectional area by 2 and the squared distance of the fibers from the neutral axis by 4, so the second moment of area rises by 8.
For a 5 mm solid PC sheet per unit width, I/b = 10.42 mm³. For a 10 mm solid PC sheet, I/b = 83.33 mm³. Using E = 2300 MPa and ν = 0.38, the flexural rigidity per unit width is 28.0 × 10³ N·mm for the 5 mm sheet and 224.0 × 10³ N·mm for the 10 mm sheet. The rigidity ratio is 8.0. By contrast, area density doubles from 6.0 kg/m² to 12.0 kg/m² at a density of 1.20 g/cm³.
When bending stiffness follows the cubic thickness relationship
Flexural stiffness measured under ASTM D790-17 Method I or ISO 178:2019 is not the same as the intrinsic modulus. The reported modulus is calculated from the slope of the load-deflection curve using specimen dimensions and span. For a three-point bend specimen, mid-span deflection δ = PL3 / (48EI). Rearranging gives P/δ = 4Ebt3 / L3. Therefore a change in solid-sheet thickness from 5 mm to 10 mm changes the load required for the same deflection by a factor of 8, provided the support span is scaled appropriately.
If the support span is not increased for the 10 mm specimen, the stiffness ratio may deviate from the cubic relationship because shear deflection and contact deformation change. This is why comparative test standards require a consistent span-to-thickness ratio. For a solid PC beam with a span-to-thickness ratio of 16:1, the shear contribution is approximately 1.3 % of the bending contribution, using E = 2300 MPa, ν = 0.38, and a shear correction factor of 5/6. The cubic thickness rule remains valid in this regime because the shear term is small.
In sheet extrusion, producing a 10 mm solid sheet instead of a 5 mm sheet requires different die lip geometry, roll gap, and haul-off speed settings, but the resin’s elastic modulus remains essentially unchanged. Polycarbonate pellets are typically dried at 120 °C for 4 h to a moisture content below 0.02 % in a desiccant dryer with dew point below −40 °C, then processed on a single-screw extruder with an L/D ratio of 30:1 to 36:1 and melt temperatures between 280 °C and 320 °C. Chill-roll polishing maintains sheet thickness and surface quality. Residual stress and molecular orientation introduced by roll dragging may cause small stiffness anisotropy, but the dominant thickness effect remains the cubic second-moment term.
What happens to the ratio when a 10 mm panel is a hollow structured sheet?
If the 10 mm panel is a multiwall or structured hollow profile, it is not equivalent to a solid 10 mm rectangle. The stiffness of hollow polycarbonate panels must be computed from the actual cross-section of the skins and ribs. For a notional twin-wall profile with overall depth 10 mm, top and bottom skin thickness 0.8 mm, and vertical ribs spaced 10 mm apart, the second moment of area per unit width is approximately 37.9 mm³. This is lower than the 83.3 mm³ value for a solid 10 mm sheet and higher than the 10.4 mm³ value for a solid 5 mm sheet. The pure bending stiffness ratio versus the 5 mm solid sheet is approximately 3.6, while the ratio versus the solid 10 mm sheet is approximately 0.45. This illustrates that a hollow 10 mm panel can be stiffer than a 5 mm solid sheet but not necessarily by a factor of 4 or 8.
The values below are geometric and isotropic; they do not include shear deformation of the webs or local buckling of the ribs.
| Parameter | 5 mm solid PC sheet | 10 mm solid PC sheet | 10 mm hollow twin-wall notional |
|---|---|---|---|
| Second moment per unit width | 10.4 mm³ | 83.3 mm³ | 37.9 mm³ |
| Flexural rigidity per unit width | 28.0 × 10³ N·mm | 224.0 × 10³ N·mm | 101.9 × 10³ N·mm |
| Area density at 1.20 g/cm³ | 6.0 kg/m² | 12.0 kg/m² | 2.7 kg/m² |
| Rigidity ratio vs 5 mm solid | 1.0 | 8.0 | 3.6 |
Shear deformation can reduce the effective stiffness of hollow panels relative to the pure bending calculation. In a simply supported beam, the mid-span deflection is the sum of bending deflection and shear deflection. For a solid PC specimen with a 16:1 span-to-thickness ratio, the shear component is approximately 1.3 % of the bending component. For multiwall panels, the shear stiffness of the webs can be lower because the webs are thin and may be discontinuous, so the actual load-deflection stiffness may fall below the pure bending prediction. This is why technical datasheets for multiwall polycarbonate panels report span-specific and boundary-condition-specific load-deflection data rather than a single stiffness factor.
Multiwall polycarbonate panels are anisotropic. In the notional cross-section described above, the ribs run along the extrusion direction. Flexural stiffness in the rib direction is higher than across the rib direction, where the cross-section consists largely of skins with interrupted webs. Any comparative stiffness statement for a hollow PC panel must therefore specify direction, support span, and boundary conditions.
Testing conditions that must be matched for a valid comparison
Comparative stiffness claims for polycarbonate panels require matched boundary conditions, loading direction, and span-to-thickness ratio. In ISO 178:2019 and ASTM D790-17, the support span is normally set at 16:1 to minimize shear effects. A 5 mm solid specimen therefore uses approximately 80 mm span, while a 10 mm solid specimen uses 160 mm. If a fixed span is used for both, the thickness scaling may deviate from the cubic relationship because the shear component and end-contact deformation are different. The modulus is also calculated differently between ISO 178:2019 and ASTM D790-17, so numerical values should not be compared across methods without correction.
Published data for specific multiwall profile stiffness is limited. If a design requires the stiffness of a commercial 10 mm PC panel, the profile-specific cross-section geometry and loading direction must be obtained from the manufacturer or measured under ASTM D790-17 or ISO 178:2019 on specimens cut without damaging the ribs. For installed glazing or cover applications, the load-deflection ratio must also be verified with boundary conditions that replicate the frame and gasket restraint. Long-term deflection calculations require a creep modulus determined under ISO 899-2:2003 or an equivalent isochronous data set rather than the short-term tensile modulus.
