3D Print Strength Calculator: Walls, Infill & Layer Direction

The section is rectangular, with nominal perimeter thickness $t_w=N_w w$ and each top/bottom skin $t_s=N_s h_l$. Flat printing uses $b_c=b-2t_w$, $h_c=h-2t_s$; on-edge printing swaps wall and skin roles. Upright printing uses perimeters on both section dimensions and skins at the two ends. Core dimensions are clipped at zero so solid regions never double-count. When end closures meet or overlap, both core dimensions become zero: stiffness, strength, mass and the drawing consistently recover the fully solid section. The mass model subtracts the porous interior from the full envelope, including solid end closures.

The cellular core uses $r_E=C_E\rho^{n_E}$ and $r_S=C_S\rho^{n_S}$. Gibson and Ashby, Cellular Solids, 2nd ed. (1997), and the open-access Bioengineering 2023 paper (s12, p8, Table 1) give limiting exponents: stretching $(1,1)$, bending $(2,1.5)$. Triangles select the stretching scenario; grid, gyroid, cubic and in-plane honeycomb select the bending scenario. These assignments are modelling assumptions, not measured pattern properties. Grid aligned with load, honeycomb along cells and different gyroid constructions may need another scenario. The cellular input and its load curves stop at 95%; above 60% they are extrapolation. A separate Printed-solid comparison choice and result table use density 1 and printed-solid properties. No continuous transition from calibrated cellular coefficients to this solid scenario is assumed or drawn.

Plane sections remain plane and shell/core strains are compatible. With $A_s=A-A_c$ and $I_s=I-I_c$:

Axial first failure occurs at the smaller shell/core strain limit. Bending first failure uses the smaller of $\sigma_s/(E_s h/2)$ and $\sigma_c/(E_c h_c/2)$ as limiting curvature. Empty cores do not impose a limit. Both tensile and compressive stress magnitudes use the same material limit. Cantilever moment and displacement are $FL$ and $FL^3/(3D)$; three-point values are $FL/4$ and $FL^3/(48D)$. Tensile extension is $FL/(EA)$. Interior section rigidity is used along the whole loaded length; stiffer end caps affect mass only. The linear material threshold is divided by the chosen design factor. For bending, the reported screening load is then the smaller of that result and the force causing displacement/span = 0.05. Every sweep candidate uses its own rigidity for this cap. Displacements at both reported loads are calculated; a material threshold beyond the small-deflection range is explicitly warned and is not a validated nonlinear failure prediction.

Slic3r flow math (s10) models a bead as a rectangle with semicircular ends: $A_b=(w-h_l)h_l+\pi h_l^2/4$, path spacing $p=w-h_l(1-\pi/4)$, and ideal vertical contact $c=w-h_l$. Lateral intersection height of overlapping capsule ends is $\sqrt{h_l^2-(p-w+h_l)^2}$. These are ideal geometric contacts, not measured weld dimensions. Strength rescaling is off by default. If explicitly enabled, the experimental Z correction divides $c/p$ by its value at $w=0.45$ mm and $h_l=0.20$ mm; it multiplies the source Z/XY strength ratio, capped at 1. It does not change XY strength or modulus, and enabling it produces a warning beside the results. Measured-property mode automatically bypasses the geometric correction. Nominal wall thickness deliberately follows count × width, rather than slicer path spacing.

The first drawing is an original schematic; the right-hand section has the correct proportions. The crack mark shows a critical section, not fracture propagation. Pattern icons are illustrative. Equal-mass curves solve for core density after subtracting shell and end-cap volume for each wall count. Blank segments are infeasible mass budgets. All curves retain the selected load case, orientation, material and calibration factors.

Published benchmarks use the same transformed-section and first-material-limit functions as the main calculation. The 2026 PLA paper (s11 pp4–7) supplies 80×10×4 mm samples, 64 mm span, 2 perimeters, 0.20 mm layers, 0.4 mm nozzle, 215 °C nozzle / 60 °C bed, cubic infill and the measured non-solid strengths. Independent 100% solid flexural coupon limits from that paper calibrate the baseline for this bending protocol only: Y 37.15 MPa and Z 22.57 MPa. The held-out infill measurements are not fitted. The paper omits line width; 0.45 mm is an explicit assumption, and its two face layers are interpreted as two skins per face. This limits reproducibility. The reference cases for Y-cubic 30% and 50% allow a stated 15% engineering comparison band, not experimental uncertainty. The table also retains the Y-10% and Z-50% disagreements; the 15% band does not validate them. All coefficients remain 1 and exponents 2/1.5 for these fixed comparisons.

• Prismatic rectangular section; perfectly bonded shell/core with a common axial strain or curvature. Solid top and bottom skins have equal thickness. No shell/core slip, shear deformation or residual stresses.
• Manufacturer presets use horizontal printed tensile yield strength and tensile modulus, plus the separate interlayer adhesion test. The TDS “Vertical xz” column is not used as true Z tensile strength. Tensile limits are also used for bending; the larger manufacturer flexural-strength numbers are not substituted.
• Preset central Z/XY ratios are PLA 0.33, PETG 0.38, ASA 0.26 and dry PA11-CF 0.48. Approximate spreads from the stated TDS ± values are 0.26–0.42, 0.29–0.49, 0.23–0.29 and 0.35–0.61 respectively. These are test spreads, not statistical confidence limits.
• The default Z/XY modulus ratio of 0.8 is an uncalibrated screening assumption; explore 0.6–1 or use coupons. Fiber direction and moisture can change PA-CF properties considerably.
• Unit core coefficients are normalized idealized envelopes, not experimental pattern fits. The open-access cellular paper reports coefficient ranges 0.1–4 for stiffness and 0.1–1 for strength; this calculator limits both to at most 1 to retain a simple normalized envelope. Quality factor 1 represents the source process; lower quality factors are user sensitivity scenarios.
• The TDS cases are data-transfer checks, the statics case checks equilibrium, and the cellular case checks scaling algebra. Two additional non-solid beam cases test the combined model conditionally after calibration from separate solid flexural coupons. Their 15% comparison band is not experimental scatter or a certified error bound; missing line-width data prevents exact reproduction. A CNC Kitchen case checks qualitative consistency with the thin-layer plateau, not hook force.
• The 5% deflection/span ceiling is a small-deflection validity rule, not an application-specific deflection allowance or a substitute for nonlinear analysis. It caps screening loads but does not extend the validity of the separately reported linear material threshold.
• The printed-solid scenario is separate from cellular extrapolation. Its stress limit and modulus still depend on orientation and process; it does not mean a void-free isotropic molded polymer.

Use for room-temperature, dry, short-duration, quasistatic comparisons in slender parts, preferably span/depth ≥10 and displacement/span ≤0.05. Several cells should fit within the section and along its length; a one-cell core is not homogenized material. Very low-density unsupported skins can buckle or sag even though this model still reports a material limit.

Local wall/skin buckling, core crushing at contacts, interlayer shear, seams, holes, notches, load introduction, fasteners, torsion, combined loading, fatigue, impact, creep, temperature and environmental degradation are outside this model. A cantilever represents the straight arm of a bracket, not its corner or mount. The tensile strength estimate does not address compression-column buckling.

The source tests show substantial process dependence. In the 2024 layer-arrangement paper (s6 p11, original G-code), PLA Z strength is 14.07 MPa at 0.16 mm but 18.25 MPa at 0.28 mm; PETG is 31.41 and 19.16 MPa respectively. Thus geometry alone cannot predict layer height effects. Bead-contact strength rescaling is disabled by default. CNC Kitchen’s 2019 tests found a useful layer-height plateau, deterioration above roughly half the nozzle diameter, and a width optimum near 1.5 nozzle diameters; the calculator does not fit or reproduce the hook forces.

The 2026 PLA flexure study (s11 p7) reports 100%-filled flexural strengths of 43.46, 37.15 and 22.57 MPa for its three build directions. These differ from the Prusament presets and cannot be transferred as universal allowables. The PETG architecture study (s13 p1) found a different strength ranking from its stiffness ranking at 30% infill, supporting separate core coefficients. No universal best pattern or guaranteed “walls always win” claim is intended.

This is a screening estimate, not a certified working load. A design factor cannot compensate for an unknown failure mode. Calibrate with representative coupons, compare mass with the slicer and test the actual part.

Measured combined-model discrepancies: with the solid-coupon calibration and geometry assumptions stated above, the fixed cubic benchmarks give Y-10% 21.71 versus 17.02 MPa (+27.5%), Y-30% 22.96 versus 20.41 MPa (+12.5%), Y-50% 25.45 versus 23.41 MPa (+8.7%), and Z-50% 20.26 versus 11.12 MPa (+82.2%). The latter is a substantial unsafe overprediction; neither the Z-direction multiplier nor a generic safety factor establishes a validated cellular failure load. Calibrate the complete section and process. These residuals are displayed even though the two flat reference cases pass their broader engineering comparison band.

CNC Kitchen’s layer-height hooks used Prusament PLA, an MK2.5, a 0.4 mm nozzle and three perimeters with constant skin thickness over 0.05–0.4 mm layers. Its extrusion-width hooks used SpoolWorks PLA, an MK2S, 210 °C nozzle, 50% fan and 0.16 mm layers. Those curved hooks combine tension and bending and are outside this rectangular-section model. The calculator therefore checks qualitative plateau consistency; it does not claim to reproduce their hook failure loads. An actual hook-force validation would require a curved-part model and documented critical geometry.