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Connector cross-section in a bridge

Is the connector large enough?

Answer: A bridge most often breaks in the connector between the joints. Each material has a minimum cross-sectional area, e.g. 9 mm² at the front and 12 mm² in the incisor area for a 3-joint bridge in IPS e.max ZirCAD. The connector is almost elliptical, so the area is π/4 × height × width. The calculator shows the area, whether it holds, and how high the connector should be at the width you have space for. Height matters most: strength grows with height squared and stiffness cubed.

Formula

Tværsnit (mm²) = π ÷ 4 × højde × bredde (konnektoren regnet som en ellipse)

Højde der kræves = 4 × minimum ÷ (π × bredde)

Strength against bending increases with width × height², stiffness with width × height³ — therefore height matters most

Symbols and units in the formula
SymbolMeaningUnit
hoejde_mmConnector height (occlusal-gingival)mm
bredde_mmConnector width (buccal-oral)mm
minimum_mm2Material's minimum cross-section (from the user manual)mm²
=Connector cross-sectionmm²
=Over (+) or under (−) minimummm²
=Height required at this widthmm
=Width required at this heightmm

Validity and source

Source
Ivoclar IPS e.max ZirCAD Labside, instructions: 3-unit bridge at least 9 mm² (front) and 12 mm² (molar); ellipse area π/4 × h × b

Does not apply when

  • The CAD programme measures the actual cross-section, and that is the number that counts. The minimum requirement depends on material, number of joints and placement in the mouth, so read it in the current instructions. Space for the papilla and cleaning sets the limit for height.

Worked example

The calculator's own default values inserted. The figures are calculated with exactly the formula the tool uses.

Substituted

  • Connector height (occlusal-gingival)4 mm
  • Connector width (buccal-oral)3.50 mm
  • Material's minimum cross-section (from the user manual)12 mm²

Giver

  • Connector cross-section11.0 mm²
  • Over (+) or under (−) minimum-1.0 mm²
  • Height required at this width4.37 mm
  • Width required at this height3.82 mm

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Sådan bruger du den

Du bruger den i CAD-designet af en zirkonia- eller keramikbro, når du skal sikre, at konnektorerne er store nok. Producenten har et mindste tværsnit for hvert materiale og område.

Step by step

  1. Find materialets mindste tværsnit i brugsanvisningen, fx 9 mm² i fronten og 12 mm² i kindtandsområdet.
  2. Mål konnektorens højde og bredde i CAD-programmet.
  3. Beregneren regner tværsnittet som en ellipse: π/4 × højde × bredde.
  4. Mangler der areal, så øg helst højden, ikke bredden.
  5. Kontrollér med CAD-programmets egen måling.

Typical errors

  • At regne højde × bredde som et rektangel. En ellipse har kun ca. 79 % af det areal.
  • At gøre konnektoren bredere i stedet for højere.
  • At gå under minimum for at give plads til papillen.

Examples from everyday life

Kindtandsbro i zirkonia

En 3-leddet bro fra 5 til 7. Konnektoren er 4,5 mm høj og 3,5 mm bred, og materialet kræver 12 mm².

Connector height (occlusal-gingival)
4.5 mm
Connector width (buccal-oral)
3.5 mm
Material's minimum cross-section (from the user manual)
12 mm²

It means: Tværsnittet er 12.4 mm², altså 0.4 mm² over minimum.

Frontbro med lav plads

En 3-leddet frontbro har kun plads til en konnektor på 3,5 × 3 mm. Materialet kræver 9 mm².

Connector height (occlusal-gingival)
3.5 mm
Connector width (buccal-oral)
3 mm
Material's minimum cross-section (from the user manual)
9 mm²

It means: Tværsnittet er kun 8.2 mm², altså -0.8 mm² i forhold til minimum. Ved samme bredde skal højden være 3.82 mm.

Bred men lav konnektor

En kindtandskonnektor er 3 mm høj og 4,5 mm bred, og materialet kræver 12 mm².

Connector height (occlusal-gingival)
3 mm
Connector width (buccal-oral)
4.5 mm
Material's minimum cross-section (from the user manual)
12 mm²

It means: Tværsnittet er 10.6 mm², altså -1.4 mm² i forhold til minimum. Gør den hellere 3.4 mm høj end 5.09 mm bred, fordi højden giver mest styrke.

Rule of thumb

En ellipse på 4 × 4 mm er ca. 12,6 mm².

How to check the answer

CAD-programmets tværsnitsmåling skal være mindst producentens minimum.