Flitch Beam Composite Deflection

Size a wood-and-steel-plate flitch beam by summing parallel EI — midspan deflection, steel share, and span ratio for a uniformly loaded simple span.

InputΣEI = n·E_w·(b·d³/12) + E_s·(t·h³/12), δ = 5·w·L⁴ / (384·ΣEI)

Simple span (m)or enter ft — converts to mUniform load (kN/m)or enter lbf/ft — converts to kN/mNumber of wood pliesWood ply width (mm)or enter in — converts to mmWood ply depth (mm)or enter in — converts to mmSteel plate thickness (mm)or enter in — converts to mmSteel plate depth (mm)or enter in — converts to mmWood modulus E (GPa)or enter 10⁶ psi — converts to GPaSteel modulus E (GPa)

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The engineering

A flitch beam sandwiches a steel plate between sawn-lumber plies, all bolted together so they deflect as one. Because every layer bends to the same curvature about a shared neutral axis, the composite stiffness is simply the sum of each layer's EI — no transformed-section gymnastics needed for side-by-side rectangles. This card sums the parallel EIs and evaluates the classic 5wL⁴/384EI midspan deflection for a uniformly loaded simple span.

The steel share output tells you whether the plate is earning its keep: a single ½ in. plate between two 2×10s typically carries about 75% of the stiffness. Watch two gotchas — the bolt pattern must actually transfer load into the plate (NDS connection provisions govern), and the plate is usually cut ¼–½ in. shallower than the lumber so it never bears directly on the plate at supports. Deflection here is stiffness only; check bending and shear stress in both materials separately.

Serviceability rule of thumb: L/360 for live load under plastered ceilings, L/240 for total load. The span/deflection ratio row makes that check immediate.

Where this math comes from

The flitch beam is a 19th-century carpenter's fix: when a timber span grew past what one tree could handle, builders bolted a wrought-iron plate between two sawn 'flitches' (the word is old English for a slab cut from a log — same word as a flitch of bacon). Thomas Tredgold's 1820 Elementary Principles of Carpentry gave English-speaking builders their first rational treatment of iron-strengthened timber, and by the 1840s flitched girders were carrying floors and short railway spans on both sides of the Atlantic.

The mechanics ride on Euler and Bernoulli's beam theory, worked out a century earlier — same curvature in every layer means stiffnesses add in parallel. Rolled steel plate displaced wrought iron by the early 1900s, and when the National Lumber Manufacturers Association published the first National Design Specification in 1944, wood engineering finally had codified E values and bolt provisions. Today's AWC NDS is where you pull the wood modulus and design the bolt schedule that makes this calc's 'acts as one beam' assumption true.

1744Leonhard EulerPublishes the elastica — the beam curvature theory under every deflection formula here.
1820Thomas TredgoldElementary Principles of Carpentry rationalizes iron-strengthened timber construction.
1840British and American buildersWrought-iron flitch girders become standard practice for long floor spans.
1944NLMA (now AWC)First National Design Specification for wood construction — codified E values and connection design.
2018American Wood CouncilCurrent NDS editions carry the design values and bolt provisions governing modern flitch assemblies.

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