Calculate the strength of a "lap joint" — two plates overlapped and held by rivets — in real time. The tool evaluates the three failure modes (rivet shear, plate bearing, plate tear-out) at once; the smallest sets the joint strength and the weakest mode is the failure mode. Tune diameter, count, pitch and plate thickness to design the riveted patterns actually used on aircraft skins and bridges.
Parameters
Rivet diameter d
mm
Number of rivets n
Rivets in a single row
Plate thickness t
mm
Rivet pitch p
mm
Center-to-center spacing between adjacent rivets
Rivet shear strength τ
MPa
Plate tensile strength σ_t
MPa
Bearing strength σ_b is approximated as σ_t
Results
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Shear strength (kN)
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Bearing strength (kN)
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Tear-out strength (kN)
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Joint strength (min) (kN)
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Failure mode
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Joint efficiency η (%)
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Lap-joint cross-section — three failure modes
Two plates (blue / grey) joined by rivets shown as cylinders. Cyan = shear plane, orange = bearing face, red = tear path; the governing mode is highlighted.
P_s: rivet shear, P_b: plate bearing, P_tear: plate tear-out. The joint strength is the minimum P_min = min(P_s, P_b, P_tear); the weakest mode is the failure mode.
Joint efficiency η compares the joint strength to the un-holed parent plate. A higher η means the plate's capacity is better used.
The strength of a riveted joint
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Rivets are those mushroom-headed pegs you see on the Eiffel Tower and old bridges, right? Are they still actually used?
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Exactly — they were the universal way to permanently join metal plates from the Industrial Revolution until the 1960s. But aircraft skin panels are still almost entirely riveted today. Three reasons: (1) welding distorts the thin skin and ruins the aerodynamic surface, (2) drilling rivet holes adds no heat to the parent metal so its mechanical properties are preserved, and (3) when a rivet fatigues the head pops off visibly, making inspection easy. The same is true for bridge restoration and historical battleship preservation — rivets are still the first choice.
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OK. So a riveted joint just comes down to "do the rivets break or not"? But this tool shows three things — shear, bearing, tear-out…
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Good catch. A riveted joint has three independent failure modes, and the joint fails as soon as the weakest one gives way — so you have to compute all three and take the minimum. (1) Rivet shear: the rivet body is cut in half by the plates sliding past each other. (2) Bearing: the rivet body crushes the edge of the hole in the plate. (3) Tear-out: the plate itself tears apart along the row of rivet holes. A well-designed joint has all three at about the same strength; an "unbalanced" joint with one weak mode is wasteful.
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The default settings say "bearing" is governing. How do I fix that?
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Bearing is P_b = σ_t·d·t·n, so the two levers are "thicker plate t" or "bigger rivet d". Shear scales with d², so increasing d strengthens both shear and bearing at once. Increasing t strengthens bearing and tear-out together but costs weight and rivet count. With the current settings (d=16, t=10) the rivets sit almost at the cross-over with shear — bump t to 12 mm and you can see bearing flip past shear. Try the slider.
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Also the "joint efficiency" reads 26.7%, which feels low. What does that actually mean?
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η is the ratio of the joint strength to "what the plate would be capable of without any rivet holes" (n·p·t·σ_t). With p = 60 mm and bearing limiting the joint, η comes out low. Increasing p raises η, but the load per rivet hole goes up too — there is an optimum. A real single-row lap joint sits at 60-70%, a two-row joint 75-80%, and a staggered two-row joint can exceed 85%. The η-vs-pitch chart below shows the shape of that curve very clearly.
Frequently Asked Questions
A single-shear, single-row riveted lap joint can fail in three independent modes, and the joint strength is the smallest. (1) Rivet shear P_s = τ·(πd²/4)·n, (2) Plate bearing P_b = σ_t·d·t·n, (3) Plate tear-out P_tear = σ_t·(p−d)·t·n. Here d is the rivet diameter, n is the number of rivets, t the plate thickness, p the pitch, τ the rivet shear strength and σ_t the plate tensile strength. This simulator evaluates all three together and reports the governing mode and the joint efficiency η = P_min / (n·p·t·σ_t) × 100%.
If rivet shear governs, increase the rivet diameter d (the shear area scales with d²) or pick a rivet alloy with higher shear strength. If plate bearing governs, increase plate thickness t or rivet diameter d (the bearing area is d·t). If plate tear-out governs, widen the pitch p (the net section p−d grows) or use a thicker plate. A well-designed joint has all three modes at roughly the same strength — designers explicitly avoid the case where one mode is far weaker than the others.
Joint efficiency is the ratio of the joint strength to the strength of the un-holed parent plate (n·p·t·σ_t). A typical single-row lap joint reaches 60-70%, a two-row joint 75-80%, and a carefully designed double-row staggered joint exceeds 85%. A low η means the plate's capacity is wasted and weight efficiency suffers. Aircraft skin panels chase the highest η for weight reasons, while bridges and boilers sometimes intentionally cap η around 70% to keep extra safety margin. This tool shows the current η instantly and the η-vs-pitch chart helps you find the best pitch.
Riveting has been the standard permanent metal-to-metal joint since the Industrial Revolution, and aircraft skin panels are still riveted today for three reasons: (1) welding distorts the thin skin and ruins the aerodynamic surface, (2) drilling rivet holes adds no heat to the parent metal, so its mechanical properties are preserved, and (3) when a rivet fatigues the head pops off visibly, giving outstanding inspectability that welded joints (with hidden crack propagation) cannot match. Rivets are also the standard choice for bridge restoration and historical ship preservation where the original construction method must be respected.
Real-World Applications
Aircraft skin panels: Fuselage and wing skins are almost entirely riveted. A single jet airliner uses 500,000 to 1,000,000 rivets, and skin seams use countersunk rivets to keep the surface aerodynamically smooth. The single-row lap joint covered by this tool is the smallest building block; real skin panels use two- or three-row staggered patterns to push efficiency even higher.
Steel bridges and historic structures: Many early-20th-century railway and road bridges were built with rivets and remain in service today. Repair and member replacement are still done with similar rivets (sometimes substituted by high-strength bolts), and joint-strength calculations like this one are mandatory. Heritage-bridge restoration also keeps rivets for visual authenticity.
Pressure vessels and boilers (historical and educational): Steam-age boilers and pressure vessels were assembled with riveted joints, and codes like the (now retired) JIS B 8201 and ASME Section I prescribed designs based on joint efficiency. Welding has taken over in modern practice, but mechanical-design textbooks still explain joint efficiency through riveted joints because the underlying mechanics is cleanly visible.
Ship and armored-vehicle restoration: Skin repairs on museum ships like HIJMS Mikasa and HMS Belfast, as well as boiler restorations on vintage cars and steam locomotives, use rivets to preserve the original construction method. This tool is useful in restoration projects for quick "what if we used modern material" strength comparisons.
Common Misconceptions and Pitfalls
The biggest pitfall is assuming "rivet shear strength = the rivet material's tensile strength". In reality the shear strength τ is roughly 0.6 to 0.8 of the tensile strength σ_u — about τ ≈ 320 MPa for steel rivets (σ_u ≈ 500 MPa) and τ ≈ 180-260 MPa for typical aluminum-alloy rivets. Setting τ = σ_u without checking the datasheet quietly designs a joint that shears in service. Also note that in double-shear configurations the rivet is cut at two planes and P_s doubles, but this tool assumes a single-shear lap joint.
Next, treating the plate bearing strength as equal to σ_t (tensile). This tool uses σ_b = σ_t as a practical simplification, but rigorously the bearing strength is usually higher than the tensile strength (the local deformation under the rivet is constrained, unlike free uniaxial tension). Some textbooks use σ_b = 1.5·σ_t. So the values this tool reports are conservative on the bearing side: the real bearing margin will be a bit larger than displayed.
Finally, assuming "wider pitch always raises efficiency". Tear-out P_tear = σ_t·(p−d)·t·n grows with pitch, but a wider pitch means fewer rivets fit in the same total length, so the load carried by each rivet rises and shear/bearing kick in earlier. Even more importantly, an excessively wide pitch lets the plate interface gap open, causing corrosion or leakage. Boilers and ships impose a maximum-pitch rule (typically p ≤ 8t) for sealing. Joint efficiency and sealing are independent trade-offs.
How to Use
Enter rivet diameter (dNum, mm) and edge distance (dRange, mm) for each rivet line
Input number of rivets (nNum) per line and spacing between rivets (nRange, mm)
Specify plate thickness (tNum, mm) and material yield strength (pNum, MPa)
Click Calculate to evaluate shear stress per rivet, bearing stress on plate holes, and tear-out stress between rivet holes
Review the governing failure mode and joint efficiency percentage
Worked Example
Two mild steel plates (Fy = 250 MPa) overlap with thickness t = 6 mm. Four rivets of diameter d = 16 mm are spaced nRange = 40 mm apart with edge distance dRange = 25 mm. Shear strength per rivet = 0.6 × π × (0.016)² × 4 × 250/√2 ≈ 67.9 kN. Bearing strength = 1.5 × 0.016 × 0.006 × 250 × 4 ≈ 72.0 kN. Tear-out strength = (0.040 - 0.016) × 0.006 × 250 × 4 ≈ 14.4 kN. Joint strength = minimum = 14.4 kN governs. Joint efficiency η = (14.4 / 250 × 0.006 × overlap width) × 100%.
Practical Notes
Tear-out typically governs in single-row lap joints; increase edge distance or rivet spacing to improve tear-out capacity
For steel: bearing strength usually 1.5 Fu per rivet; use lower factors (1.2) for aluminum rivets
Industrial lap joints in ship hulls and boiler shells often achieve 75–85% efficiency; verify spacing against classification society rules (DNV, ABS)
Rivet hole diameters assumed 1.6 mm larger than nominal rivet diameter for slip-critical design calculations