Riveted Joint
Calculate rivet shear capacity, plate tear-out, bearing pressure, minimum pitch, and joint efficiency for single or double shear riveted connections
Inputs
Formula Interpretation
Riveted Joint — Lap & Pitch
Rivet Shear Capacity — Single Shear
For a lap joint, each rivet has one shear plane. The cross-sectional area resisting shear is (π/4)d². Multiplied by the allowable shear stress τ (MPa) this gives the maximum tensile load the rivet can transmit. Note: d is the nominal rivet diameter (the shank expands to fill the hole during riveting, so the nominal diameter governs).
Rivet Shear Capacity — Double Shear
A butt joint with two cover plates creates two shear planes per rivet, doubling the shear capacity. The factor 2 in front reflects the two shear planes — each carrying half the load.
Plate Tear-out at Hole Row
The net cross-sectional area of the plate between two adjacent rivet holes is (p − d₁)·t. If the tensile stress in this net section reaches σ₁, the plate tears. The pitch p must be large enough so (p − d₁)·t·σ₁ ≥ W_shear, keeping plate tear-out from being the limiting failure mode.
Bearing Pressure on Hole Wall
The projected bearing area between rivet shank and hole wall is d·t (diameter × thickness). If the contact stress reaches σ_c (allowable bearing stress), the hole or rivet surface crushes. Because the rivet fills the hole, d (not d₁) is used.
Plate Efficiency
The plate efficiency is the ratio of the net section width (p − d₁) to the gross pitch p. It equals the fraction of the plate cross-section remaining after drilling the hole. A higher pitch p improves plate efficiency.
Rivet Efficiency
The rivet efficiency compares the shear capacity of the rivets (per pitch length) to the gross tensile capacity of the plate. n is the number of shear planes. Setting η_plate = η_rivet gives the balanced design condition for maximum joint efficiency.
Knowledge Points
- •During riveting, the hot rivet shank is hammered to completely fill the hole gap. For safety calculations, the nominal rivet diameter d (not the hole diameter d₁) is used in shear and bearing formulas. This is conservative and standard in textbook practice.
- •A riveted joint can fail by rivet shearing (①②), plate tearing at the hole row (③), or bearing/crushing of the hole wall (④). The joint strength is limited by the weakest mode. Good design balances all three so they are approximately equal.
- •Drilling holes necessarily weakens the plate. η < 1 always. The joint efficiency is the minimum of plate efficiency and rivet efficiency: η = min(η_plate, η_rivet). To maximise η, set η_plate = η_rivet by optimising pitch p and diameter d.
- •For practical rivet design: rivet diameter d ≈ √(50t) − 4 mm; pitch p ≈ 3d; rivet hole diameter d₁ ≈ d + 1.0 to 1.5 mm; rivet length (excluding head) ≈ 1.3–1.6× total clamped thickness. These rules give a starting point before strength verification.
Worked Example
A lap joint (single shear) uses plate thickness t = 12 mm, rivet nominal diameter d = 16 mm, rivet hole diameter d₁ = 17 mm. Allowable plate tensile stress σ₁ = 50 MPa, allowable rivet shear stress τ = 40 MPa. Find the required rivet pitch p.
Knowns
- • Plate thickness: t = 12 mm
- • Rivet diameter: d = 16 mm; hole diameter: d₁ = 17 mm
- • σ₁ = 50 MPa (plate tension); τ = 40 MPa (rivet shear)
- • Joint type: single shear (lap joint)
Solution
Step 1 — Rivet shear capacity (Formula ①)
Step 2 — Minimum pitch from plate tear-out (Formula ③)
Result: W_shear ≈ 8040 N. Minimum pitch p ≥ 30.4 mm to prevent plate tear-out. Use p = 32 mm in practice (rounded up to next standard size).
Extended Knowledge
- •Riveting was the dominant joining method in steel structures until the 1960s. Welding offers higher efficiency (η → 1) but requires skilled operators and heat management. High-strength friction-grip bolts have largely replaced rivets in modern steel construction because they are faster, quieter, and inspectable.
- •Hot-driven rivets develop clamping force as they cool and shrink. This clamping introduces friction between plates, which partly carries the load before the rivet shank actually bears. Cold-driven and snap rivets produce less pre-tension.
- •Boiler and pressure vessel codes specify minimum joint efficiency η ≥ 70–80% for main seams. Multiple rows of rivets (double, triple row) increase η by distributing load across more rivets per pitch. The rivet rows are usually staggered to avoid aligning weak sections.
- •Aluminium alloy rivets (2117, 2024, 7050 series) are used extensively in aircraft skins. Flush (countersunk) rivets reduce aerodynamic drag. Tolerances are extremely tight — hole diameter is typically d + 0.05 mm — and interference-fit installation induces compressive residual stress that improves fatigue life.
- •Setting η_plate = η_rivet gives (p − d₁)/p = n(π/4)d²τ / (ptσ). Solving simultaneously with p ≥ 3d and d₁ ≈ d + 1 mm yields the optimal pitch and diameter. In practice, use empirical rules first, then verify efficiency and adjust.