2.3 Sheet Metal Layout: Bend Allowance, Setback & Forming
Key Takeaways
- During sheet metal bending, outer fibers undergo tension (stretching) and inner fibers undergo compression (shrinking), while the neutral axis experiences zero length change at approximately 44.5% of sheet thickness.
- Bend Allowance (BA) is calculated using the standard empirical formula: BA = [(0.01743 × R) + (0.0078 × T)] × N, where R is inside radius, T is thickness, and N is bend angle in degrees.
- Setback (SB) is the distance from the mold point to the bend tangent line, calculated as SB = (R + T) × K, where K = tan(Bend Angle / 2); for a 90° bend, K = 1.0, making SB = R + T.
- The sight line is always marked exactly one inside bend radius (1R) from the bend tangent line positioned under the brake radius nose bar.
- Corner relief holes with a minimum diameter equal to the inside bend radius (D = R or D >= T) must be drilled at intersecting bend tangent lines to prevent severe stress concentration and corner cracking.
Sheet Metal Layout: Bend Allowance, Setback & Forming
FAA Airframe Exam Focus: Sheet metal layout calculations require exact geometric calculations for Flat Layout ($FL$), Bend Allowance ($BA$), Setback ($SB$), K-Factors, Sight Lines, and Corner Relief Holes. Mastery of these formulas is tested extensively on the FAA Airframe Knowledge and Practical Exams.
1. Mechanics of Bending & The Neutral Axis
When a flat sheet of aircraft aluminum is bent in a bending brake or over a form block, severe mechanical stress gradients develop across its cross-section:
CROSS-SECTION OF BENT SHEET METAL:
┌───────────────────────────────────────────┐ ◄── Outer Surface (TENSION / Stretching)
│░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░│
├- - - - - - - - - - - - - - - - - - - - - -┤ ◄── NEUTRAL AXIS (0.445T from inside)
│▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒│
└───────────────────────────────────────────┘ ◄── Inner Surface (COMPRESSION / Shrinking)
▲
│◄──────── Inside Bend Radius (R) ────────►
- Outer Surface (Tension): The metal fibers outside the center are stretched and thinned.
- Inner Surface (Compression): The metal fibers on the inside of the curve are compressed and thickened.
- Neutral Axis: An imaginary plane located within the sheet where the metal is neither stretched nor compressed. In aluminum alloys, the neutral axis lies approximately $0.445 \times T$ ($44.5%$ of sheet thickness) from the inside radius surface.
2. Bend Allowance ($BA$) Calculation & Empirical Formula
Bend Allowance ($BA$) represents the exact curved length of material consumed between the two Bend Tangent Lines (BTL) around the bend:
where:
- $R$ = Inside bend radius (inches)
- $T$ = Sheet metal thickness (inches)
- $N$ = Number of degrees in the bend angle ($N = 90^\circ$ for a right angle)
- Constant $0.01743 = \frac{2\pi}{360} = \frac{\pi}{180}$ (arc length per degree per unit radius)
- Constant $0.0078 = 0.4475 \times 0.01743$ (accounting for the neutral axis position)
BEND GEOMETRY & TERMINOLOGY:
Mold Line 1
│
▼ Mold Point (MP)
┆ / ◄── Setback (SB) = (R + T) * K
Flange 1 ┆ *
(Flat) ┆ / ┆
┆ / ┆
┆ BTL 1 / ┆
───────────┼──────────* ┆ ◄── Setback (SB)
│ ( ┆
│ BA ( ┆
│ Arc ( ┆
│ (BTL 2┆
│ *────┼─────────────────────── ◄── Flange 2 (Flat)
│ / ┆
│ / ┆
│ ▼ ▼
│ Bend Mold Line 2
│ Radius
│ (R)
3. Setback ($SB$) and K-Factor Calculations
Setback ($SB$) is the distance from the Mold Point (MP) (intersection of the two outer mold lines) to the Bend Tangent Line (BTL):
where $K$ is the K-factor, determined by the bend deflection angle:
Setback Behavior by Bend Type
- $90^\circ$ Bend: $K = \tan(45^\circ) = 1.0 \implies \mathbf{SB = R + T}$
- Open Bend ($<90^\circ$ deflection): $K < 1.0 \implies SB < R + T$
- Closed Bend ($>90^\circ$ deflection): $K > 1.0 \implies SB > R + T$
| Bend Angle ($N$) | K-Factor ($K = \tan(N/2)$) | Setback Formula ($SB$) |
|---|---|---|
| $30^\circ$ | $0.2679$ | $SB = (R + T) \times 0.2679$ |
| $45^\circ$ | $0.4142$ | $SB = (R + T) \times 0.4142$ |
| $60^\circ$ | $0.5774$ | $SB = (R + T) \times 0.5774$ |
| $90^\circ$ | $1.0000$ | $\mathbf{SB = R + T}$ |
| $120^\circ$ | $1.7321$ | $SB = (R + T) \times 1.7321$ |
| $135^\circ$ | $2.4142$ | $SB = (R + T) \times 2.4142$ |
4. Flat Pattern Layout ($FL$) Calculation
To cut a flat sheet that will form into precise finished flange dimensions after bending, calculate the Flat Layout ($FL$) length:
Single $90^\circ$ Bend (L-Angle Flange)
Double $90^\circ$ Bend (U-Channel Section)
Comprehensive Numerical Worked Example
Problem: Calculate the flat layout pattern length ($FL$) for an aluminum channel made from $0.050"$ 2024-T3 sheet with an inside bend radius $R = 0.150"$, two $90^\circ$ bends, outer flange legs of $1.250"$ each, and an overall outer web dimension of $3.500"$.
U-CHANNEL SPECIFICATIONS:
Flange 1 = 1.250" Flange 2 = 1.250"
┌───┐ ┌───┐
│ │ │ │
│ │ │ │
│ └───┐ ┌───┘ │
│ └─────────────────────────────┘ │
└─────────────────────────────────────────────┘
Web (Outer) = 3.500"
T = 0.050", R = 0.150", Bend Angles = 90°
- Calculate Setback ($SB$):
- Calculate Bend Allowance ($BA$) per bend:
- Calculate Flat Sections:
- $\text{Flat } 1 = \text{Flange } 1 - SB = 1.250" - 0.200" = 1.050"$
- $\text{Flat Web} = \text{Web} - (2 \times SB) = 3.500" - 0.400" = 3.100"$
- $\text{Flat } 2 = \text{Flange } 2 - SB = 1.250" - 0.200" = 1.050"$
- Sum Flat Layout Length ($FL$):
5. Sight Line Layout & Bending Brake Setup
When inserting sheet metal into a cornice brake or box-and-pan brake, the technician cannot see the bend tangent lines directly underneath the nose bar. To position the bend precisely:
SIGHT LINE IN BENDING BRAKE:
Brake Clamping Leaf / Nose Bar
┌──────────────┐
│ │
│ │
│ (R) │
──────────────────┴──────────────*─────────────── ◄── Sight Line (Marked on Sheet)
◄── Clamped in Brake ──► │
◄──── Flat 1 ────►│◄─── 1R ─────►│ ◄── BTL 1 (Bend Tangent Line)
│◄──── BA ────►│
- Sight Line Rule: The sight line is always drawn on the flat layout one inside bend radius ($1R$) from the bend tangent line that is clamped under the brake radius nose bar.
- Brake Operation: Align the sight line directly with the forward edge of the brake nose bar radius. When the brake clamping leaf is locked, the bend tangent line ($BTL$) is positioned exactly where the curvature begins.
6. Grain Orientation & Minimum Bend Radii
During rolling at the aluminum mill, alloy grains elongate in the direction of sheet rolling:
GRAIN DIRECTION vs. BEND CRACKING:
[ BEST: 90° Across Grain ] [ WORST: Parallel with Grain ]
Bend Line Bend Line
│ ═════════
═══════╪═══════ ◄── Grain Direction ───────═════════─────── ◄── Grain Direction
═══════╪═══════ ───────═════════───────
│
Maximum Ductility, Severe Tensile Cracking Along
No Cracking Grain Boundaries!
- Rule of Forming: Always bend perpendicular ($90^\circ$) across the grain of the metal whenever possible. If layout requires angular bends, keep bends at $45^\circ$ to the grain. Never bend parallel to the grain, as outer fiber tensile stresses cause grain boundary separation and cracking.
- Minimum Bend Radius ($R_{min}$): The sharpest inside radius to which an alloy sheet can be bent without cracking. Harder tempers (-T6) require larger bend radii ($3T$ to $6T$), whereas annealed sheets (-O) can be formed over tight radii ($1T$ to $2T$).
7. Corner Relief Holes (Stress Relieving)
When two flanged bends intersect at a $90^\circ$ corner (e.g., box corners, rib flanges, bulkheads), the intersecting bend tangent lines concentrate extreme shearing stresses during forming:
CORNER RELIEF HOLE LAYOUT:
Flange 1 ─────────────────────────┐
│
- - - - - - - - - - - - - - BTL 1 │
│
─────────────────────────────┐ │
│ (O)│ ◄── Relief Hole: Center at BTL Intersection!
│ │ Diameter >= Inside Bend Radius (D >= R)
- - - - - - - - - - - - BTL 2│ │
│ │
Flange 2 ────────────────────┘ │
- Relief Hole Purpose: Eliminates sharp square inside corners, replacing stress-concentrating notches with a smooth radiused circle that prevents corner tearing.
- Diameter Sizing: The hole diameter must be at least equal to the inside bend radius: $D_{\text{relief}} = R$ (or $D \ge T$, with $1/8"$ ($0.125"$) being standard shop minimum).
- Location: The center of the relief hole is drilled precisely at the intersection point of the inner bend tangent lines ($BTL$).
Where does the neutral axis lie in an aluminum alloy sheet during a bending operation, and what stress does it experience?
What is the setback (SB) for a 90-degree bend in an aluminum sheet with a thickness of 0.063 inches and an inside bend radius of 0.187 inches?
When marking an aluminum flat layout sheet for bending in a cornice brake, how far from the bend tangent line must the sight line be drawn?
Where must the center of a corner relief hole be drilled when laying out an intersecting sheet metal box corner?