Bend allowance and blank length

Bend allowance (BA) is the length of the neutral axis within the bent region. It is added to the flat lengths to get the developed length (blank length) of the sheet.

$$BA = \frac{\pi}{180}\,\theta\,(R + K\,t)$$

where $\theta$ = bend angle in degrees, R = inside bend radius, t = thickness, K = location of the neutral axis from the inside surface (0.33 for R < 2t, 0.5 for R > 2t).

Data

t = 2 mm, R = 5 mm, $\theta$ = 90°, K = 0.5, flats 60 mm, 30 mm and 30 mm.

R/t = 2.5 > 2, so K = 0.5 is acceptable.

Bend allowance for one bend

$$\begin{aligned} BA &= \frac{\pi}{180}\times 90\times(5 + 0.5\times 2) \\ &= \frac{\pi}{2}\times 6 = 9.425\ \text{mm} \end{aligned}$$

Developed length

$$\begin{aligned} L &= 60 + 30 + 30 + 2\times BA \\ &= 120 + 18.85 = 138.85\ \text{mm} \end{aligned}$$

Answer: bend allowance = 9.43 mm per bend; blank length = 138.85 mm (about 139 mm).