HANDBOOK OF MECHANICAL DESIGN 



LENGTH OF MATERIAL FOR 90 -DEG. BENDS 



As shown in Fig. 1, when a sheet or flat bar is bent, the position of the neutral plane with respect to the outer and 

 inner surfaces will depend on the ratio of the radius of bend to the thickness of the bar or sheet. For a sharp corner, 

 the neutral plane will lie one-third the distance from the inner to the outer surface. As the radius of the bend is 

 increased, the neutral plane shifts until it reaches a position midway between the inner and outer surfaces. This 

 factor should be taken into consideration when calculating the developed length of material required for formed pieces. 



The table on the following pages gives the developed length of the material in the 90-deg. bend. The following 

 formulas were used to calculate the quantities given in the table, the radius of the bend being measured as the distance 

 from the center of curvature to the inner surface of the bend. 



1 . For a sharp corner and for any radius of bend up to T, the thickness of the sheet, the developed length L for 

 a 90-deg. bend will be 



L = 1.5708 



(«-D 



2. For any radius of bend greater than 2T, the length L for a 90-deg. bend will be 



L = 1..5708 (r + ^^ 



3. For any radius of bend between IT and 2T, the 

 value of L as given in the table was found by interpolation . 



The developed length L of the material in any bend 

 other than 90 deg. can be obtained from the following 

 formulas: 



1. For a sharp corner or a radius up to T: 



L = 0.0175 (li + t) X degrees of bend 



2. For a radius of 2T or more: 



R= Inside radius 



H ^ 



-M h- 



T= Stock thickness 



Neutral 

 line 



1t-5*>2 



irl 



T 



E 



Sharp corner R=Torless 



R=iTto2T 

 Fig. 1. 



R= 2T or more 



L = 0.0175 



5(S+|) 



X degrees of bend 



For double bends as shown in Fig. 2, if fii -|- Ss is greater than B: 



X = V2BiR, +Ri- B/2) 

 With Ri, Ri, and B known: 



fl, -t- flo - B 



""^ ^ = —rT+rT 



L = 0.0175(S, + R2)A 

 where A is in degrees and L is the developed length. 

 If Ri + Ri is less than B, as in Fig. 3, 



Y = B cosec A — {Ri + fl2)(cosec A — cotan A) 

 The value of X when B is greater than Ri + Ri will be 



X = B cot A -h {Ri + 7S2) (cosec A - cotan A) 

 The total developed length L required for the material in the straight section plus that in the two arcs will be 



L = Y + 0.0175(^1 4- R2)A ' 



To simplify the calculations, the table on this page gives the equations for X, Y, and the developed length for 

 various common angles of bend. The table on following pages gives L for values of R and T for 90-deg. bends. 



EQUATIONS FOR X, Y, AND DEVELOPED LENGTHS 



