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MathCAD - Plastic Bending Using The 
Cazzone Method.xmcd 
Plastic Bending Strength Analysis Using The Cazzone Method 
by Julio C. Banks, MSME, PE 
Reference: 
1. Analysis and Design of Flight Vehicles Structures by Bruhn; Page C3.3 
2. Cozzone, F. P. Bending in the Plastic Region, Journal of the Aeronautical 
Sciences, Vol. 10, No. 5, May 1942, 1943. 
3. MMPDS-01 
4. "Plastic Bending Using Cozzone Method" by Toshihiro Tanabe, Edited by Julio 
C. Banks, PE 
The solution of plastic bending will utilize Cozzone method found in references 1 and 2. 
Geometry: 
Height: h  9.5in 
Thickness, cap: tcap  0.40in 
Thickness, web: tweb  0.08in 
Width web: bweb  4.0in 
Area: A  4.902in2 
Moment of Inertia: Ixx  84.36in4 
Radius of gyration: rx 
Ixx 
A 
  4.15 in 
CUp  4.6in 
CLow  4.9in 
Material: 2014-T3 Aluminum Extrusion [3]. 
Elastic Modulus(1): E  10.8103ksi 
Yield Strength: Fty  58ksi 
Offset strain: ε0.2  0.2% 
Ultimate Tensile Strength: Ftu  64ksi 
Ultimate Elongation(2): εu  12% 
Notes 
1. Ref. 3, page 3-35 
2. Ref. 3, page 3-56, Fig. 3.2.1.1.6(c) 
Julio C. Banks, P.E. page 1 of 2
MathCAD - Plastic Bending Using The 
Cazzone Method.xmcd 
Δe 
Ftu 
E 
  0.59% 
eP  εu  Δe  11.4% 
n 
log 
eP 
ε0.2 
 
 
 
  41.08 
log 
Ftu 
Fty 
 
 
 
ORIGIN  0 
a 
n 
2n  1 
2   
 
 
 2 1 
eP 
3 
εu 
 
(n  1) 
(n  2) 
 
eP   
1 
3 
 
T 
 
 
aT  1.628  10 3 1.114  10 1 3.333  10 1  
fo a0  a1Δe  a2Δe2 6Ftu 
εu 
2 
 
 
   61.34ksi 
For I-sections [1] η 
tcap 
h 
  0.042 η 
tweb 
bweb 
  0.020 
From Ref. 1, Pages C3.3.11, Fig. C3.8: Kb  1.08 
From Ref. 1, Pages C3.4, C3.11, Table C3.2: fm  Ftu  64.00ksi 
fbu  fm  Kb  1fo  68.91ksi 
Determine the ultimate tensile up-bending moment 
The up-bending of the main spar of the aircraft wing causes the lower portion of the 
cross section to be in tension. 
Sxx 
Ixx 
CLow 
  17.22in3 Mu  Sxxfbu  98.86kipft 
Julio C. Banks, P.E. page 2 of 2

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Plastic bending using cozzone method

  • 1. MathCAD - Plastic Bending Using The Cazzone Method.xmcd Plastic Bending Strength Analysis Using The Cazzone Method by Julio C. Banks, MSME, PE Reference: 1. Analysis and Design of Flight Vehicles Structures by Bruhn; Page C3.3 2. Cozzone, F. P. Bending in the Plastic Region, Journal of the Aeronautical Sciences, Vol. 10, No. 5, May 1942, 1943. 3. MMPDS-01 4. "Plastic Bending Using Cozzone Method" by Toshihiro Tanabe, Edited by Julio C. Banks, PE The solution of plastic bending will utilize Cozzone method found in references 1 and 2. Geometry: Height: h  9.5in Thickness, cap: tcap  0.40in Thickness, web: tweb  0.08in Width web: bweb  4.0in Area: A  4.902in2 Moment of Inertia: Ixx  84.36in4 Radius of gyration: rx Ixx A   4.15 in CUp  4.6in CLow  4.9in Material: 2014-T3 Aluminum Extrusion [3]. Elastic Modulus(1): E  10.8103ksi Yield Strength: Fty  58ksi Offset strain: ε0.2  0.2% Ultimate Tensile Strength: Ftu  64ksi Ultimate Elongation(2): εu  12% Notes 1. Ref. 3, page 3-35 2. Ref. 3, page 3-56, Fig. 3.2.1.1.6(c) Julio C. Banks, P.E. page 1 of 2
  • 2. MathCAD - Plastic Bending Using The Cazzone Method.xmcd Δe Ftu E   0.59% eP  εu  Δe  11.4% n log eP ε0.2      41.08 log Ftu Fty    ORIGIN  0 a n 2n  1 2      2 1 eP 3 εu  (n  1) (n  2)  eP   1 3  T   aT  1.628  10 3 1.114  10 1 3.333  10 1  fo a0  a1Δe  a2Δe2 6Ftu εu 2      61.34ksi For I-sections [1] η tcap h   0.042 η tweb bweb   0.020 From Ref. 1, Pages C3.3.11, Fig. C3.8: Kb  1.08 From Ref. 1, Pages C3.4, C3.11, Table C3.2: fm  Ftu  64.00ksi fbu  fm  Kb  1fo  68.91ksi Determine the ultimate tensile up-bending moment The up-bending of the main spar of the aircraft wing causes the lower portion of the cross section to be in tension. Sxx Ixx CLow   17.22in3 Mu  Sxxfbu  98.86kipft Julio C. Banks, P.E. page 2 of 2