![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 9.5in
Thickness, cap: tcap 0.40in
Thickness, web: tweb 0.08in
Width web: bweb 4.0in
Area: A 4.902in2
Moment of Inertia: Ixx 84.36in4
Radius of gyration: rx
Ixx
A
4.15 in
CUp 4.6in
CLow 4.9in
Material: 2014-T3 Aluminum Extrusion [3].
Elastic Modulus(1): E 10.8103ksi
Yield Strength: Fty 58ksi
Offset strain: ε0.2 0.2%
Ultimate Tensile Strength: Ftu 64ksi
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](https://image.slidesharecdn.com/plasticbendingusingcozzonemethod-140827020913-phpapp01/85/Plastic-bending-using-cozzone-method-1-320.jpg)
![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
2n 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 a1Δe a2Δe2 6Ftu
εu
2
61.34ksi
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 64.00ksi
fbu fm Kb 1fo 68.91ksi
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
17.22in3 Mu Sxxfbu 98.86kipft
Julio C. Banks, P.E. page 2 of 2](https://image.slidesharecdn.com/plasticbendingusingcozzonemethod-140827020913-phpapp01/85/Plastic-bending-using-cozzone-method-2-320.jpg)
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 9.5in Thickness, cap: tcap 0.40in Thickness, web: tweb 0.08in Width web: bweb 4.0in Area: A 4.902in2 Moment of Inertia: Ixx 84.36in4 Radius of gyration: rx Ixx A 4.15 in CUp 4.6in CLow 4.9in Material: 2014-T3 Aluminum Extrusion [3]. Elastic Modulus(1): E 10.8103ksi Yield Strength: Fty 58ksi Offset strain: ε0.2 0.2% Ultimate Tensile Strength: Ftu 64ksi 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 2n 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 a1Δe a2Δe2 6Ftu εu 2 61.34ksi 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 64.00ksi fbu fm Kb 1fo 68.91ksi 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 17.22in3 Mu Sxxfbu 98.86kipft Julio C. Banks, P.E. page 2 of 2