Torsion of Thin-Walled Closed Cross-Sections
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Dr. Ali Al-Gadhib orsion of Thin-Walled Closed Cross-Sections Objective: To find stress formula and angle of twist expressions for thin-walled closed section. t q avg
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Torsion of Thin-Walled Closed Cross-Sections. Objective:. To find stress formula and angle of twist expressions for thin-walled closed section. Torsion Formula. T = 2qA m. Closed thin-walled tube. q = t. dM o = dF(r) = ( dA)r = (tds)r. dM o = (qds)r. dA m = ½ rds. - PowerPoint PPT Presentation
Transcript of Torsion of Thin-Walled Closed Cross-Sections
Dr. Ali Al-Gadhib
Torsion of Thin-Walled Closed Cross-Sections
Objective:
To find stress formula and angle of twistexpressions for thin-walled closed section.
tq avg
Dr. Ali Al-Gadhib
Closed thin-walled tube.
Enclosed area Am
q = t
dMo = dF(r) = (dA)r = (tds)r
dMo = (qds)r
dAm = ½ rds
dMo = 2qdAm
mo qdA2dMT
T = 2qAm
mA2
Tq
tA2
T
m
Torsion FormulaTorsion Formula
Dr. Ali Al-Gadhib
Angle of Twist Angle of Twist
Dr. Ali Al-Gadhib
A – Elliptical Cross-SectionA – Elliptical Cross-Section
If a = b, the above equation reduces the well-known equation for solidcircular section.
Dr. Ali Al-Gadhib
Rectangular Cross-Section:Rectangular Cross-Section:
Dr. Ali Al-Gadhib
Narrow Rectangular Cross-Section:Narrow Rectangular Cross-Section:
t
l=b
L
t=a
3
max
lt3
1J
where,JG
Ttφ
J
Ttτ
Dr. Ali Al-Gadhib
Torsion of thin-Walled open-section:Torsion of thin-Walled open-section:
Equivalent narrow rectangular sections with shear stress distribution.
l1 l2
t1
t2
t
l3
a
b
t1
t2
t3t4
L1
L2
L3
L4
J
Ttτ
tlJJ
J
tTτ
minmax
3ii3
1i
11i
If ‘t’ is constant then the abovebecomes:
t
t
l1+l2+l3
l1+l2+l3+l4
Dr. Ali Al-Gadhib
