Torsion of Thin-Walled Closed Cross-Sections
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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.

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Torsion of Thin-Walled Closed Cross-Sections

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Torsion of thin walled closed cross sections

Torsion of Thin-Walled Closed Cross-Sections

Objective:

To find stress formula and angle of twist

expressions for thin-walled closed section.


Torsion of thin walled closed cross sections

Torsion Formula

T = 2qAm

Closed thin-walled tube.

q = t

dMo = dF(r) = (dA)r = (tds)r

dMo = (qds)r

dAm = ½ rds

Enclosed area Am

dMo = 2qdAm


Torsion of thin walled closed cross sections

Angle of Twist 


Torsion of thin walled closed cross sections

Torsion of Non-Circulor Cross-sections

A – Elliptical Cross-Section

If a = b, the above equation reduces the

well-known equation for solid

circular section.


Torsion of thin walled closed cross sections

Rectangular Cross-Section:


Torsion of thin walled closed cross sections

t=a

L

t

l=b

Narrow Rectangular Cross-Section:


Torsion of thin walled closed cross sections

t1

L1

t1

L2

t2

l2

l1

t

t2

t

l3

b

t3

L3

a

t4

t

L4

If ‘t’ is constant then the above

becomes:

l1+l2+l3

l1+l2+l3+l4

Torsion of thin-Walled open-section:

Equivalent narrow rectangular sections with shear stress distribution.


Torsion of thin walled closed cross sections

The enD


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