But the energy stored equals the work done = ¿Td.

The angle of twist of the tube is therefore given by

For tubes of constant thickness this reduces to

TLs xLs

4A2Gt 2AG

where s is the perimeter of the median line.

The above equations must be used with care and do not apply to cases where there are abrupt changes in thickness or re-entrant corners.

For closed sections which have constant thickness over specified lengths but varying from one part of the perimeter to another:

L 4A2G

Si S2 S3

5.7. Use of "equivalent J" for torsion of non-circular sections

The simple torsion theory for circular sections can be written in the form:

and, as stated on page 143, it is often convenient to express the twist of non-circular sections in similar form:

L GJe q where Jeq is the "equivalent J' or "effective polar moment of area" for the section in question.

Thus, for open sections:

L -ZkjdtfG GJ

eq with Jeq = Hk2db3 (= \ Zdb3 for d/b > 10). Similarly, for square tubes of closed section:

9 TLs T

L 4A2Gt G[4A2t/s] GJ

The torsional stiffness of any section, i.e. the ratio of torque divided by angle of twist per unit length, is then directly given by the value of GJ or GJeq i.e.

0 0

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