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Application of ‘Torque - angle of rotation relations’to statically
determinate and statically
indeterminate structuresRemember for Statically indeterminate structures you need both ‘Torque - angle of rotation relations’ and Compatibility equation
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Lec notes 3, sl 19-25
A hollow cylindrical steel shaft is 1.5 m long and has inner and outer diameters 40mm and 60mm. What torque should be applied to the end of the shaft to produce a twist of 2 degrees? Shear modulus is 77 GPa.
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Solution
Using eqn from sl 14 and that
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The shaft is attached to fixed supports
at both ends, and a 120 N.m torque is
applied at its midsection.Determine the torque exerted on the
shaft by each of the supports.
Divide the shaft into two components which
must have compatible deformations and
observing that portions AC and CB of the shaft
are twisted in opposite senses:
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ϕ =ϕ1 +ϕ2 =TAL1 J1G− TBL2 J2G= 0 | ||
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4. Example 3.3, Beer et al (2015)
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5. Example 3.9, Beer et al (2015)
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6. Example 3.12, Beer et al (2015)
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