Statically Indeterminate Torsional Members

statically indeterminate

when all internal and reaction torques cannot be determined using only equilibrium equations

 

solution steps for analyzing statically indeterminate torsional members

1. generate equilibrium equations (ΣF, ΣM)
2. generate compatibility equations (constrains)
3. generate torque-displacement relations (φ = TL / GJ)
4. simultaneously solve all equations

 

recall the sign convention

An internal torque is positive when its vector points away from the cut section and negative when its vector points toward the section.

 

standard forms

T = T1 + T2 φ1 = φ2
T = T1 + T2 φ1 + φ2 = 0