Solid Mechanics-I (ME-202)
CHAPTER-5
INDETERMINANCY
AND
NON-CIRCULAR CROSS-SECTIONS
Course Teacher: Dr Maaz Akhtar (Associate Professor)
Mechanical Engineering Department
, STATICALLY INDETERMINATE SYSTEM
• Consider a prismatic shaft fixed from both ends as shown below:
• To determine reactions at fixed support,
equilibrium equations are applied
T = 𝑇𝐴 + 𝑇𝐵
• Since we have only one equation and two
unknowns, hence this problem is an
example of indeterminate systems
Solid Mechanics-I 15 Torsion
, STATICALLY INDETERMINATE SYSTEM
𝑇 − 𝑇𝐴 − 𝑇𝐵 = 0
𝜙𝐴 𝐵 =0
𝑇𝐿
𝜙=
𝐺𝐽
𝑇𝐴 𝐿𝐴𝐶 𝑇𝐵 𝐿𝐵𝐶
− =0
𝐺𝐽 𝐺𝐽
𝑇𝐿𝐵𝐶
𝑇𝐴 =
𝐿
𝑇𝐿𝐴𝐶
𝑇𝐵 =
𝐿
Solid Mechanics-I 15 Torsion
CHAPTER-5
INDETERMINANCY
AND
NON-CIRCULAR CROSS-SECTIONS
Course Teacher: Dr Maaz Akhtar (Associate Professor)
Mechanical Engineering Department
, STATICALLY INDETERMINATE SYSTEM
• Consider a prismatic shaft fixed from both ends as shown below:
• To determine reactions at fixed support,
equilibrium equations are applied
T = 𝑇𝐴 + 𝑇𝐵
• Since we have only one equation and two
unknowns, hence this problem is an
example of indeterminate systems
Solid Mechanics-I 15 Torsion
, STATICALLY INDETERMINATE SYSTEM
𝑇 − 𝑇𝐴 − 𝑇𝐵 = 0
𝜙𝐴 𝐵 =0
𝑇𝐿
𝜙=
𝐺𝐽
𝑇𝐴 𝐿𝐴𝐶 𝑇𝐵 𝐿𝐵𝐶
− =0
𝐺𝐽 𝐺𝐽
𝑇𝐿𝐵𝐶
𝑇𝐴 =
𝐿
𝑇𝐿𝐴𝐶
𝑇𝐵 =
𝐿
Solid Mechanics-I 15 Torsion
