A composite shaft with a total length L, where L = L1 + L2, is created by connecting two shafts of equal diameter (d) at joint B. The shaft segment AB is characterized by a shear modulus G1, while segment BC has a shear modulus G2. An external torque Tg is applied at joint B, and the ends A and C are immobilized to prevent rotation. (a) Using Displacement Method, determine a formula for os, which represents the angle of rotation at joint B. (b) Calculate expressions for T1 and T2, representing the internal torques in segments AB and BC, respectively. (c) Find the maximum shear stress in each segment. Express all responses in terms of the given torque Ty and the physical parameters of the composite shaft: d, G1, G2, L1, and L2.
A composite shaft with a total length L, where L = L1 + L2, is created by connecting two shafts of equal diameter (d) at joint B. The shaft segment AB is characterized by a shear modulus G1, while segment BC has a shear modulus G2. An external torque Tg is applied at joint B, and the ends A and C are immobilized to prevent rotation.
(a) Using Displacement Method, determine a formula for os, which represents the angle of rotation at joint B.
(b) Calculate expressions for T1 and T2, representing the internal torques in segments AB and BC, respectively.
(c) Find the maximum shear stress in each segment. Express all responses in terms of the given torque Ty and the physical parameters of the composite shaft: d, G1, G2, L1, and L2.
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