Question 3 - Torsion ( A composite shaft is shown in the figure below which is fixed against rotations at ends A and E. Section AC is a solid cylindrical shaft made from aluminium and Section CE is a solid cylindrical shaft made from steel Diameters of sections ACand CE are dencted as dac and dog respectively. Both sections are perfecty joined at C such that there is strain compatibility at the interface. There is a torque Ti applied at the mid-span of Section AC, and a torque T applied at the mid-span of Section CE. Directions of the applied torques are as shown in the Figure. The shear modulus of aluminium is Gat = 50 GPa and the shear modulus of steel is G = 110 GPa The dimensions of the shafts and the magnitude of applied torques are given by: T = 0.5 kNm T= 4.5 kNm dAc = 120 mm dce = 70 mm LAB = LBC = 4 m Lcp = LDe = 2 m Assume the shaft to remain linear elastic during loading. T, T T, A. T, В D E Part One: Equilibrium Write an equation of equilibrium for the structure by filling in the coefficients: TA+ Te+ Note that any expression that can be simplified to a correct equilibrium equation will be occepted. You may or may not need both unknowns. If you do not need one of the unknowns, then please enter 0 as the coefficient. DO NOT LEAVE ANY BOX EMPTY Part Two: Compatibility Write an equation of compatibility for the structure in terms of thne unknown reactions by filling in the coefficients: ]Te+[ Note that any expression that can be simpiified to a correct compatibility equation will be accepted. You may or may not need both unknowns. If you do not need one of the unknowns, then please enter O as the coefficient. DO NOT LEAVE ANY BOX EMPTY 2.
Question 3 - Torsion ( A composite shaft is shown in the figure below which is fixed against rotations at ends A and E. Section AC is a solid cylindrical shaft made from aluminium and Section CE is a solid cylindrical shaft made from steel Diameters of sections ACand CE are dencted as dac and dog respectively. Both sections are perfecty joined at C such that there is strain compatibility at the interface. There is a torque Ti applied at the mid-span of Section AC, and a torque T applied at the mid-span of Section CE. Directions of the applied torques are as shown in the Figure. The shear modulus of aluminium is Gat = 50 GPa and the shear modulus of steel is G = 110 GPa The dimensions of the shafts and the magnitude of applied torques are given by: T = 0.5 kNm T= 4.5 kNm dAc = 120 mm dce = 70 mm LAB = LBC = 4 m Lcp = LDe = 2 m Assume the shaft to remain linear elastic during loading. T, T T, A. T, В D E Part One: Equilibrium Write an equation of equilibrium for the structure by filling in the coefficients: TA+ Te+ Note that any expression that can be simplified to a correct equilibrium equation will be occepted. You may or may not need both unknowns. If you do not need one of the unknowns, then please enter 0 as the coefficient. DO NOT LEAVE ANY BOX EMPTY Part Two: Compatibility Write an equation of compatibility for the structure in terms of thne unknown reactions by filling in the coefficients: ]Te+[ Note that any expression that can be simpiified to a correct compatibility equation will be accepted. You may or may not need both unknowns. If you do not need one of the unknowns, then please enter O as the coefficient. DO NOT LEAVE ANY BOX EMPTY 2.
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter3: Torsion
Section: Chapter Questions
Problem 3.4.21P: A nonprismatic bar ABC with a solid circular cross section is loaded by distributed torques (sec...
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