Question

A steel shaft is to be force fitted into a fixed-ended cast-iron hub. The shaft is subjected to a bending moment M, a torque T, and a vertical force P as shown. Suppose that at a point Q in the hub, the stress field is represented by: ?x = ?, ?y = 4.6, ?z = -8.3 ?xy = -4.7, ?xz = 6.45, ?yz = 11.8 (MPa) If we decide to limit the maximum shear stress in the element to 25 MPa, determine the allowed range of ?x. Note: The maximum shear stress or maximum principal shear stress is equal to one-half the difference between the largest and smallest principal stresses. Hint: Write a user-defined function, which takes ?x as input, sets up stress matrix, calculates maximum shear stress (?max) and returns y = ?max - 25 as output. Then find the value of ?x such that y = 0. Answer: -35.645 ? ?x ? 32.083 MPa

          A steel shaft is to be force fitted into a fixed-ended cast-iron hub. The shaft is subjected to a bending moment M, a torque T, and a vertical force P as shown. Suppose that at a point Q in the hub, the stress field is represented by:
?x = ?, ?y = 4.6, ?z = -8.3
?xy = -4.7, ?xz = 6.45, ?yz = 11.8 (MPa)
If we decide to limit the maximum shear stress in the element to 25 MPa, determine the allowed range of ?x.
Note: The maximum shear stress or maximum principal shear stress is equal to one-half the difference between the largest and smallest principal stresses.
Hint: Write a user-defined function, which takes ?x as input, sets up stress matrix, calculates maximum shear stress (?max) and returns y = ?max - 25 as output. Then find the value of ?x such that y = 0.
Answer: -35.645 ? ?x ? 32.083 MPa

A steel shaft is to be force fitted into a fixed-ended cast-iron hub. The shaft is subjected to a bending moment M, a torque T, and a vertical force P as shown. Suppose that at a point Q in the hub, the stress field is represented by:
?x = ?, ?y = 4.6, ?z = -8.3
?xy = -4.7, ?xz = 6.45, ?yz = 11.8 (MPa)
If we decide to limit the maximum shear stress in the element to 25 MPa, determine the allowed range of ?x.
Note: The maximum shear stress or maximum principal shear stress is equal to one-half the difference between the largest and smallest principal stresses.
Hint: Write a user-defined function, which takes ?x as input, sets up stress matrix, calculates maximum shear stress (?max) and returns y = ?max - 25 as output. Then find the value of ?x such that y = 0.
Answer: -35.645 ? ?x ? 32.083 MPa

Added by James G.

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