Physics,2.01x

posted by .

The shaft ACB, of constant outer diameter 2R and length 2L, is fixed to walls at both ends A and B. The left half of the shaft (AC) is solid, while the right half (CB) is hollow, with an inner diameter 2√R. The right half, CB, is subjected to a uniform distributed torque per unit length q0[N⋅m/m]. The material of the shaft is linear isotropic elastic with shear modulus G.
Obtain symbolic expressions in terms of R, G, L, q0, and x for the quantities below. (In your answers, leave rationals as fractions and enter q0 and π as q_0 and pi, respectively.)

EQ2_1_1

The x-component of the reaction torques at A and B:
TxA=
TxB=

The axial torque resultant in the bar T(x), and the position x0 along the shaft where this torque resultant goes to zero (T(x0)=0):
for0≤x≤L,T(x)=
forL≤x≤2L,T(x)=
T(x0)=0 at x0=

EQ2_1_3

The maximum absolute value of the shear stress in the shaft (τmax) and its location (rτmax, xτmax):
τmax=
rτmax=
xτmax=

EQ2_1_4

the maximum value of the rotation field φ(x) along the shaft (φmax), and the position along the shaft where the maximum rotation occurs (xφmax):
φmax=
xφmax=

  • Mechanics of Solids 2.01x -

    Q2_1_1
    TXC=-t_0*L

    Q2=1_2
    a) 0<=x<L ===>> (2*t_0*L)/(pi*G_0*R4)

    b)L<=x<=3L =>>(2*t_0*(2*L-))/pi*G_0*R^4)

    c) x=2*L

  • Physics,2.01x -

    Help please!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. applied mechanics

    A solid shaft of 65mm outside diameter and a hollow shaft of 85mm outside diameter are connected by 6 bolts with the mean pitch of thread being 155mm. The shear stress due to the torque on the shafts is equal to the shear stress on …
  2. Torque and shear stress

    A solid shaft of 65mm outside diameter and a hollow shaft of 85mm outside diameter are connected by 6 bolts with the mean pitch of thread being 155mm. The shear stress due to the torque on the shafts is equal to the shear stress on …
  3. physic

    A solid shaft of 65mm outside diameter and a hollow shaft of 85mm outside diameter are connected by 6 bolts with the mean pitch of thread being 155mm. The shear stress due to the torque on the shafts is equal to the shear stress on …
  4. Physics

    A solid shaft of 65mm outside diameter and a hollow shaft of 85mm outside diameter are connected by 6 bolts with the mean pitch of thread being 155mm. The shear stress due to the torque on the shafts is equal to the shear stress on …
  5. applied mechanics

    A solid shaft of 65mm outside diameter and a hollow shaft of 85mm outside diameter are connected by 6 bolts with the mean pitch of thread being 155mm. The shear stress due to the torque on the shafts is equal to the shear stress on …
  6. physics

    A hollow steel shaft has an external diameter of 120 mm and is 10 mm thick. It is coupled to a solid shaft of the same material, 100 mm in diameter. If the length of the hollow shaft is 960 mm, find the length of the solid shaft, so …
  7. Physics,2.01x

    The shaft ABC is a solid circular cylinder of constant outer diameter 2R and length 3L. The shaft is fixed between walls at A and C and it is composed of two segments made of different materials. The left third of the shaft (AB) is …
  8. MITx: 2.01x

    Q2_1: QUIZ 2, PROBLEM #1 The shaft ABC is a solid circular cylinder of constant outer diameter 2R and length 3L. The shaft is fixed between walls at A and C and it is composed of two segments made of different materials. The left third …
  9. MIT 2.01x

    The shaft ABC is a solid circular cylinder of constant outer diameter 2R and length 3L. The shaft is fixed between walls at A and C and it is composed of two segments made of different materials. The left third of the shaft (AB) is …
  10. Physics

    Hi everybody! can someone please help me with this problem?

More Similar Questions