Net angle of twist at the free end - steel shaft, Mechanical Engineering

Net angle of twist at the free end - steel shaft:

 The stepped steel shaft illustrated in Figure is subjected to a torque (T) at the free end and a torque (2T) in the opposite direction at the junction of the two sizes.

What is the net angle of twist at the free end, if the maximum shear stress in shaft is limited to 70 N/mm2?

Suppose the modulus of rigidity to the 0.84 × 105 N/mm2.

227_Net angle of twist at the free end.png


Torque at C = T (anticlockwise)

Torque at B = 2T (clockwise)

 Maximum shear stress, τm = 70 N/mm2

G = 0.84 × 105 N/mm2

Assume θ be the angle of twist at C.

Free Body Diagram

A reaction torque shall be induced at section A. Consider this torque be TA clockwise. Then total torque should vanish for equilibrium, thus,

TA  + TB  - TC  = 0


∴          TA  = TC  - TB  = T - 2T = - T

which means torque at A is equal to T in magnitude but opposite the supposed clockwise direction. TA is equal to T anticlockwise as illustrated in free body diagram of Figure .

1035_Net angle of twist at the free end1.png

Figure: Free Body Diagram

The situation is that the equal torques T (but opposite in direction behaves on two portions). The similar magnitude of torque in BC shall induce higher stress than in AB because of diameters as illustrated in Figure. Hence, T should be determined from the portion BC.

T =  (π /16) τm d 3  = (π /16) × 70 × (50)3  = 17.2 × 105  Nmm

J AB=  (π /32 )× (100)4  = 982 × 105  mm4

J BC =  (π/32 ) × (50)4  = 6.14 × 105  mm4

The angle of twist is the difference of twist of C w.r.t. B and the twist of B with respect to A. (As two are in opposite directions).

θBC = T LBC / G J BC       (anticlockwise)

θ AC= T LAB / GJ AB           (clockwise)

θ=θAC   =   (T /G) [LBC/ J BC - LAB / J AB ]          (anticlockwise)

849_Net angle of twist at the free end2.png

= (17.2 × 105 /0.84 × 105)[   (1.8 × 103/ 6.14 × 105 ) - (1.2 × 103  / 98.2 × 105) ]?

= 20.5 [0.293 - 0.0122] × 10- 2

= 0.058 rad. = 3.3 deg.

or θ = 3o 18′

Posted Date: 1/21/2013 2:57:20 AM | Location : United States

Related Discussions:- Net angle of twist at the free end - steel shaft, Assignment Help, Ask Question on Net angle of twist at the free end - steel shaft, Get Answer, Expert's Help, Net angle of twist at the free end - steel shaft Discussions

Write discussion on Net angle of twist at the free end - steel shaft
Your posts are moderated
Related Questions
(a) What are fluids? How are they classified? (b) Classify the several kinds of manometers. (c) Define the following (d) Define metacenter (1) Steady flow (2) Unsteady

Illustrated about the term bending moment? Bending Moment The critical section for bending moment for masonry or concrete block walls is half-way between the centre line and

Relationships among VM, Virtual Prototyping, the Virtual Enterprise Virtual Manufacturing (VM) VM is a synthetic, integrated manufacturing environment exercised to improve

Elastic Limit: Sol. : When external force acts on the body, the body tends to undergo some deformation. If external force is removed and body comes back to its original shap

Q. Illustrate Wood and Silica Flour? Wood Flour : It is ground wood particles or other cellulose materials such as grain hulls. They serve the same purpose as cereals except t

For an automotive component of your choice that is traditionally metallic, review how it could be re-engineered as a composite? How factors such as fibre & matrix type, fibre volum

Why dryness fraction are importance for steam power plant in terms of safety and economic ?

The following steps are taken to decarbonise the engine : Remove the exhaust muffler. Disconnect the spark plug. Remove the intake pipe bolt. Loosen the bolt de

Q. Design lay-down areas for plant? Designated lay-down areas are areas specifically positioned to enable equipment maintenance to be carried out. These are normally assigned f