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

Solution

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
Explain a cone clutch. How this clutch is designed. It is needed to design a rigid type of flange coupling to connect two shafts. The input shaft transmits 37.5 kW power at 180

Reduce expressions for the hydrostatic center and force of pressure in case of an inclined plane surface submerged in a fluid.

Q. Describe Elastic and plastic deformation? When a sufficient load is applied to a metal or other structural material, it will cause the material to change shape. This chang

general characteristic of bulk deformation and different process and corresponding product properties

Disc clutch friction thickness: Check disc clutch friction thickness which should be minimum of 2.6 mm.

Thin wall round tube has diameter of 60mm. The end of it will be compressed to square for. How many percents torsion strenght will become lower at the end tube?


A smooth sphere of radius 15 cm and weight 2 N is supported in contact with a smooth vertical wall by a string whose length simlar the radius of sphere. The string joins a point on


ELECTRO SLAG WELDING   This process is similar to the electro gas welding process designed for making butt welding in the vertical position in one single pass and the plate