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
Q. Define Oxidation Process? Oxidation is defined as a loss of electrons, as when a metal goes from the metallic state to the corroded state. When a metal reacts with oxygen,

Two insulated and identical tanks are filled with nitrogen.  One tank is at 1 bar, 250 o C and the other is at 5 bar, 25 o C.  If the two tanks are connected with a pipe and the v

Define rpm

Illustrates the concept of bearing capacity of soil? The concept of bearing capacity of soil is the very essence of design and analysis of shallow foundations. In order to inve

Draw the Gas welding System and label its parts. Illustrate the several types of flames used in gas welding along with temperature range.

Determine the horizontal component of the force: A force of 80 N is working on a bolt as illustrated in Figure. Determine the horizontal and vertical components of the force.

The 13ft long beam

Piston Area : The area of a circle of diameter equal to the cylinder bore is called the piston area and is designated by the letter A and is usually expressed in square centimetr

Q. Two coils with self inductances 1H and 4H have a mutual inductance of 1H. The RMS value of current flowing in the two coils is 4A and 1A respectively. Find  the coupling factor

The basic aim of synthesis in design process is to provide information which can tell you how to improve the design. In general the synthesis process gives many alternatives of