What is the net angle of twist at the free end, Mechanical Engineering

What is the net angle of twist at the free end:

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.

848_What is the 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 .


                                                      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)

= (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 3:10:22 AM | Location : United States

Related Discussions:- What is the net angle of twist at the free end, Assignment Help, Ask Question on What is the net angle of twist at the free end, Get Answer, Expert's Help, What is the net angle of twist at the free end Discussions

Write discussion on What is the net angle of twist at the free end
Your posts are moderated
Related Questions
Importance of angle of twist: Q: What is the importance of angle of twist? From relation T / J = G. θ / L ;  we have               θ= T . L / G . J As G , L , J

(a) Show that two statements of Second Law of thermodynamics are equivalent to each other. (b) A house that was heated by electric resistance heater consumed 1200 KWh of electri

(a) Briefly explain the various efficiency terms associated with an engine. (b) A four cylinder engine running at 1200 rpm delivers 20 KW. The average torque when one cylinder w

hardness of bore well water is less than sea water .justify

A hermite curve passes through the points (1,0), (0.866, 0.5), (0.5, 0.866), (0,1) which are parameterized at u=0,0.25,0.75,1 respectively. determine geometric coefficient of the c

Composite Materials While two various materials which neither react chemically nor dissolve in every other are combined together so they form a composite materials. Individual

CONDUCTION OF ELECTRICITY IN GASES Electricity can pass through different media. In the case of gases, the atoms or molecules are not packed and they are free to move. In fact

Equilibrium in concurrent force system:   Sol.: The steps for solving problems of equilibrium in concurrent force system are as follows: 1.  First draw free body diagram

It is essential to select a flat belt drive for a compressor running at 720 r.p.m which is driven by a 25kW, 1440 r.p.m. motor. Space is available for a distance of 3m. The belt is

Produce as individuals a single tab Excel spreadsheet which shows a rough initial design for a water treatment plant taking 15MLD of water with 100 mg/l SS from a lake at 750mAOD,