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 investment casting with neat sketch

Automated Material Handling We have dealt along with the automated guided vehicles and Robots utilized in the industry. Because of the industrial automation, various changes h

Expected quarterly sales in Year 1 (vehicles) The work content of a single unit of each product in each process has been estimated at: Using MS-Excel, calculate the workloads

Evaluate secure axial load: A small piece of ISA (200 × 100 × 15) angle carries a compressive load, the line of action of which coincides along the intersection of the middle

Qusetion: A body when projected vertically up covers a total distance s, during its time of flight. If we neglect gravity then how much distance, the particle will travel during

Magnitude of a couple: So l.: For system, magnitude of couple is equal to algebraic sum of the moment about any point If the system reduces to couple, the resultant forc

WELDER PERFORMANCE QUALIFICATIONS Requirement of Welder Qualification In performance qualification, the basic attempt is to establish the ability of the welder to dep

Drive Chain Cleaning and Adjustment :  The service life of the drive chain depends on proper lubrication and adjustment. Poor maintenance can cause premature wear or damage to driv

advantages and disadvantages of locomotive boiler

state principle of virtual work