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

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 .

 

                                                      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
Resulting structure of steel: Heat treatments as mentioned below are given to thin steel strips for which TTT diagram is as shown in Figure 19. What will be the resulting stru

A cantilever beam of 4 metre length is loaded with uniformly distributed load of 20 KN/m throughout the whole beam. It is also loaded with 30 KN operating at 3m from the fixed end

please help me to calculate the diameter of a brake drum for using in a "brake drum dynamometer engine test rig" the engine specs are as follows: - 6Hp single cylinder 4stroke engi

Occupational Safety Acts The occupational safety Acts are intended to cover every employees (even if single) and all kinds of employers from manufacturing and construction to

How is works watery flayer?

Tunnels: Tunnels become unavoidable for negotiating hills, where detours are costly. The tunnels in rock are not lined, but those in loose strata require a lining of cement c

Explain modified Rankine cycle in detail with T-S and p-v diagrams. Explain Carnot cycle in detail with P-V and T-S diagram, and also write down expression for work ratio, therm

INVERTER TYPE POWER SOURCES For site welding and repair applications, a need was felt for long time to have light weight arc welding power source. Even though, a petrol driven ro

difference between pinhole and porosity

Q= In an investigation of the thermodynamic properties of alpha-manganese,the following heat contents determined H 700  - H 298 = 2895 cal/g-atm H 1000 - H 298 = 5450 cal