Angle of twist is zero on the shaft, Mechanical Engineering

Angle of twist is zero on the shaft:

A shaft 10 m long and 100 mm diameter during its length is fixed at the ends and is subjected to two opposite torques of 8 kN-m and 10 kN-m at a distance of 3 m and 8 m from one end. Discover the fixing torques at the ends. What is the maximum angle of twist and the maximum shear stress in the shaft? At what section the angle of twist is zero on the shaft?

Take E = 80 GPa.

Solution

Σ T = 0

⇒  TA  - 8 + 10 + TD  = 0

∴          TA  + TD  = - 2

G = 80 GPa = 0.8 × 1011 N/m2              -------------- (1)

d = 100 mm = 0.1 m

 J =  (π /32)d 4 = (π/32) × (0.1)4  = 9.8 × 10- 6 m4

R = d /2= 100/2 = 0.05 m ,   ZP = 1.96 × 10- 4 m3

1451_Angle of twist is zero on the shaft.png

Figure (a)

2003_Angle of twist is zero on the shaft1.png

Figure (b) : Line Diagram

 

Portion AB

θ 1 = (TA . l )/GJ = (TA × 3 )/GJ                         ---------- (2)

Portion BC

θ2 = ((TA  - 8) × 5 )/     GJ               -------- (3)

Portion CD

θ3 = ((TA - 8 + 10) × 2)/ GJ = ((TA + 2) × 2)/ GJ                      ---------- (4)

Angle of twist at D co.r.t A = 0

(TA × 3 )/ G J + ((TA  - 8) × 5 )/ GJ + ((TA  + 2) × 2)/ GJ = 0

∴          TA  = 3.6 kN-m                                       ----------- (5)

From Eqs. (1) and (5),

3.6 + TD = - 2

TD = - 5.6 kN-m = 5.6 kN-m    (  )

Angle of Twist

θ1 = ((3.6 × 103 ) × 3) / ((0.8 × 1011 ) (9.8 × 10- 6 ))

= 1.4 × 10- 2 radians

θ2 =      ((3.6 - 8) × 103 × 5 )/(0.8 × 1011 ) (9.8 × 10- 6 )= - 2.8 × 10- 2 radians

θ3 =      (3.6 + 2) × 103  × 2 /((0.8 × 1011 ) (9.8 × 10- 6 ))= 1.4 × 10- 2 radians

θAB  = θ1 = 1.4 × 10- 2 radians

θ AC  = θ1 + θ2  = 1.4 × 10- 2 - 2.8 × 10- 2 = - 1.4 × 10- 2 radians

θAD  = θAC  + θ3 = - 1.4 × 10- 2

Shear Stress

 + 1.4 × 10- 2  = 0

τ max     = (T/ J) . R =  T/ Z P

Portion AB

τmax = 3.6 × 103 / (1.96 × 10- 4) = 18.4 × 106 N/m2  = 18.4 N/mm2

Portion BC

τ max = (3.6 - 8) × 103/ (1.96 × 10- 4)

= - 22.4 × 106 N/m2  = - 22.4 N/mm2

Portion CD

τ max      = (3.6 + 2) × 103/1.96 × 10- 6 = 28.6 × 106 N/m2  = 28.6 N/mm2

Zero Angle of Twist

It occurs between B and C

θ1 = 1.4 × 10- 2 radians

243_Angle of twist is zero on the shaft2.png

1682_Angle of twist is zero on the shaft3.png

∴ x = 2.5 m from B.

Posted Date: 1/21/2013 5:14:58 AM | Location : United States







Related Discussions:- Angle of twist is zero on the shaft, Assignment Help, Ask Question on Angle of twist is zero on the shaft, Get Answer, Expert's Help, Angle of twist is zero on the shaft Discussions

Write discussion on Angle of twist is zero on the shaft
Your posts are moderated
Related Questions
Find out the recoil-velocity of the gun: As shell of mass 200 gm is fired at a velocity of 50 metres/second by a gun of mass 20 kg. Find out the recoil-velocity of the gun.

Machine and Tool Selection The quality of a product largely depends on the type of machine, the type of process, machining conditions and the right selection of tools. The cur

simply supported beam subjected to point loads results

A motor cycle with rider, weight of 250 Kg., the centre of Gravity of the machine and rider combined being 60 cm above from ground level when the machine is standing upright. Each

Working of Impulse turbine: The technique in which multiple system of rotors are keyed to a common shaft, in series and the steam pressure of jet velocity is absorbed in stage

Hazardous Waste and Material Standards Each hazardous site must be examined and evaluated for its characteristics before workers are allowed entry. This will pre decide an

some suitable examples

To design a cantilevered truss to support the loads shown in the figures, two layouts are proposed as shown in Figs. A and B. All truss members are steel with allowable stress of 2

What is the aim of PDES The aim of PDES is to provide an interface which permits the exchange of data of the entire product development cycle and production cycle, see also PDE

Short answer Type. a) Write the difference Between Dry clutch and Wet ? b) What is difference Between Chasis and Frame? c) Illustrate the Future trends in Automobile