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
what are the anti refection coating.expretion for thicknessrefractive index of coating material to act as anti reflacting coating

Determine an expression for the minimum number of teeth on a pinion which is in mesh with a rack in order to avoid interference and show the minimum number of teeth needed on a pin

Evaluate the motion - Smooth pulley: Block B is accelerated along the horizontal plane via mass A attached to it by a flexible inextensible massless rope passing over a smooth

what makes a pump not to take load required

An engine repair workshop in County Durham has identified a need  for a winch which is  to lift complete engine assemblies from floor level up to workbench level  to allow  remedia


CO 2 WELDING CO 2 welding is one of the variations of t he GMAW (Gas Met al Arc Welding) process which is now used for welding most structural and alloy steels. The operating

Q. External coatings on vessels? All pressure vessels that will be installed underground shall have an external coating applied according to the following procedure: • All e

how can i do an assignments

A steel tube of 30 mm external diameter and 20mm internal diameter encloses a copper rod of 15mm diameter to which it is rigidly joined at each end. If at a temperature of 10 o C,