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
Force on String: A string ABCD , attached to the two fixed points A and D has two weight of 1000N each attached to it at points B and C . The weights rest with portio

What is floating foundation? Floating Foundation: Raft or mat is also recommended when the soil mass contains compressible layers or the soil stratum is variable. In such ca

Stores for hazardous substances shall be segregated from, and located at a safe distance from accommodation spaces and control room. Indoor storage areas require access from an ope

Describe Mould Surface Coating? Mould surfaces are coated (after the pattern is drawn out) with certain materials possessing high refractoriness. It eliminates the poss

In designing piping systems, it is sometimes desirable to estimate the appropriate pipe length for a given diameter, pump power and flow rate. In such cases, if minor pipe losses a

A rectangular block of material is subjected to stresses 65N/mm 2 (tensile) in x- direction and 35 N/mm 2 (tensile) in perpendicular direction. It is accompanied by shear stress

Can you explain about MIS ? What is the role of MIS in decision making ? Illustrate standardization, specialization and simplification in product design and development.

The specifications for use on a project will be as defined in the Project Execution plan. The Specification requirements will be clarified in the Engineering Estimate or at the Pr

A lifting shackle in a glass-making factory is made from a special high-temperature stainless steel. It is expected that the shackle will experience a tensile load of 5kN and th

what is sin2P ,if angle q is 90 degree.