Discover the angle of twist - uniformly varying shaft:

A uniformly varying shaft of length 2 m is subjected to a torque of 2 kN-m. The diameter at the ends shall be 60 mm and 120 mm. If G = 80 kN/mm2, discover the angle of twist. If the average diameter is utilized in the estimate of angle of twist, what is the percentage error?

Solution

d₁ = 60  mm;   d₂ = 120 mm

R₁ = 30 mm;    R₂ = 60 mm

T = 2 kN-m = 2 × 103 N-m,     l = 2 m

G = 80 kN/mm₂ = 0.8 × 1011 N/m₂

=2 × (2 × 10)³ × 2/ (3π× 0.8 × 10¹¹) (( 0.03²  + 0.03 × 0.06 + 0.06² )/ (0.03³ × 0.06³))

= 0.011 radians

If average diameter is used :

d = 60 + 120 /2 = 90 mm

J =  (π/32) d ⁴  = π (0.09)⁴  = 6.44 × 10^{- 6} m4

∴          θ₂ = Tl / GJ =   ((2 × 10³ ) (2) )/((0.8 × 10¹¹ ) (6.44 × 10^{- 6} )) = 0.008 radians

% error = ((θ₁ - θ₂ )/ θ₁ ) × 100

=( (0.011 - 0.008) /0.011 )× 100 = 27.3%

Posted Date: 1/21/2013 4:58:13 AM | Location : United States

Ask an Expert

Related Discussions:- Discover the angle of twist - uniformly varying shaft, Assignment Help, Ask Question on Discover the angle of twist - uniformly varying shaft, Get Answer, Expert's Help, Discover the angle of twist - uniformly varying shaft Discussions

Write discussion on Discover the angle of twist - uniformly varying shaft
Your posts are moderated

Write your message here..

Related Questions

Tolerance analysis, Tolerance Analysis This discusses the importance o... Tolerance Analysis This discusses the importance of assigning tolerances to the dimensions. Tolerance analysis is the process of assigning suitable tolerances. Proper assignme

Uniformly distributed load and uniformly varying load, Uniformly Distribute... Uniformly Distributed Load and Uniformly Varying Load: Uniforml y Distributed Load (UDL) A UDL is one which is spread over beam in such a manner that the rate of loading

Calculate the internal pressure, A pressure vessel is to be treated to ge... A pressure vessel is to be treated to generate compressive residual stresses on it inner surface. This involves increasing the pressure until taking 75% of the wall thickness goe

co2 welding, CO2 Welding CO2 Welding is a variation of GMAW. Here the ... CO2 Welding CO2 Welding is a variation of GMAW. Here the inert gas is replaced by gas mixtures or carbon dioxide, which are chemically active. The carbon dioxide decomposes in

Ytyyy66, ygyyytttt ygyyytttt

Axis of symmetry, Axi s of symmetry If in diagram half part of diagram... Axi s of symmetry If in diagram half part of diagram is mirror image of next ½ part, then there is a symmetry in diagram. The axis at which symmetry is create, called as axis

Foundry, properties of moulding sand properties of moulding sand

Stress, Difference between direct and shear stress Difference between direct and shear stress

What do you mean by heat balance sheet, What do you mean by heat balance sh... What do you mean by heat balance sheet? Illustrate.

Complex variables and rlc circuits, history and background and use history and background and use