Find the maximum shear stress - stepped circular bar, Mechanical Engineering

Find the maximum shear stress - stepped circular bar:

A stepped circular bar ABC 4 m long fixed at one of the end 'A' is subjected to a torque of 10 kN-m. If the portion AB is solid shaft of 100 mm diameter & the portion BC is a hollow with an external diameter 100 mm and internal diameter 80 mm. discover the maximum shear stress & maximum angle of twist.

AB = 2 m; BC = 2 m; G = 80 kN/mm2.

Solution

G = 80 kN/mm2  = 0.8 × 1011 N/mm2

2202_Find the maximum shear stress - stepped circular bar.png

Figure

 Portion BC

l = 2 m, d1 = 100 mm, d2 = 80 mm, T = 180 kN-m = 10 × 103 N-m

1792_Find the maximum shear stress - stepped circular bar1.png

=  π (0.14  - 0.084 ) = 5.8 × 10- 6 m4

R = 100 = 50 mm = 0.05 m

T / J = τmax/ R = G θ/ l

τmax = (T/J) × R =  (10× 103 )(5.8 × 10- 6 ) × (0.05)

= 86.2 × 106 N/mm2  = 86.2 N/mm2

Portion AB

Solid T = 10 kN-m

d = 100 mm

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

R = d /2 = 50 mm = 0.05 m

τ max     = T R / d J = ((10 × 10 3) (2) / (9.8 × 10- 6 ) )(0.05) = 51 × 106 N/m2  = 51 N/mm2

θ= Tl / GJ   = (10 × 103) (2) / ((0.8 × 1011) (9.8 × 10- 6))

= 2.55 × 10- 2 radians

 ∴         Maximum shear stress = 86.2 N/mm2

θA = 0

θB  = 4.3 × 10- 2 radians

θC  = 4.3 × 10- 2  + 2.55 × 10- 6  = 6.85 × 10 6 radians

Posted Date: 1/21/2013 5:00:12 AM | Location : United States







Related Discussions:- Find the maximum shear stress - stepped circular bar, Assignment Help, Ask Question on Find the maximum shear stress - stepped circular bar, Get Answer, Expert's Help, Find the maximum shear stress - stepped circular bar Discussions

Write discussion on Find the maximum shear stress - stepped circular bar
Your posts are moderated
Related Questions
Define universal portable radial drills Drilling machine is mounted on a trolley base to have a greater degree of mobility. In order to move the machine to any position on or a

What is the initial velocity of the ball: A ball is horizontally thrown from the top of a building 60 m height, hits the horizontal ground 25 m from the base of the building a

An open belt connects two flat pulleys. The pulley diameters are 300 mm and 450 mm and the corresponding angles of Cap are 160 o and 210 o . The smaller pulley runs at 200 r.p.

Difference between path function and point function

Explain End Relief Angle It is the angle between the plane perpendicular to base and end flank. The angle prevent\s the cutting tool from rubbing against the job where as if th

Steam table - Thermodynamics: Sol.: Steam table offers various physical data regarding the properties of saturated water and steam. This table is very helpful in solving the

The Leader Command The Leader command can be used to annotate at any point on a drawing. The command sequence below was used to draw the leader shown in the Figure Below.


A large hydraulic cylinder is to be treated using autofrettage, taking 80% of the wall thickness into the plastic range. The external diameter of the vessel is 200mm and the inter

Introduction You are now working as a FEA engineer for a Computer Aided Engineering (CAE) consultancy company called Dantech. This morning, your manager assigned you a new contr