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







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