Find the maximum shear stress at free end, Mechanical Engineering

Find the maximum shear stress at free end:

A stepped shaft ABCD, with A is fixed end and D is free end. AB = 1 m, BC = 2 m, CD = 1 m. AB is a hollow shaft of 100 mm outer diameter and 80 mm internal diameter. BC is solid shaft of 75 mm diameter CD is a solid shaft of 69 mm diameter. The torque applied at end D is 2 kN-m clockwise at C is 3 kN-m anticlockwise at B is 4 kN-m clockwise. Take G = 80 kN/mm2. Find the maximum shear stress and the angle of twist at free end.

Solution

G = 80 kN/mm2  = 0.8 × 1011 N/mm2    

520_Find the maximum shear stress at free end.png

Portion CD

T =+ 2 kN-m = + 2 × 103 N-m ,            l = 1 m

d = 60 mm = 0.06 m

J =  (π /32 )d 4  = π (0.06)4  = 1.3 × 10- 6 m4

R = d/2 = 60 /2= 30 = 0.03 m

T / J = τmax/ R = G θ/ l

τ max     = (T/ J) × R = ((2 × 103 ) /(1.3 × 10- 6 )) × 0.03 = 46.2 × 106 N/mm2

θ= Tl / GJ   = ((+ 2 × 103 ) × 1 )/((1.3 × 10- 6 ) (0.8 × 1011 ) )= + 1.9 × 10- 2 radians

Portion BC

l = 2 m,            T = + 2 - 3 = - 1 kN-m

d = 75 mm = 0.075 m

J =  (π /32 )d 4  = (π/32) × 0.0754  = 1.3 × 10- 6 m4

R = d/ 2 = 0.0375 m

τ max     = (T / J) × R = (1 × 103 /3.1 × 10- 6 )× 0.0375 = 12.1 N/mm2

θ= Tl / GJ   = -( (1 × 103 ) × 2) / ((0.8 × 1011 ) (3.1 × 10- 6 ))

= - 0.8 × 10- 2 radians

Portion AB

l = 1 m

T = + 2 - 3 + 4 = + 3 kN-m

d1 = 100 mm = 0.1 m

d2 = 80 mm = 0.08 m

 J =  (π /32) (0.14  - 0.084 ) = 5.8 × 10- 6 m4

R = d1/2 = 50 mm = 0.05 m

τ max     = (T/J)  × R =   (3 × 103 ) (0.05) /(5.8 × 10- 6 ) = 259 × 10  N/m   = 25.9 N/mm

θ= Tl/ GJ   =((+ 3 × 103 ) × (1)) / ( (0.8 × 1011 ) (5.8 × 10- 6 ))

= + 0.65 × 10- 2 radians

∴          Maximum shear stress = 46.2 N/mm2

θA = 0

θB  = 1.9 × 10- 2 radians

θC  = + 1.9 × 10- 2  - 0.8 × 10- 2  = 1.1 × 10- 2 radians

θD  = 1.1 × 10- 2  + 0.65 × 10- 2  = 1.75 × 10- 2 radians

∴Angle of twist at free end = 1.75 × 10- 2 radians

Posted Date: 1/21/2013 5:04:09 AM | Location : United States







Related Discussions:- Find the maximum shear stress at free end, Assignment Help, Ask Question on Find the maximum shear stress at free end, Get Answer, Expert's Help, Find the maximum shear stress at free end Discussions

Write discussion on Find the maximum shear stress at free end
Your posts are moderated
Related Questions
Q. Design Temporary Storage? It is sometimes acceptable to store drums temporarily on spill containment pallets. Each pallet should be capable of capturing the contents of at l

Define the term linear non-uniform soil pressure. See that the eccentric load on a column as in demonstrated figure also produces a similar effect. The linear non-uniform soil

Evaluate maximum shear stress: Derive equation subjected to combined bending and torsion for finding out maximum shear stress and its equivalent twisting moment.

Heat Treatment and Surface Treatment Processes Heat treatment processes are employed to improve of a work piece. The category includes the processes. Annealing, Normalizing,

The steam that leaves the super-heater is expanded from 130bar at 535°C to 25.2bar at 310°C in a high pressure turbine. The steam from the exit of the HP turbine is reheated to 535

What are the basic components of an automobile ? Explain them briefly. Show a schematic diagram showing the layout of the transmission system of a rear wheel driven automobile.

REACTIO N TURBINE: The turbine in which the steam expands while passing over the moving blades as well as while passing over the fixed blades and the pressure of steam dec

why single point cutting tool used in lathe

W orking stress and Factor for Safety Working Stress: Working stress is safe stress taken within elastic range of material. For the brittle materials, it is taken equal to

Transmission Through a LiNb0 3 Plate Examine the transmission of an unpolarized He-Ne laser beam (λ o = 633 nm) normally incident on a LiNb0 3 plate (ne = 2.29, no = 2.20) of th