Find the maximum shear stress at free end, Mechanical Engineering

Assignment Help:

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


Related Discussions:- Find the maximum shear stress at free end

Shm, How we say that motion of the follower is simple harmonic motion descr...

How we say that motion of the follower is simple harmonic motion describe in practical approch

Turnning fixtures, what are the forces acting on workpiece during turning p...

what are the forces acting on workpiece during turning process. how workpiece should be clamp

Compute a creative design solution, It is really significant of using a Gan...

It is really significant of using a Gantt chart in order to respect the deadline of a client. Show the five main areas that must be explored for a good time management. There

Calculate the closed loop transfer function, Draw schematic diagram of a po...

Draw schematic diagram of a position control system using armature controlled DC Servo motor. Graph the signal flow graph and hence calculate the closed loop transfer function.

Evaluation of heat required - thermodynamics, Evaluation of heat Required: ...

Evaluation of heat Required: Heat which is required to generate steam is different from 'total heat' or enthalpy of steam. Heat required for generating steam means heat needed

Employability skills, Employability skills required for effective employmen...

Employability skills required for effective employment

Define the application of abrasive jet cutting machines, Define the Applica...

Define the Application of Abrasive Jet Cutting Machines Cleaning purpose. Cutting fine lines. Machining semiconductors. Drilling and cutting thin section of har

Water jet machining, Water jet machining is an advanced method for cutting ...

Water jet machining is an advanced method for cutting plates using a high-velocity water jet mixed with abrasive powder. The jet comes out of a nozzle A of diameter d and follows t

Heat pump - thermodynamics, Heat Pump - thermodynamics: Heat Pump: H...

Heat Pump - thermodynamics: Heat Pump: Heat pump is reversed heat engine that removes heat from a body at low temperature and transfer heat to the body at higher temperature

Define supports pins and jack pins - locating devices, Define Supports Pins...

Define Supports Pins and Jack Pins When the work is clamped directly in the body of the jig or fixtures, there is always a chance of error due to improper supports on accounts

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd