Maximum stress in each material, Mechanical Engineering

The maximum stress in each material:

A copper tube of external diameter 60 mm and internal diameter 40 mm is closely fitted to a steel rod of 40 mm diameter to compose a composite shaft. If a torque of 6 kN-m is to be resisted by the shaft, discover the maximum stress in each material and the angle of twist in 2 m length.

Take  G = 80 kN/mm for steel, and

G = 40 kN/mm2 for copper.

Solution

Copper Tube

G = 40 kN/mm2  = 0.4 × 1011 N/m2 , l = 2 m

d1 = 60 mm = 0.06 m

d2 = 40 mm = 0.04 m

2451_Maximum stress in each material.png

TC = torque resisted by copper tube

θ= Tl/ GJ    =  (TC ) (2) /((0.4 × 1011 ) (1 × 10- 6 )) = 2 TC × 10- 5 radians       ---------- (1)

τmax =  (T/J )× R = (1 × 10- 6 ) × (0.03) = 0.03 TC  × 10  N/m

         = 0.03 TC N/mm2                             ------------ (2)

1689_Maximum stress in each material1.png

Figure

G = 80 kN/mm2  = 0.8 × 1011 N/m2 ,   l = 2 m

d = 40 mm

J =  (π/32) d 4 = (π /32)× 0.044  = 2.5 × 10- 7 m4

R = 20 mm = 0.02 m

θ= Tl  / GJ  = (TS ) (2) / ((0.8 × 1011 ) (2.5 × 10- 7 )) = TS × 10- 4 radians  --------- (3)

τmax =(T/ J) × R =  Ts / ((2.5 × 10- 7 ) (0.02)) = 0.008 TS  × 107  N/m

= 0.08 TS N/mm2                                    --------- (4)

In composite shafts, θC = θS

 ⇒        5 TC  × 10- 5  = TS  × 10- 4

∴          TC  = 2TS                                  -------- (5)

TS  + TC  = T

⇒         TS = 2TS  = 6

∴          TS = 2 kN-m             TC  = 4 kN-m

∴ Angle of twist, θ= (2 × 103 ) × 10- 4  = 0.2 radians

Maximum Shear Stress

For copper shaft : For steel shaft :

τmax  = 0.03 × 4 × 103  = 120 N/m2

τmax  = 0.08 × 2 × 103  = 160 N/m2

Posted Date: 1/21/2013 5:07:19 AM | Location : United States







Related Discussions:- Maximum stress in each material, Assignment Help, Ask Question on Maximum stress in each material, Get Answer, Expert's Help, Maximum stress in each material Discussions

Write discussion on Maximum stress in each material
Your posts are moderated
Related Questions
Scalar and Vector quantities: A quantity is a scalar if it is completely defined by its magnitude alone. For example: Length, area, and time. While quantity is said to be vect

A Torsion dynamometer is used in a propeller shaft of a marine Engine. It is found that the shaft twists 2 o in a length of 20 meters at 120 r.p.m. If the shaft is hollow with 300

Q. Explain the procedure of Rockwell hardness tests? Rockwell hardness tests per ASTM of the deposited weld, and heat affected zone shall be required for procedure qualificatio


Drum Brake: The construction of drum brake is clearly shown in Figure 2.40. In a rotating brake drum stationary brake shoes are attached concentric to the axle hub. A back plate

steam boilar

Screw Conveyors: Screw conveyors are used principally for transmitting materials in the form of powder or paste with the application of rotating screw. For example feedin

please tell me names of machine involed in making sewing machine table with their work involved...


Q. Heavy traffic areas in pumps? These are areas around pumps, filters, control valves, PSV's and other equipment requiring frequent maintenance or servicing. Piping attache