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Give lots of explanation for every step or else it won't be marked complete. Make sure to write out equations first before subbing in. Be consistent and carry units properly.

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Q6. The thin-walled (do 22mm and di 20mm) tube T is welded to the two pistons K and H placed in a rigid enclosure J. The piston K is fixed to the enclosure and the walls of the piston H are perfectly smooth. These are the pressures P and P that feed the system (Figure a). Figure (b) shows the stress-strain diagram (or E) of tube material in case of uniaxial tension. Determine the maximum value of P given that the flow (yielding) in the tube should be avoided for the following two conditions and using two different failure criteria (Tresca and von-Mises) a) P P b) P 0; P>0 30 mm 100 mm (a) (MPa) 320 0 1,6 4.8x10

Explanation / Answer

STEP1:

Commencement of plastic deformation in materials is predicted by yield criteria. Yield criteria

are also called theories of yielding. A number of yield criteria have been developed for ductile

and brittle materials.

Tresca yield criterion:

It states that when the maximum shear stress within an element is equal to or greater than a

critical value, yielding will begin.

max k

Where k is shear yield strength.

Or

max = (1 – 3)/2 = k where 1 and 3 are principal stresses

Or

1 – 3 = Y

For uniaxial tension, we have k = Y/2

Here Y or k are material properties. The intermediate stress 2 has no effect on yielding.

STEP 2 :

Given that

max = 320 mpa = 1--- in case of p =p1

strain e = 1.6

CASE 1: P =P1

d0 = 30 mm and di = 20 mm

p=0 , P> 0

p = 1*pi/4 *(do2 - di2)

p = 320* 22/7 *(302-202)

p= 502.8KN

case 2: p=0 , P> 0

d0 = 22 mm and di = 20 mm

p = 1*pi/4 *(do2 - di2)

p = 320* 22/7 *(222-202)

p= 84.48 KN

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