8/14/2019 concrete technology homework 2.pdf

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CIEM 5240 HOMEWORK 2

Due: 12 Nov. 2013

1. A type of steel has a KIc value of 66 MPa m and yielding stress, ys , of 400 MPa. Thespecimen is a plate with very large size and a central crack.

a) If the allowed stress in the material is half of its yielding stress, what will be thecorresponding allowed crack length.

b) Plot the stress, yy , distribution along = 0o, 45oand 90o with the conditions in a);c) Calculate the length of yielding zone in front of crack tip ( = 0o) and then plot the

yy distribution along = 0o;

d) For a crack length of 1.25 mm, what will be the allowed stress value?2. In fracture mechanics, the stress intensity factor is defined as:

)b

a(faKI

where )

b

a(f is a geometrical function. It depends on crack length, a, the size of specimen and

loading pattern. For a plate specimen with an edge crack loaded by uniaxial tension as shown

in Fig. 1, the expression of )b

a(f is

432

3930722155102310121

b

a.

b

a.

b

a.

b

a..

b

af

where b is the width of the specimen.

a

b

Fig. 1 A plate with an edge crack under uniaxial tension

For 100 MPa, calculate the KI values with a=20 mm, 10 mm, and 0.2 mm and b=200 mm.

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3. Consider a crack located in parallel to the edge of a thin semi-infinite plate. The edge of the plate

is loaded by a concentrated force, P, as shown in the figure. The thickness of the plate is b.

Determine an approximation for the stress intensity factor of the configuration.

Hint: The solid part above the crack can be considered as a beam under concentred load.

a a

h

h

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)2(2 2 baaa

KI

Fig. 4 A penny-shaped crack under tensile stress only in the area of r