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thephysicsman
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Homework Statement
[PLAIN]http://img232.imageshack.us/img232/8514/unbenannthz.png
In this system, a single-span beam is exposed to the following stresses:
[tex]\sigma_{max}= 255 Mpa[/tex] at [tex]F_{max} = 50 kN[/tex] and
[tex]\sigma_{min}= 102 MPa[/tex] at [tex]F_{min} = 20 kN[/tex]
The stress range is accordingly [tex]\Delta\sigma = 153 MPa[/tex]
A crack is detected during an inspection of the construction. This runs in the bottom flange of the support, and has a length of 2a = 5 mm. The flange has a thickness of 2t = 10 mm.
[PLAIN]http://img62.imageshack.us/img62/3403/unbenanntcc.png
[tex]f(\frac{a}{t})[/tex] = 1.186
a) Calculate the stress intensity K for the maximum and minimum stress!
b) Calculate stress intensity difference [tex]\Delta K[/tex]!
c) A fracture test of the steel of the beam is carried out. The test specimen has a [tex]a_{0}/W[/tex] ratio of 0.5335. The data record below was recorded during the test.
[PLAIN]http://img830.imageshack.us/img830/6829/unbenannthty.png
Determine the fracture toughness [tex]K_{IC}[/tex] using the following formula and check if the crack is critical!
[tex]f(\frac{a_{0}}{W})=2.97[/tex]
[tex]K_{IC}=\frac{F_{max}*S}{\sqrt{B*B_{N}}W^{1.5}}f(\frac{a_{0}}{W})[/tex]
[tex]a_0 = 13,87 mm[/tex], W = 26 mm, B = 13 mm, [tex]B_N = 10,4 mm[/tex], S = 104 mm!
Homework Equations
[tex]K_{component}=\sigma \sqrt{\pi a} f(\frac{a}{t})[/tex]
The Attempt at a Solution
a)
[tex]K_{component, max}=255 MPa \sqrt{\pi 0.0025 m} 1.186 = 26.80 Mpa \sqrt{m}[/tex]
[tex]K_{component, min}=102 MPa \sqrt{\pi 0.0025 m} 1.186 = 10.72 Mpa \sqrt{m}[/tex]b)
[tex]\Delta K = 26.80-10.72 = 16.08 Mpa \sqrt{m}[/tex]
c)
[tex]K_{IC}=\frac{50 000 N*0.104m}{\sqrt{0.013m*0.0104m}0.026^{1.5}}2.97=317 MPa\sqrt{m}[/tex]Is this correct, or is there something that I have not understood?
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