The article Withdrawal Strength of Threaded Nails (D. Rammer, S. Winistorfer, and D

Chapter 4, Problem 7

(choose chapter or problem)

The article "Withdrawal Strength of Threaded Nails" (D. Rammer, S. Winistorfer, and D. Bender, Journal of Structural Engineering 2001:442-449) describes an experiment comparing the ultimate withdrawal strengths (in  ) for several types of nails. For an annularly threaded nail with shank diameter \(3.76 \mathrm{~mm}\) driven into spruce-pine-fir lumber, the ultimate withdrawal strength was modeled as lognormal with \(\mu=3.82 \text { and } \sigma=0.219\). For a helically threaded nail under the same conditions, the strength was modeled as lognormal with \(\mu=3.47 \text { and } \sigma=0.272\)

a. What is the mean withdrawal strength for annularly threaded nails?

b. What is the mean withdrawal strength for helically threaded nails?

c. For which type of nail is it more probable that the withdrawal strength will be greater than

\(50 \mathrm{~N} / \mathrm{mm}\)?

d. What is the probability that a helically threaded nail will have a greater withdrawal strength than the median for annularly threaded nails?

e. An experiment is performed in which withdrawal strengths are measured for several nails of both types. One nail is recorded as having a withdrawal strength of \(20 \mathrm{~N} / \mathrm{mm}\), but its type is not given. Do you think it was an annularly threaded nail or a helically threaded nail? Why? How sure are you?

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Text Transcription:

3.76 mm  

\mu=3.82 and \sigma=0.219    

\mu=3.47 and \sigma=0.272

50 N/mm      

20 N/mm