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Download Geotechnical Earthquake Engineering (Prentice-Hall by Steven L. Kramer PDF

By Steven L. Kramer

This can be the 1st e-book out there focusing particularly at the subject of geotechnical earthquake engineering. The ebook attracts from the fields of seismology and structural engineering to offer a vast, interdiciplinary view of the basic recommendations in seismology, geotechnical engineering, and structural engineering.

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Extra resources for Geotechnical Earthquake Engineering (Prentice-Hall International Series in Civil Engineering and Engineering Mechanics)

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This cannot be correct. This error occurs due to the large value of n and therefore the smallness of r=100n. 171 × 10–16, respectively. Since floating-point numbers have at most 16 significant digits, adding two numbers that have a magnitude difference of 1016 results in the loss of significant digits or information as described in this section. To illustrate this point further, if the calculation were performed for a compounding frequency of every nanosecond, the maturity amount is calcuated by MATLAB to be $250 000 – the principal amount!

In the code below, the variables are converted to the single data type by using the single conversion function. 24%. The magnitude of this error is not insignificant considering that the digital floating-point representation of single numbers is accurate to the eighth decimal point. 33 × 10–12 %. Double precision allows for much more accurate representation of floating-point numbers and should be preferred whenever possible. In the real world, when performing experiments, procuring data, or solving numerical problems, you usually will not know the true or exact solution; otherwise you would not be performing these tasks in the first place!

Then, μ ðs ¼ 1:0 g=lÞ ¼ 0:6666=hr; μ ðs ¼ 1:1 g=lÞ ¼ 0:6875=hr; μ ðs ¼ 0:9 g=lÞ ¼ 0:6428=hr: Using a forward difference approximation to determine μ0 , we obtain 0:6875 À 0:6666 ¼ 0:209 l=ðg hrÞ; relative error Er ¼ 5:94%: 0:1 Using a backward difference approximation to determine μ0 , we obtain μ0 ffi 0:6666 À 0:6428 ¼ 0:238 l=ðg hrÞ; relative error Er ¼ 7:11%: 0:1 Using a central difference approximation to determine μ0 , we obtain μ0 ffi 0:6875 À 0:6428 ¼ 0:2235 l=ðg hrÞ; relative error Er ¼ 0:585%: 2 Â 0:1 Note the smaller error in the approximation of μ0 when using the central difference formula.

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