## what is the new yield strength of the material, using the 0.1 percent offset?

10. A steel specimen is cyclically loaded in tension to a stress of 15 ksi and fails after 2,000 cycles. A structural member of the same steel is loaded in tension to 20 ksi. Using Miner’s rule, how many cycles of this loading can it withstand before failure?

11. A round bar of A36 steel has a length of 2 feet and diameter of 0.25 inches. The stress strain curve for this material is given by the equation in which the units for s are kips per in2 (ksi). You decide to strain harden the material by loading to a strain e=0.015. Assume that the slope of the unload-reload line is the same as the initial tangent modulus.

a. What is the initial tangent modulus for the material? Use the exact method (i.e., take the derivative).

b. After the strain hardening and unloading sequence, what is the new yield strength of the material, using the 0.1 percent offset? You should graph this using a spreadsheet, with stress increments of 5 ksi up to 95 ksi.

### Explain why attenuation is not a big problem in PET.

Consider a 2-D object consisting of two triangle compartments, as shown in Figure P9.4. Suppose a solution containing a 511 KeV gamma ray emitting radionuclide with concentration f = 0.5….

### Give the mean and the variance of the reconstructed image, mean[ˆ f(x, y)] and var[ˆ f(x, y)].

Ignoring the inverse square law and attenuation, an approximate reconstruction for SPECT imaging is given by where c˜() =  {||W()} and W() is a rectangular windowing filter that cuts off at = 0…..

### Find the numerical responses in each to an event in crystal C(4, 6).

Suppose a PET detector comprises four square PMTs (arranged as a 2 by 2 matrix) and a single BGO crystal with slits made in such a way that it is….