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.
