HW$3$ problems

Due $10/16/2024$

It is important to record calculations neatly and completely on engineering paper.

$6-1$ A $10-mm$ steel drill rod was heat$-$treated and ground. The measured hardness was found to be $300$ Brinell. Estimate the endurance strength in MPa if the rod is used in rotating bending.

$6-3$ A steel rotating$-$beam test specimen has an ultimate strength of $120$ kpsi $.$ Estimate the life of the specimen if it is tested at a completely reversed stress amplitude of $70$ kpsi $.$

$6-8$ Estimate the endurance strength of a $1\mathrm{.}5-$in$-$diameter rod of AISI $1040$ steel having a machined finish and heat$-$treated to a tensile strength of $110$ kpsi $,$ loaded in rotating bending.

$6-12$ A $1-$in$-$diameter solid round bar has a groove $0\mathrm{.}1-$in deep with a $0\mathrm{.}1-$in radius machined into it$.$ The bar is made of AISI $1020$ CD steel and is subjected to a purely reversing torque of $1800lbf*in.$

$($a$)$ Estimate the number of cycles to failure.

$($b$)$ If the bar is also placed in an environment with a temperature of $750F,$ estimate the number of cycles to failure.

$6-13$ A solid square rod is cantilevered at one end. The rod is $0\mathrm{.}6$ m long and supports a completely reversing transverse load at the other end of $+-2kN.$ The material is AISI $1080$ hot$-$rolled steel. If the rod must support this load for ${10}^4$ cycles with a design factor of $1\mathrm{.}5,$ what dimension should the square cross section have? Neglect any stress concentrations at the support end.

$6-17$ The shaft shown in the figure is machined from AISI $1040$ CD steel. The shaft rotates at $1600$ rpm and is supported in rolling bearings at A and $B.$ The applied forces are $F_1=2500lbf$ and $F_2=1000lbf.$ Determine the minimum fatigue factor of safety based on achieving infinite life. If infinite life is not predicted, estimate the number of cycles to failure. Also check for yielding.