A steel shaft loaded in bending is 32 mm in diameter, abutting a filleted shoulder 38 mm in diameter. The shaft material has a mean ultimate tensile strength of 690 MPa. Estimate the size factor (k_(b)) if the shaft is used in a) A rotating mode k_(b)=((d)/(7.62))^-0.107=((32)/(7.62))^-0.107=0.858 b) A nonrotating mode d_(e)=0.370d=0.370(32mm)=11.84mm k_(b)=((d)/(7.62))^-0.107=((11.84)/(7.62))^-0.107=0.954

The size factor $(k_{b})$ is a dimensionless parameter used to account for the effect of the shaft diameter on its strength. It is used to estimate the strength of the shaft in different modes of operation, such as rotating or non-rotating.<br /><br />In the given problem, the steel shaft has a diameter of 32 mm and is loaded in bending. The shaft material has a mean ultimate tensile strength of 690 MPa.<br /><br />a) For the rotating mode, the size factor $(k_{b})$ is calculated using the formula:<br /><br />$k_{b}=(\frac {d}{7.62})^{-0.107}$<br /><br />where $d$ is the shaft diameter. Substituting the given value of $d=32$ mm, we get:<br /><br />$k_{b}=(\frac {32}{7.62})^{-0.107}=0.858$<br /><br />b) For the non-rotating mode, the effective diameter $(d_{e})$ is calculated using the formula:<br /><br />$d_{e}=0.370d$<br /><br />where $d$ is the shaft diameter. Substituting the given value of $d=32$ mm, we get:<br /><br />$d_{e}=0.370(32)=11.84$ mm<br /><br />The size factor $(k_{b})$ is then calculated using the same formula as in the rotating mode:<br /><br />$k_{b}=(\frac {d}{7.62})^{-0.107}$<br /><br />Substituting the calculated value of $d_{e}=11.84$ mm, we get:<br /><br />$k_{b}=(\frac {11.84}{7.62})^{-0.107}=0.954$<br /><br />Therefore, the size factor $(k_{b})$ for the rotating mode is 0.858, and for the non-rotating mode is 0.954.