Question

1. (25 pts) Chapter 8 Consider a 3.0-in.-diameter 1045 Hot-Rolled steel bar. Draw the S-N curves for: (a) Torsional loading (b) Bending, and (c) Axial. (You need to cite the references that you get the tensile properties of the steel)

Answer 1

Given data 1

Sut 82 ksi

Syt 45 ksi

d= 3.5 in

Solution →

Endurance limit (10) cycle strength

Se=S! * Ka* K * K * Kd

For Torsional loading +

S = 0.5 * Sut → for Sut <200 kpsi

Surface factor (K) = a (Sut)

For hot rolled

a = 14.4 kpsi

b= -0.718

(K) = 14.4 * (82)-0.71€

(K) = 0.6084

Size factor (K) →

0.6 to 0.7 →d>2 in

Кр 0.65

Load factor (K) →

K = 0.577 → for Torsional loading

temperature factor (K)

Ру

Se=S! * Ka* K * K * Kd

Se 0.5 * 82 * 0.6084 * 0.65 * 0.577 * 1

Se = 9.3553 ksi

For bending →

S = 0.5 * Sut

Surface factor (K) = a (Sut)

For hot rolled

a = 14.4 kpsi

b= -0.718

(K) = 14.4 * (82)-0.71€

(K) = 0.6084

Size factor (K) →

0.6 to 0.7 →d>2 in

Кр 0.65

Load factor (K) →

K=1 for bending

temperature factor (K)

Ру

Se=S! * Ka* K * K * Kd

Se 0.5 * 82 * 0.6084 * 0.65 * 1* 1

Se 16.213 ksi

Se=S! * Ka* K * K * Kd

For Axial

S = 0.5 * Sut → for Sut <200 kpsi

Surface factor (K) = a (Sut)

For hot rolled

a = 14.4 kpsi

b= -0.718

(K) = 14.4 * (82)-0.71€

(K) = 0.6084

Size factor (K) →

0.6 to 0.7 →d>2 in

Кр 0.65

Load factor (K) →

$K_{c}=0.923\rightarrow \textup{ for Axial}\left ( S_{ut}\leq 220\textup{ kpsi} \right )$

temperature factor (K)

Ру

Se=S! * Ka* K * K * Kd

$S_{e}=0.5*82*0.6084*0.65*0.923*1$

$S_{e}=14.965\textup{ ksi}$

$\textbf{10}^{3}\textbf{ cycle strength}$

$\textup{For torsional}\rightarrow$

$0.9S_{us}=0.9*0.8*82=59.04\textup{ ksi}$

For bending →

$0.9S_{ut}=0.9*82=73.8\textup{ ksi}$

$\textup{For Axial}\rightarrow$

$0.75S_{ut}=0.75*82=61.5\textup{ ksi}$

$\textbf{S-N curves}$

73.8 ksi 61.5 ksi 59.04 Ksi Bending Stress ksi 16.213 ksi Axial 14.965 ksi Torsional 9.3553 ksi 103 104 105 LOS 107 cycles

73.8 ksi 61.5 ksi 59.04 Ksi Bending Stress ksi 16.213 ksi Axial 14.965 ksi Torsional 9.3553 ksi 103 104 105 LOS 107 cycles