Question

A hot-rolled steel bar is subjected to a repeated axial tensile load as shown. The material has ultimate tensile stress S_ut=1300MPa. The bar has a diameter of 30mm. The notch sensitivity factor, theoretical stress concentration factor, and factor of safety are q=0.52,K_t=2.42 and n=1 respectively. Find the maximum force F that the bar can carry for 10^4 cycles at 90% reliability

Figures                                                                10 Points

Endurance limit                                                   10 Point

Endurance strength                                             10 Points

Fatigue stress concentration factor                      5points

Determination of force                                        15points

Answer 1

Given Information :

• Hot rolled steel bar subjected to repeated Axial tensile load
• 
• Diameter :
• Stress concenetration factor (theorititcal) :
• Notch sensititvity factor :
• Reliability :

Solution :

NOTE : The above figure is only for representational purposes, not drawn to scale. The graph is on log scale

Calculating the endurance limit :

The given material is hot-rolled steel, the endurance limit of this material is given by :

Substitute the values

Therefore the endurance limit is :

Calculating the endurance strength :

The endurance strength is calculated taking into account various factors, depending on the component :

Where
Surface condition modification factor
Size modification factor
Load modification factor
Temperature modification factor
Reliability factor

(a) Surface modification factor :

(b) Size modification factor :

(c) Load modification factor :

(d) Temperature modification factor :

Assuming that the shaft is operating at room temperature :

(e) Reliability factor :

for 90% reliability :

Using all the above mentioned the endurance strength is calculated as follows :

Calculating the Fatigue stress concentration factor :

Calculating the actual Endurance strength :

The acutal endurance strength is :

Calculating the Force

From the above figure, we can find the maximum stress at 10⁴ cycles

Using the slope :

Therefore the maximum stress is :

Since the loading is axial load :

Therefore the maximum Force that the bar can carry for 10^4 cycles at 90% reliability is :