Question

Consider a cantilevered steel bar shown below. The bar must support a static load P of 900 lb and steel with a yield point of 68 kpsi will be selected for the bar. Assume the selected steel is ductile, even material and the stress concentration can be neglected, but a safety factor of 6.0 should be used. * d = ? (a) Write the names of two different failure criteria you want to apply, and also briefly discuss about the expected accuracy from those two methods. (b) Determine the diameter of the circular cross-section for the stress element at A as shown in the figure below by using one of the methods you selected. (c) Again, apply the second approach you selected to the same problem and write the obtained diameter.

Answer 1

vis Ру a) Names of two different failure criteria you want to apply. ③ Maximum shear stress Theory 2 Maximum Distortion Energy Theory

- The accuracy obtained from maximum Distortion Energy Theory is greater because maximum shear stress theory gives more safe results so dimensions of component increases. (6) Diameter of circular cross Section. Griven Data :- yield strength = 68 kPsi Factor of Safety = 6 So yield strength considering factor of safety = T = 686103 = 11333.33 Ipsi load Consider equal and opposite P acting at point B for Calculation of diameter

- So from it we can see that the structural member is under combined effect of bending and Torsion. Here, Moment = 900 x 5 = 4500 pound inch - Torque = 90084 = 3600 pound inch The and combined Torsion effect of bending can be calculated as Maximum shear stress = 16 ✓M²+7² 6 V (4500)²+(3600)? TDB

- As per maximum distortion energy Theory shear strength T = 0.577 yield strength considering of safety factor 0.577 x 11333; = 6539.331 psi Now to avoid failure 6539.331 Psi > 16 V64500)? + (3600) 2 To calculate diameter 6539. 331 = 16 V65009624 (3600) 2 TO ТТ 3 3 = 16 X (5762.81) TX 6539.33)

De 4.48818 ID=1.6495 inch / c) As per Maximum Shear Stress Theory. Shear strength Tee 0.58 yield strength Considering factor of safety = 0.5 x 1333.33 psi - 5666,66 psi Now to avoid failure, 5666.66 > 16 V (4500) ²+ (360072 7 TD3 To calculate diameter 5666.66 = 16 x (5762.81)

D3 - 16 x (5762.81) TTX 5666.66 D3 = 5.1793 D = 1.730 inch where D= Diameter of cross section.