Maths questions full workings out please and engineering question explain in detail please
Question 1: A tensile load F is to be applied to a tie bar shown in figure. The tie bar is 50 mm diameter. The surface of the bar has defects resulting from the manufacturing process, these have a maximum depth of 1.5 mm and have a shape factor of 1.4.
If the fracture toughness of the material used is 120 MPa m-0.5, determine the maximum load which can be applied if brittle fracture is not to occur. Use a factor of safety of 3.
Question 2: Consider that we need to predict the fatigue life of the bracket shown in figure. If we are given that the following relationship applies for the bracket:
Da/dV = 4 x 10-12 (ΔK)3 where Δk is in MPa m1/2
and that the stress varies cyclically between 30 and 150 MPa, determine the number of cycles for a defect to grow from 1.5mm to 4 mm.
