a cantilever beam of rectangular shape is subjected to a con

tilever beam of rectangular shape is subjected to a constant force F2 and a time-varying force Fi at room temperatu of [1000, 10000] N. Points P and Q are at top and middle on the root cross-section area. The beam surface is machined, and is made of a steel material of an ultimate strength 620 MPa. 90% of reliability and infinite life are required. Calculate the minimum and maximum von Mises effective stresses at points P and Q respectively. A can . Calculate the mt pins ranD Q 1. Calculate the minimum an 2. Calculate the mean and alternating von Mises effective stresses at points P and 0. 3. Find all correction factors, and the uncorrected and corrected endurance limits. respectively 4. Calculate the fatigue factors of safety at points P and Q respectively. 1.5 m 0.05m 0.05 m Fi 0.05 m

Solution

GIVEN:- F1 = (1000N to 10000N), F2 = 5000N, St = 620Mpa, Reliability = 90%,

SOLUTION:-

POINT P is subjected to normal stress and bending (Tensile stress).

POINT Q is subjected to only normal stress.

(1) For point P > Sx = F2 / A = 5000 / (0.05 x 0.1) = 1000000 N/m2

Sy1 = M x c / I = (1000 x 1.5 x 0.05) / (0.05 x 0.05 x 0.005) = 6000000 N/m2

Sy2 = (10000 x1.5 x 0.05) / (0.05 x0.05 x 0.005) = 60000000 N/m2

Only bending tensile stress Smax = (Sx + Sy)/2 + (Sy-Sx/2)^0.5 and normal stress will be present at point P.

So, Smax = 3.50 Mpa for F1 = 1000N (ANSWER) and Smax = 30.50 Mpa for F1 = 10000N (ANSWER)

  For point Q > Only Normal stress is evident, So Effective stress Sx = S = 1 Mpa (ANSWER)

(2) For point Q, effective stress Sx = S = 1 Mpa (ANSWER)

For point P > Mean stress = (Sx + Sy) / 2 = 3.5 Mpa for F1 = 1000N (ANSWER)

   Mean stress = (Sx + Sy) / 2 = 30.5 Mpa for F1 = 10000N (ANSWER)

   Effective stresses at point P will also be approx = 3.5 Mpa and 30.5 Mpa respectively for

F1 =1000 N and 10000 N (ANSWER)