Question

Part A -Normal Strain at a Specified Point Consider the pre-deformation cross-section of a bar, a side view of which is shown in the figure below The dia meter of the bar is d- 120 mm. A bending moment is applied that causes the neutral axis to become conca o up. What is the normal strain h Express your answer to three significant figures. View Available Hint(s) 20 mm from the bottom of the bar if the radius of curvature measured to be ρ -7.5 m? Submit X Incorrect: Try Again ▼ Part B-Maximum Normal strain When a cylindrical bar of diameter d-38.4mm is subjected to a moment the strain at a distance y-8.8 mm from the neutral axis is -6.027 x 10 mm/mm. What is the maximum compressive normal strain in the ba? Express your answer to three significant figures. View Available Hint(s) 0回] Emax= Submit

Answer 1

Distance of point from N. A = 60 -h = 40 mm so, Radius CA unstretched at h = rho + 40 mm now if delta x is stretched length, then, delta x^'/rho^' = delta x/rho implies delta x^' = 7540/7500 delta x = 1.0053 delta x so, strain, epsilon = delta x^' -delta x/de;ta x = 0.0053 implies epsilon = 0.0053 part B epsilon_y = -6.027 times 10^-4 mm/mm: y = 8.8 mm, r = d/2 = 38.4/2 = 19.2 mm so, considering linear profile of strain epsilon_y/y = epsilon_r/r implies epsilon_r = -19.2 times 6.027 times 10^-4/6.8 implies Max strain implies -1.3149 times 10^-3 = epsilon_r R = 42 in, rho = 72 in: rho_i = rho -d/2 = 72 -4.5/2 = 69.75 in outer Radius, eho_0 = rho + d/2 = 74.25^' now, l/ rho = li /rho_i = l_0/rho_0 implies li = 42/75 times 69.75 =