Question

2. For the section below, Obtain the second moment of area, the location of the neutral axis, and the distances form the neutral axis to the top and bottom surfaces a) b) If the section is subjected to a positive bending moment about the z-axis of 1.13 kN-m, determine the resulting stresses at the top and bottom surfaces, as well as at every abrupt change in the cross section. (dimensions in mm) 100 ← 12.5 2.5 → 12.5 50一小25 100

Answer 1

Let's divide the cross - section into (3) areas Area of region 1(A_1) = 625 mm^2 (50 times 12.5) Area of region 2(A_2) = 75 times 75 = 5625 mm^2 Area of region 3(A_3) = = 100 times 100 = 10,000mm^2 Therefore Required Area of cross-section (A) = 10,000- 5625 - 625 A = 3750 mm^2 Now, calculating the centroid distance to cross section NKt y^- = Sigma y_1 A_i/Sigma A_i A_i = Individual segment area y_i = Individual segment's centroid distance from a datum y^-_1 = 6.25 mm, y^-_2 = 50 mm y^-_3 = 50 mm y^- = 10,000 (50) - 5625 (50) - 625 (6.25)/3750 y^- = 57.29 mm c_1 = 100 - 57.29 = 42.71 mm Area moment of inertia for rectangular section I = bh_3/12 I_1 = 50 times (12.5)^3/12 = 8133 mm^4 I_2 = 75 times 75^3/12 = 2.63 times 10^6 mm^4 I_3 = 100 times 100^3/12 = 8.33 times 10^6 mm^4