4) Determine the coordinates of the centroid of the shaded area in Figure 4 using Integration Method a) x b) y 4 Figure 4 y = √x 6 ft

Be sure to include units with your answers. Show your work. 40 mm X = Y = 60 mm 50 mm X 1) 8 pts) Find X for the centroid of the shape above. 2) 8 pts. Find Y of the shaded shape below. Ľ

a) A simply supported beam has a symmetrical rectangular cross-section. If the second moment of area (I) of a beam with a rectangular cross-section is11.50 x 106 mm4 about its centroidal x-axis and the depth dimension (d) of the rectangular section is 180 mm, determine the breadth dimension (b) for this beam section. Give your answer in millimetres (mm) and to 2 decimal places. Assume the beam section material is homogeneous. b) The same rectangular cross-section beam in Q2b is subjected to a maximum bending moment of 25,000 Nm and experiences sagging. Assuming that the centroidal axis passes through the beam section at (d/2), calculate the maximum bending stress (σmax) the beam will experience. Give your answer in N/mm2 and to 2 decimal places.

a) Determine the Area and the centroid of the shape. Show the calculations using integration. b) Find the Area Moment of Inertia about the X-axis using integration. Then find the Area Moment of Inertia about the x-x centroidal axis (x-bar) using the Parallel Axis Theorem. 2.0 in c) Find the Area Moment of Inertia about the Y-axis using integration. Then find the Area Moment of Inertia about the y-y centroidal axis (y-bar) using the Parallel Axis Theorem. 2.0 in