Chapter 9, Problem 55P

The cross-sectional area shown below has dimensions h = 152 mm, t₁ = 23 mm, t₂ = 21 mm, and b = 245 mm. Determine the y-coordinate of the centroid (y), where y is the signed distance from the z-axis to the z-axis. The z-y axes pass through the centroid of the cross section and are positive in the directions shown. y = 60.33 1 t₁ 1 Y b mm B h

Locate the centroid of the cross section below Hint: Cut the cross section into a rectangular shapes and determine thecentroids of the each rectangle. Use the formula AT (X) = A1 (x1) + A2(x2) + A3 (x3) to solve for x and AT (y)= A1(y1) + A2 (y2) + A3y3t o solve for Y. AT = A1+A2 + A3

Determine the centroid of the given figure. 120 mm 60 mm 40 mm 80 mm 60 mm O x = 55.45 mm and y = 35.65 mm %3D O x = 53.70 mm and y = 37.70 mm O x = 56.83 mm and y = 37.62 mm O x = = 54.10 mm and y = 36.30 mm O x = 53.56 mm and y = 35.63 mm O x = 56.80 mm and y = 37.10 mm O x = 55.76 mm and y = 36.65 mm O x = 54.80 mm and y = 36.60 mm

Find the centroid (x̄, ȳ) of the shaded area, given the functions:  yUPPER = 2·x   and   yLOWER = (1/8)·x3.The functions intersect at the origin and x = 4.

Find the area between the curve y=x^2 and the line 2x+y=8. Determine also the x and y component of the centroid of the area.

For a beam with the cross-section shown, calculate the moment of inertia about the z axis. Assume the following dimensions: by-83mm h₂ = 15 mm by 9 mm b₂-72 mm by-35 mm h-24 mm The centroid of the section is located 65 mm above the bottom surface of the beam. M₂ H Answer: mm by

3. From the given figure shown. Compute for the total length of the circular arc and the straight line and also find the location of its centroid with respect to the x and y-axis. R-0.6m 0.2 m 0.5 m 0.8 m-

From the Figure. A. Which of the following gives the total length of the circular arc and the straight line? B. Which of the following gives the location of its centroid with respect to the y-axis? C. Which of the following gives the location of its centroid with respect to the x-axis?

A chord in a bridge truss is composed of the elements shown in the figure. Refer to the table for the properties of the angle bars and locate the centroid of the built – up section.