Chapter 9, Problem 34P

Determine the reactions at A for the cantilever beam subjected to the distributed and concentrated loads. 3.0 kN 6.7 kN/m 3.7 m 1.8 m 1.8 m Part 1 The free-body diagram of the body is shown. The distributed loading has been replaced with a single equivalent force R at a distance d to the right of point A. Find the magnitude of the force R and the distance d. R 3.0 kN d Answer: R = i kN d = i m

Determine the centroid x and y of the parabolic area. Let n = 3, L = 10, b = 3. L - b L bn y = - xn X

Find the centroid of the given plane lamina. where PQ=16 cm, PS = SU = 8 cm, WX=4 cm, SX=PQ/3, ST=8 %3D cm. S X W

Determine the location of the centroid of a parabolic spandrel by direct integration.

The cylindrical container will have maximum stability against tipping when its centroid is located at its lowest possible position. Determine the depth h of the cylindrical portion that must be removed to achieve this.

Determine the centroidal coordinates of the plane region.

A cross section of a beam is bounded by the x-axis and the positive values of the function y = 4 – x. Find the coordinates of the centroid of the cross section.

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

For a ship with a water-line cross section as shown has a displacement of 5350 kN. Determine the maximum distance GB, that the center of gravity may lie above the center of buoyancy if the ship is to remain stable. Tip: MB. = GB, for 75 30 stable equilibrium.