Question

In a gusset plate, there are six rivet holes of 21.5 mm diameter as shown in Fig. Find the position of the centroid of the gusset plate.

Answer 1

The composite area is equal to a rectangle of size 160 × 280 mm plus a triangle of size 280 mm base width and 40 mm height and minus areas of six holes. In this case also the Eqn. 4.4 can be used for locating centroid by treating area of holes as negative. The area of simple figures and their centroids are as shown in Table 

A = ΣAi = 48221.70

ΣA_i x_i = 44800 × 140 + 5600 × 560/3 – 363.05 (70 + 140 + 210 + 70 + 140 + 210)

= 7012371.3 mm³

Thus, the coordinates of centroid of composite figure is given by: 

\(\bar x\) = 145.42 mm 

\(\bar y\) = 90.39 mm