Let us now solve an example using here concepts.

Example 3 : In figure 13 a beam on supports A and B is shown with two triangular loadings. All the parameters of the loading are shown in the figure. We wish to know the reaction at supports A and B.

If we represent the total loads of the triangles on the left and that on the right by L₁ and L₂ , respectively then

L₁ acts at the centroid of the first triangle which is at a distance

From A. Similarly L₂ acts at the centroid of the second triangle so its distance from A is

Let the reaction at supports A and B be N_A and N_B , respectively. Then

Further, taking moment about A gives

Therefore .