Q1: If the length of a combined footing for two columns l metres apart is L and the projection on the left side of the exterior column is x, then the projection y on the right side of the exterior column, in order to have a uniformly distributed load, is (where x is the distance of centre of gravity of column loads).

ANS:D -

To ensure that the load on the combined footing is uniformly distributed, the projections of the footing from the exterior columns need to be adjusted accordingly. Let's denote the length of the combined footing as L, the distance between the two columns as l, and the distance of the center of gravity of the column loads as x. We want to find the projection y on the right side of the exterior column. Since the load is uniformly distributed, the center of gravity of the column loads will be at the midpoint of the distance between the two columns. Therefore, the distance of the center of gravity of the column loads from either column is l/2​. Now, let's consider the left exterior column. The distance from the center of gravity of the column loads to the left exterior column is x. Therefore, the total projection of the footing on the left side of the exterior column is L−x. For the right exterior column, the distance from the center of gravity of the column loads to the right exterior column is l​/2−x. Therefore, the total projection of the footing on the right side of the exterior column should be the same as on the left side, which is L−x. Mathematically, we can express this as: y=L−x So, the projection y on the right side of the exterior column to have a uniformly distributed load is L−x.