Final answer:
To replace the distributed loading by an equivalent resultant, you need to determine the total force exerted by the load. If the load is uniform, the equivalent resultant force is equal to the total force multiplied by the distance from the centroid. If the load is not uniform, the concept of moment is used to find the equivalent resultant force.
Step-by-step explanation:
To replace the distributed loading by an equivalent resultant, you need to determine the total force or weight exerted by the distributed load. This can be done by integrating the load function over the given range. Once you have the total force, you can find the equivalent resultant force by considering the weight acting at the centroid of the distributed load.
If the distributed load is uniform, the equivalent resultant force will be equal to the total force multiplied by the distance from the centroid to the point where you want to calculate the resultant. If the distributed load is not uniform, you will need to use the concept of moment to find the equivalent resultant force.
For example, let's say you have a distributed load of varying weight along a beam. You can find the total weight by integrating the load function over the given range. Let's say the total weight is 100 N. If you want to calculate the equivalent resultant force at a certain distance from the centroid, you can multiply the total weight by the ratio of the distance from the centroid to the point of calculation.