Loads spread over length or area are replaced by an equivalent resultant for analysis.
Distributed loads w(x) (N/m) are replaced by a resultant R=∫w dx acting at the centroid of the load diagram. Uniform load: R=wL at mid-span; triangular load: R=wL/2 at L/3 from the large end.
A 5 kN/m load over 4 m is equivalent to 20 kN at the centre.
Real loads are spread over areas or lengths, and replacing them with an equivalent resultant lets you use the simple equilibrium methods.
Loads spread over length or area are replaced by an equivalent resultant for analysis.
Real loads are spread over areas or lengths, and replacing them with an equivalent resultant lets you use the simple equilibrium methods.
Multiply the intensity by the length or area to get the total load, and place it at the centroid of the loaded region.
Yes. The resultant gives the same reactions, but the internal forces near the load depend on how it is distributed, so use the true distribution where it matters.
Typical applications include replacing the snow load on a roof with a single equivalent force, finding the resultant of water pressure on a dam face and simplifying the self-weight of a uniform beam for reactions.
Study "Centre of gravity and centroid" first (topic 15 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Only for statics, not internal forces. Pressure from fluids is distributed. Reactions use the equivalent point load.
A 5 kN/m load over 4 m is equivalent to 20 kN at the centre.
The next topic is "Frames and machines", which builds directly on this one.
It is classed as Beginner in Engineering Mechanics (topic 16 of 106). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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