# Percentage error in calculated Forces during simple structural analysis for a truss pin-jointed strucures

I am currently trying to design a simple truss (pin-jointed) structure able to withstand a 1.2 kN load.

I carried all the analysis and found the forces, stresses and strains in the members. My question now is how good and accurate are those forces I calculated.

Say I found that in a particular member the force was 10000N (tensile) and the proof stress of the alloy I'm using = 100 MPa. Theoretically, using any bar with area > 100mm^2 should be fine, right? However, in the analysis I made several assumptions (massless bars, no firction, loaded through centroid...) and the calculated Force might not be exactly the real-life one. As a rule of thumb, what margins should I take to account for these assumptions? Should I systematically allow for 10% error for example?

Secondly, how safe is it (with regards to failure of the member) to go close to the proof stress? Should I there again allow for a margin for error?

Best wishes,

NB1: I do not have access to a Finte Elements Sotware to run it computationally and check!

NB2: The structure is statically determinate.

This is a question which cannot be answered conclusively, because the issues you are raising are matters of risk and probability. There is no such thing as a calculation which guarantees that the final structure will be secure. All you can do is state that the adopted calculations imply in an acceptable (and very, very low) level of risk.

After all, as you mention, there are a multitude of random variables with behaviors out of your control:

• Might the load be greater than what you actually expect?
• Might the material be faulty, with a strength below what you expect?
• Will the structure behave exactly like the structural model, or will imperfections modify the internal stresses?
• And countless other potential risks...

So, what is that acceptable level of risk? Who has the authority to determine that? Well, the answer is "not you." Instead, every country/state/whatever has a set of codes which determine the adequate methods and considerations to be taken into account when performing your calculations in order to reach the level of risk which the country/state/whatever believes is acceptable.

When dealing with structures, there tend to be two general methodologies: allowable strength design (ASD) and load and resistance factor design (LRFD).

In ASD, the required strength to resist a given load is calculated and compared to the "allowable strength" of the material, which is a fraction (50%, for example) of the material's nominal strength.

In LRFD, the expected loads are increased by a given factor and then the required strength for this increased load is compared to the allowable strength of the material, which is again a fraction of the nominal strength (but higher than in ASD).

For example, in Brazil, bridges have their dead loads increased by 35% and their live loads by 50% (and the dynamic factor). Meanwhile, concrete bridges have their strength reduced by ~30%, while steel bridges are reduced by only ~13%. This is an example of the LRFD method. (Brazil doesn't really use ASD nowadays).