Applied statics in real life

This article will show how theoretical knowledge can be used in order to optimize the available materials.

The problem: We need to cover spans of 3’5 meters but we only have acacia poles of 2 meters in length and some wire.

The solution: build a simple truss combining small pieces to make a long, resistant beam.

Reinforced beam

The calculated computer model


We have employed a general purpose structural application to have a model of the behavior so we can design the pieces. In the figure above, the lines in clear blue represent wood, that will work under compressive forces, while the dark blue lines represent the wire.

A little bit of research in the web gave us a value for the oak wood’s elastic modulus (Young’s modulus) around 11.000 MPa, so we have assumed that our acacias might have a similar behavior. For the steel wire we have assumed 200.000 MPa, which is also quite a standard value.

Once the geometry has been fitted in the program and the material properties have been assigned, we only needed to input the loads, for which we have transformed the 200 Kg per squared meter of our future green roof plus snow into a linear load along the upper part of the truss. This, in KN, is the 0,03 KN/linear meter that appears in the picture above.

Below, we can see how the mathematical model’s deflection and the reality compare to each other.


The truss put together and tested

Reinforced beam-iso

The deflection of the truss as calculated by the program

The construction:

The most complicated part is always to pass from theory to practice. In our case, the biggest issue was the proper design of joints among elements of different materials.


Joint in the middle of the truss


Union between steel wire and wood

For the union in the middle of the truss, that according to our model is only under compression, we have a very big problem of buckling given the irregularity of the acacia. This means that under strong pressure the joint opens and the truss loses stability. A better design is needed in order to neutralize these eccentric forces and keep the pieces together or maybe another element could be used when more trusses work in a whole building.

Regarding the meeting point between steel wire and wood, there is need for a very good design of this point as it is here where the highest tensions are encountered. If the wire is not properly attached, it would either slide or break the wood, in which case we might have serious problems for it is the solidary work of the wire and the wood what makes the truss strong.

Future work:

In the next beam, we hope we will find more solid constructive solutions for the joints in either center and extremes.

Also we would like to verify the correlation between the computer deflections and those that happen in reality in order to adjust the model’s parameters and be able to predict with more accuracy.


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