What Are Reasonable Spans of Carriers made of Various Materials

Introduction to the span and general application of a carrier

At this part a simple method is presented for finding out if a carrier that supports a roof has a resonable span or not. For this purpose some simple calculations have to be performed. In figure 1 one can see a carrier having a circular crosssection. This carrier is supported from the walls of the building. In the middle of the carrier the roof will be mounted. This can be shown in a simple way by placing a heavy sandbag on the midle of the carrier as can be seen in figure 1

Figure 1: An overview of a the most common use of a carrier

For reasons of simplifying future calculations and understanding the above figure 1 is remade and represented as in figure 2

Figure 2: A simplified figure of the previous overview to allow easier calculations

Three Main factors influencing the allowable span of a carrier

For the start it is Importatnt to remember that the allowable span which a carrier can have so that it will not collapse depends on three important factors:

+ its cross-section geometry (see examples in figure 3 below)

+ its material (steel, wood or reinforced concrete)

+ on how you will apply the load on it (is the weight in the middle of the carrier or at an other point)

Remember: NEVER use concrete or similar brittle materials without reinforcements for a carrier! The possibility that it will colappse is almost certain!

The geometry factor

The dimensions of the cross section geometry are concentrated in a single value which forms the geometry factor (In engineering this factor is called area moment of inertia). For instance 100000 mm^4 in which mm^4 is a unit of measure for this factor (like meters or hours would be for length and time).

Figure 3: An overview of the most common carrier crossections

Notice that from the above mentioned cross-section geometrys the best choice conserning the weight of the carrier and its resistance to the loading in our case would be to use the "H-shaped" cross-section as for instance one can find in railroad tracks. Never the less it is more probable that you will find tree stems or wooden carriers with round or rectangular cross-section that also do the job very good.

If you are interested in detailed how the area moment of inertia is found please see this link to Wikipedia (If you do not have a good mathematical foundation I would not recommend to have a look at it because it is more frightening than helpful). Some values to get a notion of the area moment of inertia for the most common cross section geometries can be obtained from the table below

The Material factor

As you may have experienced yourself every material has a certain strength. For instance if you take two rods of the same diameter one of wood and one of metal you will see that to brake the wooden rod in half would need much less effort than the metal rod. This shows that exactly the same carrier made of metal will for sure be able to resist to a much higher load than a the wooden one. This phenomenon is described using a certain number for each material (called yield stress). For instance for metal a value of 200 MPa is a comon value. MPa is a unit to measure this phenomenon (like meters or hours would be for length and time). A perfect reference for the values of the different carrier materials can be found under the site Wolfram aplha

where one just has to write "yield strength of YYYYY" where YYYY signifies a material like wood, steel or concrete

The Load Application factor

As we have shown in the above example the load is applied in the middle of the carrier. Never the less if it would be possible to apply the load instead of one point in the middle at several point of the carrier there would be a big benefit. Since distributed loading leads to smaller loads in the inside of the carrier and allows so higher spans. For the case of the sandsack this would mean that more ropes have to be applied or for the case of a roofing several vertical links would be needed.

Is finally the span reasonable or not?

<math> \sigma=\frac{M}{I} \cdot z_max</math>

<math>\sqrt{1-e^2}</math>

Remember: A calculation is made so that some addtional safty for the construction is provided. This does not exclude collapse due to other external factors. Its is therefore of big importance to alway keep on eye on the construction and its state. The best thing that could be done would be to make a test by hanging a load of about the one that is expected finally under the condition that no one could get hurt so that one can be confident of the stability of the construction

to be CONTINUED........ Notice: The author accepts no responsibility for the safety of a construction or the correctness of the article

--HTP Petros