## Bracing

gabuilder
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### Bracing

Created to organize the repeated questions on bracing:

gabuilder
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### Re: Bracing

X-Bracing is not considered significantly stronger than V-Bracing, right?

Also, is there a significant advantage to adding perpendicular support between the diagonals of bracing? For example, among the two below, the left would represent a bracing with the horizontal part in between (ignore the large spacing), while the right would depict it without the bracing.

|/| |/|
|-| |\|
|\| |/|

Among my team, we have arguments for both sides. The horizontal bracing is not contributing to holding the vertical force of the weight, but it is helping the long pieces of wood from bowing outward.

Perhaps light horizontal bracing would be sufficient?

Thanks!

SLM
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### Re: Bracing

gabuilder wrote:X-Bracing is not considered significantly stronger than V-Bracing, right?

Also, is there a significant advantage to adding perpendicular support between the diagonals of bracing? For example, among the two below, the left would represent a bracing with the horizontal part in between (ignore the large spacing), while the right would depict it without the bracing.

|/| |/|
|-| |\|
|\| |/|

Among my team, we have arguments for both sides. The horizontal bracing is not contributing to holding the vertical force of the weight, but it is helping the long pieces of wood from bowing outward.

Perhaps light horizontal bracing would be sufficient?

Thanks!
X-bracing is stronger than V-bracing. But, it is possible to build a competitive tower without using X-bracing.

Neither diagonal nor horizontal bracings directly carry the applied load. Assuming the tower is a rectangular prism, the applied load is carried by the main compression members (the verticals) only, not the bracings. The bracings are used for maintaining the stability of the tower. That is, they are used to prevent (1) excessive deformation of the tower, especially the movement of one side relative to the other side, and (2) buckling of the compression members.

A bracing system divides the 35-cm-long compression members into smaller segments, as shown below.

The length of each segment is referred to as the “un-braced length.”

With respect to buckling, the bracing pattern (K,V, X or Z) is less important than the length of these segments. If the un-braced length is too long, then the compression member would buckle under the load, regardless of the bracing pattern.

Although understanding how a bracing system contributes to the stability of a tower is beyond the scope and purpose of this forum, let's look at a simple case to illustrate the role of horizontal pieces in a bracing system. Suppose we have a long compression member that is about to buckle, as shown below.

The deformed shape of the member, after it buckles, is shown using a dashed line.

To prevent this buckling from happening, we need to brace the member. If there is a fixed (immovable) object (like a wall) close to the member, then we use it to brace the member, Otherwise, we use an adjacent structural member (like another compression member) for bracing the member. Regardless, the most effective way to prevent the buckling is to have a horizontal piece connecting the mid-point of the compression member to the supporting member, as shown below.

It is possible to use inclined pieces (see below) , instead of a horizontal one, to brace the member. But, the most effective way to control this buckling involves using a horizontal piece as it provide more resistive (compression or tensile) force than an inclined member against the outward movement of the compression member.

However, a horizontal piece by itself is insufficient as it does not prevent the relative vertical movement of the compression member, as shown below.

So, to reduce this type of movement, it is necessary to use diagonal bracings as well. Below are three plausible bracing patterns involving horizontal pieces and one pattern with just inclined pieces.

As what bracing pattern is best suited for your tower, only experimentation can tell.

gabuilder
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### Re: Bracing

Thank you so much for the VERY informative post!

gabuilder
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### Re: Bracing

Reconsidering this, I tend to disagree. If one were to place a diagonal bracing under the top corners, such that it is totally nested, would it not bear some of the downward vertical force of the weight?

For example, consider the bracing at the top of the following image.

In my towers, I generally build the bracing so that the weight can be carried from one diagonal to the next, all the way to the bottom, in a "zig-zag" fashion. I tend to think this helps because at the the base of my tower, when I add bracing from the connection point (that between the base and the tower) to the ground, those sticks seem to carry weight (they break when the rest of the base does, as if in compression). Thoughts?

SLM
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### Re: Bracing

gabuilder wrote:Reconsidering this, I tend to disagree...Thoughts?
Two types of forces are generally present in structural members: primary and secondary forces. The primary forces are caused by the applied loads. The secondary forces are caused by nodal displacements and/or the buckling tendency of compression members. The bulk of the primary forces are carried by main structural members, not bracings. Bracings are mainly responsible for carrying the secondary forces in the structure.

How primary forces are distributed in a tower?
The distribution of primary forces in a structure is a function of two things: the geometry of the structure and the stiffness of its members. Since bracings are generally smaller in size than the primary members, they tend to be less stiff than the compression members in the tower. Furthermore, since the applied loads are vertical and the compression members are vertical (or almost vertical) they tend to carry the bulk of the load. Here are a couple of examples to illustrate this point. Let’s take the top part of the tower and makes it rest on the ground, as shown below.

For the following bracing patterns, let’s assume the primary members are 1/4” x 1/8” in size, and the bracings are 1/16” x 1/16” in size. All members have the same density.

Bracing Pattern 1:

The analysis of this structure reveals that 98% of the applied load (P) is distributed to the vertical members. That is, if P is assumed to be 100 N, then the vertical members carry a force of at least 98 N. The diagonal (bracing) members carry about 1% to 2% of the load. That is, the force carried in the top or the bottom diagonal member is about 2 N.

Bracing Pattern 2:

Here, at least 99% of the load is being carried by the vertical members. The diagonal bracings carry at most 1% of the load. That is, if P = 100 N, then the vertical members carry a force of at least 99N whereas the bracings carry forces than range from 0.1 N to 1.1 N.

I highly recommend you verify these results by analyzing your tower.

Where does the force in a bracing come from?
A bracing system tends to maintain the stability of the tower. That is, it tries to prevent the tower and its members from deforming significantly. This causes the development of member forces in the bracings. Here is an example to illustrate the point. Suppose a compression member has a tendency to buckle at its midpoint, as shown below.

To prevent this from happening, let’s braced the member at the midpoint using a horizontal member, as shown below.

For the bracing to work, that it, for it to prevent the outward deformation of the compression member, it has to exert a horizontal force F to the member. Think of it as the force that is required to push the deformed member, at its midpoint, to the right by distance d. This is the main reason why bracings carry force, to prevent the deformation of the structure.
Last edited by SLM on February 15th, 2011, 5:48 pm, edited 2 times in total.

SLM
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### Re: Bracing

As a continuation of the discussion on bracing I thought it might be useful to do a rudimentary comparison of several bracing patterns.

More specifically, let’s compare seven bracing patterns in the context of the following questions.

1. Which pattern requires the most/least amount (length) of bracing?
2. Which pattern causes the most/least amount of axial force in the secondary members?
3. Which pattern creates the most/least amount of sidesway?

These three factors (total brace length, axial force, and sidesway) have a direct effect on the efficiency of the design. Why?

1. The total length of the bracing (secondary) members is directly proportional to the weight of the tower. Everything else equal, the less bracing is used the lighter the tower would be.
2. Generally, brace pieces are considered secondary members in a structure and are not supposed to carry a significant portion of the applied load. If they do, then they need to be designed as main structural members, which means they will end up having a bigger cross-section (heavier member).
3. If a tower has a significant sidesway (lateral movement), then it could fail prematurely due to the additional forces caused by the movement. Imagine a compression member that is somewhat free to move at the top but is restrained at the bottom. If the member, subjected to an axial force of P, has a lateral displacement equals to D at the top, then an additional force (bending moment) of P times D develops at the bottom. Depending on the magnitude D, this additional force could become significant leading to a premature failure of the member and the tower.

Here is the basic tower used in this comparison.

The tower has a height of 36 cm and a width of 4 cm. It is pin connected at the bottom and carries two identical vertical concentrated loads at the top. The main (primary) load carrying members, the vertical ones, are assumed to be 1/4" x 1/8” in cross-section. All secondary (bracing) members are taken to be 1/16” x 1/16” in cross-section. All primary and secondary members are assumed to have the same material properties (i.e., modulus of elasticity).

The comparison is done for the following bracing patterns.

The seven towers were analyzed in order to determine their member forces and nodal displacements. The following picture shows the exaggerated deformed shape of each tower.

Here is a comparison of the patterns based on the total length of the secondary members.

The chart indicates that patterns P2 and P3 lead to the lightest tower (because they require the least amount of material) whereas pattern P4 makes the tower the heaviest (because it requires the most amount of material).

Here is a comparison of the patterns based on the amount of axial load each bracing system carries. The amount of load is given as a percentage of the applied load (P).

According to the chart, most of the patterns carry less than 10% of the applied load. The Bracing pieces in pattern P3 carry virtually no load where as their counterparts in pattern P7 carry at most 17% of the applied load.

Here is a comparison of the patterns based on the amount of lateral displacement. The magnitude of displacement is given in terms of the modulus of elasticity (E) of the material.

The chart shows that pattern P3 is the least efficient one because it produces the most sidesway in the tower. Patterns P6 and P7 are the best choices because they result in the least amount of sidesway.

A comparison like this can be used as a basis for building and testing a few bracing systems in search of one that yields the most efficient tower.

soccerkid812
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### Re: Bracing

how effective are the horizontal pieces (such as in P2 and P3)?

SLM
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### Re: Bracing

soccerkid812 wrote:how effective are the horizontal pieces (such as in P2 and P3)?
How effective are the horizontal pieces? They are very effective in making the pattern work. How effective is the pattern itself? Difficult to quantify. As the above charts indicate, the pattern has its strengths and weaknesses compared to the other patterns.

Here is a picture of an elevated bridge that uses pattern P3.

The bridge weighed 7.72 g and held 14.45 kg. It was placed 5th at the national tournament last year. Here is a noisy video clip of the testing of the bridge at the nationals. Would the structure have hold the load without the horizontal pieces? Absolutely not! Would another pattern have worked as well? Most definitely.
Last edited by SLM on February 16th, 2011, 5:01 pm, edited 1 time in total.

phillies413
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### Re: Bracing

For the bracing in towers in general, it it optimal to use butt (end) joints, or lap joints?

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