When a beam is loaded, it can experience either an increase in flexural rigidity ei or decrease in ei. When this happens, it can have significant consequences for structural design.
The flexural rigidity ei of a beam is determined by two factors: the material used to build the beam and the load that is applied to the same. The more influence the two factors have, the greater the ei.
When a heavy object is being supported by a narrow beam, there may be an increased influence of one factor on the other. This factor may be called a influencing factor or variable in this article due to its role in determining how stiff the beam must be.
It influences whether or not a piece of engineering trusses or roofing material must be loaded, when an object is placed on top of it.
Beam with a uniform load
If the beam has a uniform load, then it can be considered to have a constant ei. This is typically the case when there is no load placed on another part of the beam to balance it.
The only way for the load to change the ei is for something else to shift or transfer its load to another part of the beam. In this case, it may be helpful to consider the beam as having two identical laminations with different loads applied in parallel.
This condition results in an almost infinite elastic range which allows for very high strains before failure occurs. An important note to make is that this condition must always be met for a beam to have infinite elastic range.
If one of these conditions does not match up, then thebeam has an orthotropic (changing) elasticity which can result in failure.
Beam with a triangular load distribution
When there is a high amount of load distributed between several areas of the beam, the stiffness of the beam changes dramatically. This is most notable in large open spaces with lots of ceiling space to spread the load.
The linear elasticity of the beam decreases and its rheological properties increase. A change in rheology occurs when a material changes in size or shape as it stresses. A change in size can occur due to concentration of stress on one area of the material.
A change in shape occurs because different stress points need to move toward or away from that area to create pressure. If a point needs to be removed, it will look like an arc with a thinner perimeter. These changes cause beams with higher triangular load distributions to be more rigid than those with less distribution.
These shapes can affect performance as well. A thickened corner may not allow as much movement for flexibility when placed on furniture.
Beam with a square load distribution
When the maximum stress concentration occurs, the beam experiences a moment of flexural rigidity. This is called a flexural moment and it is important to consider when it occurs.
A moment of flexural rigidity happens when there is a change in stress concentration on one area of the beam due to another area of the beam being placed under greater stress. These moments can be gradual or rapid, depending on whether you are placing a load on the bend or upon insertion into an installation.
In order for a Moment of Flexural Rigidity (mo fr) to occur, two conditions must be met: 1) there must be a region of greater stress concentration and 2) there must be no region of less stress concentration. Both conditions must be present for a neutral Moment Of Flexure ( mo fi).
The mo fr event happens more often than the mo fi event, so it is important to know which one occurs in order to calculate installation force (i.e.: weight of load).
Understanding the effects of load distribution on beam behavior
When designing a ceiling installation, it is important to consider the effects of load distribution on the beam. A large portion of a ceiling installation is exposed roof space.
Since these spaces are rare, having an accurate way to determine how much weight can be supported is important. A piece of software such as a DVD or computer monitor can easily determine how much weight can be supported, but a full-size light fixture cannot be estimated.
An understanding of the effects of load distribution on a full-size light fixture is important. A typical full-size light bulb has an Ei of 0.5 and a beam width of 1 ft. As mentioned earlier, a 0-in.-thick slab covers 1 ft., so the 0-in.-thickbeam only has an Ei of 0.5 × 0.5 = @ .25= @ .
Practical considerations for designing beams with triangular or square load distributions
When a beam has a load distribution that is almost entirely horizontal, it is possible to create a loading system that does not require an anchor point. The weight of the person on the bottom side of the beam determines how much weight must be supported by the support system.
This is true at the top and bottom of the beam. With this method, you do not need to support more material at the top than at the bottom. The only exception is if there is more material below than above to support against shifting or other conditions that require more material.
The only way to determine if this method is appropriate for you is to test it! Take your design into consideration and see if it works for you.
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