Behold the Beam

Behold the beam, an amazing structural element that bends when loaded - but one that must not bend too much. A fallen tree spanning the banks of a river was perhaps the first beam used by primitive man for a specific purpose: to see what's on the other side. That fallen tree was an accidental...


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Behold the beam, an amazing structural element that bends when loaded - but one that must not bend too much. A fallen tree spanning the banks of a river was perhaps the first beam used by primitive man for a specific purpose: to see what's on the other side. That fallen tree was an accidental beam.

Part I

Behold the most basic of structural elements, the beam. Because a beam can bend, it can support a load. However, if a beam is overloaded, and bends too much, it will fail. Every beam has a sort of bending sweet spot. As long as there is a neutral axis with compression on one side and tension on the other side, a beam can support a load. In this article, we will review basic beam behavior and offer the six beam configurations that you are likely to observe during pre-incident planning — or while waiting in line at your local big-box super-duper-mart.

For decades, the late, great Professor Frank Brannigan implored the fire service to "know your buildings." I would add that you should also know how your buildings work. Knowing how different structural systems function and behave will give you a better understanding of what to expect when a particular building is being assaulted by gravity, time and heat.

What You Need to Know About Beams

A beam made of wood or steel will bend when loaded. Anything that bends (deflects) experiences tension and compression. Here's the official description of the internal reaction of a beam to bending: The deflection of a beam at any point is its vertical displacement (strain) from the unstressed (neutral) position.

Here's what you need to know about the beams you'll behold as you meander from building to building from week to week: beams bend when loaded, but must not bend too much. What you also need to know is that not all beams bend when loaded. I know that is confusing, so allow me to explain. A beam is defined as "a rigid structural member designed to support and transfer transverse loads across space to supporting elements." (Say what?) Here's a simple translation: A beam is a horizontal structural element that resists a load by deflecting (bending), which sends the load sideways to a vertical compressive support element. Although beams may bend when loaded, a beam must not bend too much; just-right bending is good, too much bending is bad.

A fallen tree spanning the banks of a river was perhaps the first beam used by primitive man for a specific purpose: to see what's on the other side. Fast forward a million or so years after prehistoric man crossed that river and we now have beams that can be pre-stressed so that there is no bending and thus no tension: behold the pre-tensioned, precast concrete beam. Technically, since a pre-stressed, pre-cast concrete horizontal member does no conventional beam deflection, there is no tension and thus it is not a true beam (think of it as pre-bent beam). Likewise, because each component is directly stressed in tension or compression, a truss is not a beam; think of a truss as a surrogate beam. Prehistoric man had no idea there was such a thing as geometry, let alone that you could use geometry to span a river. (More on pre-stressed, pre-cast concrete beams in upcoming articles.)

Consider the simply supported beam shown by Figure 1.

Long ago, Professor Brannigan explained that a simple beam is supported at two points near its ends. As shown in Figure 2, when a force (load) is applied, the simple unrestrained beam bends along its entire length into a smile shape. Because the ends of a simple beam are not restrained, they are free to rotate when the beam is loaded. This freedom of the beam ends to rotate allows the top of the beam to shorten (compression) and the bottom of the beam to lengthen (tension).

Notice that when bending, or deflecting, the top portion of the beam became shorter (strain); when the strain is shortening, the stress has to be compression. Likewise, notice that the bottom of the beam became longer; the strain is lengthening, thus the stress has to be tension. This internal combination of compression and tension is referred to as bending stress. There is an area within the beam that did not become shorter or become longer, the length of this portion of the beam did not change (no strain = no stress; no stress = no strain). This longitudinal portion within the beam is referred to as the neutral axis.

The neutral axis is an end-to-end imaginary line within a loaded beam where compression meets tension, thus it is "neutral." As you travel up from the neutral axis, compression increases and the beam shortens; as you travel down from the neutral axis, tension increases and the beam lengthens. As long as the neutral axis exists, the beam will support its load. As soon as the tension at the bottom of the beam crosses through the neutral axis (due to overloading), the beam is compromised.

Beam Quiz 1

Considering the loaded beam shown in Figure 2, what portion of the beam has the greatest amount of compression and what portion of the beam has the greatest amount of tension?

  1. Immediately above and below the neutral axis
  2. Along the very top and along the very bottom of the beam
  3. At each supported end
  4. Top midspan and bottom midspan

Answer:

b. Along the very top and along the very bottom of the beam

The evidence is the visible strain. Maximum strain means maximum stress. Stress generates strain; strain is change in shape (deformity) caused by the stress. Notice that the greatest amount of shortening is along the top of the beam. Conversely, notice that the greatest amount of lengthening is along the very bottom of the beam. The least amount of compression and tension would be immediately above and below the neutral axis. This stress/strain relationship is pretty basic: the greater the change in dimension (lengthening/shortening), the greater the stress (compression/tension).

Beam Quiz 2

Again considering the beam shown in Figure 2, at what point would there be the maximum compression and at what point of the beam would there be the maximum tension?

  1. Immediately above and below the neutral axis
  2. Along the very top and along the very bottom of the beam
  3. Where the neutral axis and end supports intersect
  4. Top mid-span and bottom mid-span

Answer:

d. Top mid-span and bottom mid-span

Again, the evidence is the visible strain. The greatest amount of deflection can be seen mid-span. Thus the greatest accumulation of compression and tension is dead center between its supports (mid-span).

Beam Quiz 3

Once again considering the beam shown in Figure 2, at what point within the beam would there be the greatest shear?

  1. Immediately above and below the neutral axis
  2. Along the very top and along the very bottom of the beam
  3. Where the neutral axis and end supports intersect
  4. Top mid-span and bottom mid-span

Answer:

c. Where the neutral axis and end supports intersect

Under design load conditions, evidence of internal beam shear cannot be observed. However, it is possible to visualize internal beam reactions to deflection (bending) and what happens to these reactions when they encounter the resistance of the supported beam ends. All these reactions happen so that the dead load of the beam and the energy within the beam reach the earth as compression.

Structural engineers say that "internal beam shear is generated by the beam's effort to maintain the equilibrium of external forces." In other words, as long as the structural system remains static (not dynamic) and in equilibrium (axial and balanced), the beam itself will not fail.

Next: Beam configurations

MARK EMERY, EFO, is a shift battalion chief with the Woodinville, WA, Fire & Life Safety District. He is a graduate of the National Fire Academy's Executive Fire Officer program and an NFA instructor specialist. Emery received a bachelor of arts degree from California State University at Long Beach and is a partner with Fire Command Seattle LLC in King County, WA. He is in no way affiliated with or an advocate for the truss manufacturing or building construction industries. He may be contacted at fci@usa.com or access his website www.competentcommand.com.

 

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