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...


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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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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