PDD Practice Exam Question
Can someone please help me understand this question from the NCARB practice exam? I thought bending stress was maximized at mid span, which made me eliminate answer B....
Thank you!
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Three initial facts to keep in mind:
- Beams are designed to handle moment and shear (and to limit deflection but shhh.)
- The magnitude of these forces varies along a beam's span and within the section.
- A W24's geometry doesn't vary along the span.
#2 and #3 together mean that for most of a beam's span, there's a mismatch between the forces being resisted and the material + geometry that's there to resist those forces. Since we size beams to handle the worst-case scenario, outside that condition the beam will have excess capacity to resist the forces it's subjected to.
But consider this excess capacity in the context of fact #1: while there's ultimately one worst case scenario that determines the size of a beam, to determine what that value is we have to look at the worst-case scenarios for each force: moment, shear, and deflection. For example, as you noted, moment is at its maximum in the midspan. Shear, however, is highest at the supports, while there's (theoretically) zero shear at the midspan, and no moment at the supports.
Moreover, bending forces are highest at the extreme fiber, which for a wide flange means the top and bottom flanges, while shear forces are highest in the middle of the section, which for a wide flange means within the web.
When we put a ~2-inch hole through a 24-inch-deep beam, that opening is in the web, not the flange. Therefore, wherever we put this hole, we're going to be reducing the beam's shear resistance, not (significantly) its moment resistance. Since shear is lowest in the middle of the span but we know this beam had to (at least) be sized to resist the maximum shear it's subjected to (at the ends), the code allows for (limited) openings within the middle third of the span.
Some other thoughts that may be helpful:
- You can't just put any size hole in without affecting a beam's moment resistance, which is probably why the question gave a pipe size and depth - in this case, you'd very likely be safe.
- If you're familiar with steel construction, consider the fact that it's common for non-moment connections to have the top flange coped. If you think through why this might not be a problem, it's similar to why you can put a small hole through a beam's web in the middle: you can take a chunk out of the flange (which resists moment) where there's no moment force just like you can put a hole in the web (which resists shear) where there's no shear force. (You'd also have to remember that a coped connection is effectively a pin connection; instead of transferring moment, the beam just rotates.)
- The question also mentions that this beam spans between a beam and a wall. This is very much "NCARB question-speak" for "the beam is pinned at one end and can slide and rotate at the other end." So, to Valerie's point, NCARB probably feel like this is extra "insurance" for claiming we should understand that there's nothing unusual or exciting about the beam's loading. None of the answers allow you to say "let's cut a hole in the flange!", so the fact this is a (really, really) bad idea is irrelevant.
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