Almost all structural design engineers I’ve known, myself included, would kill for a chance to design a high-rise building situated in a seismic design category D to F.
Why not? Just the mere mention of special moment frame, derivation of probable shear and proportioning of links and longitudinal bars can get ones excitement skyrocketing at speeds more than “c” in the formula E = mc^2!
You sure are one bad ass structural engineer if you know how to detail these babies.
It’s been quite a while since I last detailed a special moment frame particularly a beam, so let’s have a review shall we?
Say we already have a structural framing…
But before we proceed with the detailing below, let us first assume that our seismic forces came from a properly defined LFRS, and that the correct proportioning of forces had been religiously observed as required by the code.
And for our example, let’s say this beam is part of a moment frame of a dual system. Remember that the frame elements should be capable of resisting 25% of the design seismic forces. What does that mean? 25% of the storey shear per floor should be adequately resisted by moment frames.
And since we cannot dictate the program to be able to meet that requirement per floor in one ETABS run or whatever software you are using, you need to carry out a “scaling up” exercise for every floor that doesn’t meet the 25% shear requirement (imagine doing that for more than 150 storeys!) to make sure that the forces we will be using are correct.
Does that sound a bit gray to you? Ok no worries, we can have a separate discussion for that. But just so we can get on with this, let’s assume that we already have the correct analysis results with the correct seismic forces. Capeesh?
Welcome to the jungle!
Below is our sample beam which we need to detail per the requirements of section 18.6. Further assumption is that the derived flexural reinforcement is the result of ETABS analysis and design.
Let us now check the following requirements one by one:
1. Are the beams and columns in the proper geometrical proportions?
This is to ensure that the design forces during a seismic event is effectively transferred from the beam, to the joint and to the columns. These are self-explanatory and easy to check. Remember, 18.6.2.1(a) through 18.6.2.1(c) should be satisfied.
2. Are the provided flexural bars within the maximum and minimum limits?
Next, we must ensure that our provided reinforcement is within the prescribed minimum and maximum limits as per clause 18.6.3.1.
The minimum allowable reinforcement ratio is the greater of the two all too familiar equations in 9.6.1.2 which is (a) 0.25*[(f’c)^0.5]/fy, and (b) 1.4/fy.
The maximum allowable reinforcement ratio on the other hand, in our example where we used Grade 420 bars, is 0.025. Why limit it to such instead of the one that limits the ratio to a certain percentage of the balanced steel ratio? One reason is to prevent congestion. (One good thing about ACI is, there is a commentary column alongside the provisions explaining the bases for such assumptions/empirical values and equations. I advise you to read those as they are indeed enlightening.)
Then we tabulate our results below to check if all sections in the span of the beam meet the max-min reo criteria.
Of course, all should be ok. No buts, no ifs.
3. Are the half and the quarter bending moment rules satisfied?
Earthquake induces cyclic stresses due to load reversals. What does that look like? Under normal circumstances, gravity loads produce negative bending moments at the support, meaning there are tensile stresses on the topmost part of the beam and compressive stresses on the underside.
But because earthquake loads are cyclic in nature, the stresses will switch: i.e. the upper part will also experience compression and the underside will experience tension. How? More of that on succeeding discussions.
The important thing here is this: proper reinforcement should be provided in the joints before these load reversals happen.
First let’s check on this excerpt from 18.6.3.2:
“Positive moment strength at joint face shall be at least one-half the negative moment strength provided at that face of the joint.”
In the illustration above, the bottom bars on the face of support clearly doesn’t meet the required half of the negative moment strength. So in order to satisfy this requirement, we need to change the bottom bars such that it will have at least half the negative moment strength. So from 7T16, we need to provide 7T25.
Were you able to follow thus far? Next:
“Both the negative and the positive moment strength at any section along member length shall be at least one-fourth the maximum moment strength provided at face of either joint.”
Notice that both midspan top and bottom bars have at least a quarter of the maximum moment strength at the joints. However, since we already changed the bottom bars at the support, it is but proper to change the midspan bottom bars as well while making sure that the bending moment strength required is maintained or exceeded for an ample amount of factor of safety. Makes sense, right? So to finish checking this clause, this should be the amendment.
And to tally the final results of the flexural requirement within the span:
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