Envelope #13: Let’s play “detective”

Good morning – this is Back of the Envelope, where we play “engineering detective” for fun.

In today’s email, I am going to share a mistake (not mine) that a colleague and I came across on a set of as-builts. I’ll go through our thought process for uncovering the error.

It serves as a good reminder to pay attention to the little things because sometimes they could have cascading effects on the design.

Here we go.

(Estimated read time = 2 minutes & 54 seconds)


Here’s what’s shown on the General Notes for the said as-built (see if you can spot the oddity):

  • Seismic importance factor = 1

  • Ss = 33.0%

  • S1 = 9.0%

  • Sds = 0.338

  • Sd1 = 0.144

  • Site class = D

  • Seismic force-resisting system = Ordinary steel concentrically braced frame

  • Response modification factor = 3.25

  • Design base shear = 0.015W

First impressions

Let’s see if you have the same thoughts.

…At first glance, the base shear seems extremely low at 0.015W.

I do know that the project is located in an area traditionally known to have low seismic activity… so maybe OK?

But then, Sds is not that low at 0.338.

Running a quick check per ASCE 7 equation 12.8-2:

Cs = Sds/(R/Ie) = 0.330/(3.25) = 0.102…(significantly larger than the 0.015 shown)

Something is obviously off here. What could it be?

Building fundamental period, maybe? (Not likely since this is a braced framed building but let’s check.)

With a height of 57’, approximate fundamental period is 0.02*57^0.75 = 0.415 sec.

ASCE 7 equation 12.8-3:

Cs = Sd1/(T*(R/Ie)) = 0.144/(0.415*3.25) = 0.107 >> 0.015.

Hmm still not it.


Could the little 0.015 come from the minimum required per equation 12.8-5?

Cs = 0.044*Sds*Ie = 0.044*0.338 = 0.015

Alright there we go.

But why would someone mistakenly use the minimum? I have three hypotheses:

Hypothesis #1: Incorrect set up in a spreadsheet

This could be someone putting the Cs equations into Excel for the first time and somehow messing up the minimums and maximums. Although it’s not likely, it could be possible.

Hypothesis #2: Copy/paste error

Another possibility is that the engineer handed off their calc to a drafter and said something like, “please copy all these factors and show them on the general notes.”

Since equation 12.8-5 is one of the last lines, the wrong Cs simply got incorrectly copied.

Still unlikely but it could happen.

Hypothesis #3: Copy/entry error into the spreadsheet

Here is an imaginary but potentially realistic scenario:

  • The engineer has a trustworthy spreadsheet for calculating Cs that he/she has used for years.

  • The required input for the spreadsheet are: Risk Category, R, Site Class, Ss, S1, structure type, and building height (basically the bare minimum to calculate Cs if the spreadsheet is fully set up including all of the tabulated values from ASCE 7.)

Now, here is a mistake that we’ve all experienced one way or another:

Reading the geotechnical report, the engineer sees that the S1 value is 9.0%. BUT, instead of entering 0.090 into the spreadsheet, he/she enters 0.009!

This will result in Sd1 = 0.014... and running equation 12.8-3:

Cs = Sd1/(T*(R/Ie)) = 0.014/(0.415*3.25) = 0.010 < 0.015

And now the 0.015 from equation 12.8-5 incorrectly governs, and the value gets copied onto the drawings.


(Note that without checking all of the members, it is unclear whether this is a “presentation error” where the number is simply shown incorrectly, or an actual design error where the lateral system is under-designed. Also, wind load could govern in this area, so the system might not be entirely hopeless.)

Still, the point is:

1/ Be extra careful and double/triple check the seismic factors when designing a structure. Make sure to take an extra second to process the percent conversion and decimal points.

2/ When reading the codes, watch out for terms like “need not exceed” or “not required to be taken greater/less than.” If the maximum or minimum limits are significantly larger/smaller than other calculated numbers, take another look to be sure.

3/ Don’t completely rely on a spreadsheet or backbox software. Periodically run some back-of-the-envelope calcs to make sure things make sense.

And that’s all – thanks for reading!

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All the best, and enjoy the rest of your week.

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