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# 1630.9.1 Determination for Delta sub-S

• To: <seaint(--nospam--at)seaint.org>
• Subject: 1630.9.1 Determination for Delta sub-S
• From: "Dennis Wish" <dennis.wish(--nospam--at)verizon.net>
• Date: Thu, 8 Jul 2004 19:12:43 -0700

I believe that there is an error in both the seismic design manual volume I and the 97 UBC – maybe not an error, but certainly a confusing explanation for the static deflection where ASD methods are used. What is clear is that the calculated story drift for a building with a fundamental period less than 0.7 seconds is:

Delta sub-m = 0.7*R*Delta sub-s.  However, in the definition for Delta sub-s the code only refers to the mathematical model within ASD methods to comply with section 1630.1.2 – which states (for seismic zone 4) “The mathematical model of the physical structure shall include all elements of the lateral force-resisting system. The model shall also include the stiffness and strength of elements, which are significant to the distribution of forces, and shall represent the spatial distribution of the mass and stiffness of the structure. In addition the model shall comply with the following;

1. Stiffness properties of reinforced concrete and masonry elements shall consider the effects of cracked sections.
2. For steel moment frame systems, the contribution of panel zone deformations to overall story drift shall be included.”

Now what the hell does this mean? If I go to the ICBC Seismic Design Manual Volume I – Example 30 for Drift analysis uses a fundamental period of 0.6 seconds and each story is 12-feet. They reference section 1630.10.3 Limitations;

“The design lateral forces used to determine the calculated drift may disregard the limitations of Formula (30-6) and may be based on the period determined from Formula (30-10) neglecting the 30 or 40 percent limitations of Section 1630.2.2, Item 2. “

Assuming the fundamental period T is 0.6 seconds, then the calculated deflection Delta sub-s works out to be 0.3-inches for a 12-foot height. This works out to 0.025H but does not convert to inches. The assumption is that 0.025 contains a conversion to inches in this case, but when considering the maximum calculated story drift of Section 1630.10.2, the drift Delta sub-m need not exceed 0.020H where H is converted to inches.

In the design example, Delta sub-s is equal to 0.025(12-feet) and equals 0.3 inches. Therefore Delta sub-m is calculated for a 0.6 second period as 0.6*8.5*0.3 or 1.79-inches. This value need not exceed the calculated drift of 0.025*12*12 or 3.6-inches.

Am I missing something here? This does not make sense to me nor does it define how to calculate Delta sub-s other than to calculate the maximum story drift. Delta sub-m is the allowable story drift – so what should I be designing to – the maximum or the allowable or should the allowable simply default to the maximum? Furthermore, this appears to yield higher story drifts than the original values of 0.005*12*12 or 0.72 inches.

Can somebody help me with this – how do I calculate the allowable story drift?

TIA

Dennis

### Dennis S. Wish, PE

California Professional Engineer

Structural Engineering Consultant

dennis.wish(--nospam--at)verizon.net

http://www.structuralist.net

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