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Concrete shear wall shear equa 11-32 & 21-7

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This is a summary of a previous discussion of shear design for concrete
shear walls. I fear there are shear wall programs not checking both
equations 11-32 and 21-7. Equation 21-7 is for the special case of high
seismic zones. Some design cases equation 11-32 will require more shear

There are three discussed affects of a higher shear demand in equation
11-32, comparing to 21-7.

I. Varying phi factors.
UBC requires 0.6 in zone 3&4. It was intended that phi is 0.85 for equation
11-32 and 0.6 for equation 21-7.
ACI 318-99 requires a phi of 0.85 for shear in all shear wall applications.
ACI 318-02 requires a phi of 0.75 for shear in all shear wall applications.

II. Varying shear wall length.
Equation 11-32 is limited by the tension steel position, leaving about 80%
of the wall for shear resistance.

III. Varying concrete strength.
For a 10ft tall, 5.5ft long wall with an OTM only due to the shear at the
top. The factor of sqrt(fc') is 89% of the equivalent factor in equation
21-7. The equation 11-32 is reduced further when an OTM is increased, but
limited by code section 1911.10.5 with a value of 2*sqrt(fc').  The largest
factor for equation 21-7 is 3*sqrt(fc'). This is independent of any OTM. Eq
11-32 is dependent on OTM. For a large OTM the smallest factor is 2*sqrt(fc
'). Equation 11-32 then has a strength 66% of equation 21-7.

In summary, the ratio of strength for equation 11-32 divide by equation 21-7
is as follows.

***UBC: 83% If wind is not less than 83% of zone 3&4 EQ, then wind will
control shear. Literal interpretation of UBC concludes that equation 11-32
may also control EQ shear design. Zone 2 seismic forces (67% to 74% of zone
3) are required to have more shear strength than zone 3 (11% to 19%). I hope
and suspect that equation 21-7 is based on better research. The later ACI
codes exclude equation 11-32 for seismic shear of zones 3&4.

***ACI 318-99 59% If wind is not less than 59% of zone 3&4 EQ, then wind
will control shear.

***ACI 318-02 59% If wind is not less than 59% of zone 3&4 EQ, then wind
will control shear.

Because design examples may only design for a seismic force in zone 3&4,
they leave out equation 11-32. The omission of equation 11-32 may have
worked its way into design programs. If so, one will need to check for wind
shear by setting the seismic zone to 1 or 2. This will not work if the
program does not do equation 11-32 for any zone or wind check. That goes to
another issue of protected computer code and whose is responsible. One could
also find 41 and 26 year-old research, and prove that equation 11-32 might
be too conservative and hope the opposite is not concluded. (ACI 318-02 ref.
21.3 & 21.38)

As always, this is for discussion only. I do hope readers will review what
is said and comment.

David Merrick, SE
Sacramento, Ca

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