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Re: Masonry Shear Pier Design - Balanced Strain Condition

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Bill,

I modified a program I wrote for concrete column design to try to account for the different PHI factors for masonry, from 0.65 to 0.85.
The program does a strain compatibility analysis of the section for an assumed neutral axis location.  With a max masonry strain of 0.003.

For Pu max = 0.8 * phi * Po

Po = 1477 kips
phi = 0.65
Pu max = 0.8 * 0.65 * 1477 = 768 kips


For Pu = 0.97 kip ( approximately zero ) the program came up with
phi * Mn = 575.84 kip feet



Program output follows:

       CONCRETE STRENGTH (ksi) =  1.50
       STEEL YIELD STRENGTH (ksi) = 60.0
       GROSS CONCRETE AREA (in^2) =   875.00
       TOTAL # OF REINFORCING BARS =    7
       TOTAL AREA OF BARS (in^2) =    6.16
 
     GEOMETRY OF CONCRETE COLUMN.
 
       VERTEX       X(in)           Y(in)
          1                 0.00            0.00
          2                0.00           56.00
          3              15.63           56.00
          4               15.63            0.00
          5                 0.00            0.00
 
     REINFORCING GEOMETRY.
       BAR #     X(in)      Y(in)      AREA(in^2)
          1          7.81       4.00         0.88
          2          7.81      12.00         0.88
          3          7.81      20.00         0.88
          4          7.81      28.00         0.88
          5          7.81      36.00         0.88
          6          7.81      44.00         0.88
          7          7.81      52.00         0.88
 
     RESULTS OF COLUMN ANALYSIS.
 
       Pu max (kips)= 768.2329 
 
              C                PHI             PHI*Pn            PHI*Mn
             (in)                                    (kips)               (ft_k)
           56.00          0.650            768.78            318.29
           54.88          0.650            753.19            341.08
           53.76          0.650            737.46            363.02
           52.64          0.650            721.59            384.12
           51.52          0.650            706.29            402.94
           50.40          0.650            690.10            422.39
           49.28          0.650            673.73            441.04
           48.16          0.650            657.18            458.89
           47.04          0.650            640.42            475.95
           45.92          0.650            623.45            492.25
           44.80          0.650            606.25            507.79
           43.68          0.650            589.52            521.62
           42.56          0.650            571.80            535.70
           41.44          0.650            553.78            549.09
           40.32          0.650            535.45            561.80
           39.20          0.650            516.77            573.87
           38.08          0.650            497.49            585.00
           36.96          0.650            477.56            595.23
           35.84          0.650            457.88            604.38
           34.72          0.650            436.95            613.47
           33.60          0.650            415.45            622.06
           32.48          0.650            393.32            630.18
           31.36          0.650            370.48            637.89
           30.24          0.650            348.36            642.29
           29.12          0.650            327.17            642.82
           28.00          0.650            306.00            642.64
           26.88          0.650            283.31            641.79
           25.76          0.650            260.63            639.08
           24.64          0.650            239.87            631.85
           23.52          0.650            218.31            623.60
           22.40          0.650            195.83            614.32
           21.28          0.650            172.38            603.93
           20.16          0.650            152.25            589.45
           19.04          0.650            131.94            574.03
           17.92          0.650            109.82            556.61
           16.80          0.680             90.37            562.38
           15.68          0.715             72.75            568.46
           14.56          0.750             53.07            570.07
           13.44          0.795             30.03            573.82
           12.32          0.850              0.97            575.84
 

I have a column interaction diagram I can fax to you if you want.  I can't get it attached to the e-mail.
Let me know if you want it.

Patrick Ebner




>>> Bill(--nospam--at)AllenDesigns.com 08/25/00 01:27PM >>>

I understand a balanced strain condition for a shear pier with bars only on
the outermost cells, but how does one determine a balanced strain condition
for a shear pier with distributed steel (bars in every cell)? It would seem
like to me that, if the outermost bars only were at a strain of Fy/Es, then
the interior bars would be at fs<Fy and the Moment Mn would be less than
that for the condition where P=0.

Any help?

TIA,

Bill Allen, S.E. (CA #2607)
ALLEN DESIGNS
Consulting Structural Engineers
Laguna Niguel, CA


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