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# Columns with less then 1% vert. reinforcement

• To: seaoc(--nospam--at)seaoc.org
• Subject: Columns with less then 1% vert. reinforcement
• From: Sam Chang <szchang(--nospam--at)pacbell.net>
• Date: Thu, 25 Dec 1997 00:06:59 -0800
• Cc: szchang(--nospam--at)pacbell.net

```Hi:

Working with some old buildings (35 - 50 years vintages) and are
troubled by the insufficiency of vertical reinforcement in those
columns.  New design tables I have seen usually shy away on addressing
these type columns which are OK for new constructions.  For these older
buildings, I thinking of using this approach on figuring the strength on
these columns.  On the other hand, I am not totally comfortable on my
method.   I don't own the ACI's PACCOL program.  I don't know how are
they address this kind of situation.

Here is my example on it:  (Assume short columns)

Proving with the following information:
f'c  = 4000.0 psi
Fy  = 60,000 psi
width of column = 18.0 inches
depth of column = 18.0 inches
Es = 29000 ksi
Reinforced with (4) #9 bars which can then be grouped in two rows
row #1  steel area = 2.00 square inches  & distance to the compression
face =15.5 inches
row #2  steel area = 2.00 square inches  & distance to the compression
face = 2.5 inches

While  (A_st) / (A_g) = 4.00/324.00 = 1.235%,
at the upper limit 		moment = 110.7 k-ft,  P load = 743.7 kips
at the balance point	moment =230.0 k-ft,  P load = 329.3 kips
at the zero compression	moment =130.9 k-ft,  P load = 0 kips
at all tension 		moment =0.0 k-ft, P load = -216.0 kips (in tension)

If the building is not located in the high seismic area and
(A_st) / (A_g) = 3.16/324.00 =  0.975%   ?.. below 1% !!!!!!
Reinforced with (4) #8 bars which can then be grouped in two rows
at the upper limit 		moment = 96.8 k-ft,  P load = 717.1 kips
at the balance point	moment =208.4 k-ft,  P load = 322 kips
at the zero compression	moment =105.5 k-ft,  P load = 0 kips
at all tension 		moment =0.0 k-ft, P load = -170.6 kips (in tension)

What are your opinions on this approach of determining the strength of
columns
that are 0.5% to 1.0 % in ratio?

Thanks

Sam Chang, PE   e-mail  szchang(--nospam--at)pacbell.net

Should you be interested in this software, it is posted on the
web site: http://members.tripod.com/~stlshape/index.html
This is a full feature structural engineering software (not a demo.)

If you run into any difficulty to get the software or document, just
give me a note on my e-mail.  I can send it to you directly. They are
610K not
zipped or 190K zipped (for the slow modems).

======== Following are outputs from StlShape ==========
======== in case you not want to run it yourself =========

On  the First Condition:

CONCRETE TIE COLUMNS -- DESIGN FOR PURE COMPRESSION

f'c =4.00 ksi  Fy =60.00 ksi.  width =18.00 in   depth =18.00 in
Clear column height = 10.00 ft.
Vertical bar size =  9   tie size =  3
(P)u =200.00 kip,   (M)u =120.00 ft-kip
Ec =4031 ksi  eu =0.003 in/in   Es =29000.0 ksi
Block stress profile, Beta1 =0.85
number of rows of steel reinforcements= 2
row(0)  area = 2.000 in^2  & dist= 15.500 in
row(1)  area = 2.000 in^2  & dist=  2.500 in
Ag =324.00 in^2    Ixx =8748.0 in^4    Iyy =8748.0 in^4
(A_st) / (A_g) = 4.00/324.00 = 1.235%

Mom= 0.000 kip-ft,  P= 1062.400,   phi= 0.700   P*phi= 743.680 kip
Mom= 93.238 kip-ft,  P= 1062.399,   phi= 0.700   P*phi= 743.679 kip
Mom= 35.704 kip-ft,  P= 1062.399,   phi= 0.700   P*phi= 743.679 kip
Mom= 0.000 kip-ft,  P= 1062.399,   phi= 0.700   P*phi= 743.679 kip
Mom= 22.750 kip-ft,  P= 1062.399,   phi= 0.700   P*phi= 743.679 kip
Mom= 11.375 kip-ft,  P= 1062.399,   phi= 0.700   P*phi= 743.679 kip
Mom= 110.692 kip-ft,  P= 1062.398,   phi= 0.700   P*phi= 743.679 kip
Mom= 129.422 kip-ft,  P= 1010.577,   phi= 0.700   P*phi= 707.404 kip
Mom= 156.393 kip-ft,  P= 919.510,   phi= 0.700   P*phi= 643.657 kip
Mom= 175.714 kip-ft,  P= 840.517,   phi= 0.700   P*phi= 588.362 kip
Mom= 189.945 kip-ft,  P= 770.935,   phi= 0.700   P*phi= 539.654 kip
Mom= 200.723 kip-ft,  P= 708.830,   phi= 0.700   P*phi= 496.181 kip
Mom= 209.123 kip-ft,  P= 652.764,   phi= 0.700   P*phi= 456.935 kip
Mom= 215.868 kip-ft,  P= 601.646,   phi= 0.700   P*phi= 421.152 kip
Mom= 226.224 kip-ft,  P= 511.060,   phi= 0.700   P*phi= 357.742 kip
Mom= 230.425 kip-ft,  P= 470.404,   phi= 0.700   P*phi= 329.283 kip
Mom= 227.281 kip-ft,  P= 434.388,   phi= 0.700   P*phi= 304.072 kip
Mom= 223.149 kip-ft,  P= 402.267,   phi= 0.700   P*phi= 281.587 kip
Mom= 217.732 kip-ft,  P= 371.495,   phi= 0.700   P*phi= 260.047 kip
Mom= 212.234 kip-ft,  P= 344.035,   phi= 0.700   P*phi= 240.825 kip
Mom= 206.761 kip-ft,  P= 319.310,   phi= 0.700   P*phi= 223.517 kip
Mom= 201.378 kip-ft,  P= 296.870,   phi= 0.700   P*phi= 207.809 kip
Mom= 196.123 kip-ft,  P= 276.359,   phi= 0.700   P*phi= 193.451 kip
Mom= 191.015 kip-ft,  P= 257.492,   phi= 0.700   P*phi= 180.244 kip
Mom= 186.066 kip-ft,  P= 240.036,   phi= 0.700   P*phi= 168.025 kip
Mom= 181.276 kip-ft,  P= 223.801,   phi= 0.700   P*phi= 156.661 kip
Mom= 173.650 kip-ft,  P= 199.064,   phi= 0.700   P*phi= 139.345 kip
Mom= 168.601 kip-ft,  P= 176.645,   phi= 0.709   P*phi= 125.273 kip
Mom= 166.712 kip-ft,  P= 156.239,   phi= 0.731   P*phi= 114.246 kip
Mom= 164.389 kip-ft,  P= 137.441,   phi= 0.752   P*phi= 103.291 kip
Mom= 161.726 kip-ft,  P= 119.938,   phi= 0.770   P*phi= 92.404 kip
Mom= 158.813 kip-ft,  P= 103.625,   phi= 0.788   P*phi= 81.663 kip
Mom= 154.073 kip-ft,  P= 80.907,   phi= 0.813   P*phi= 65.745 kip
Mom= 149.004 kip-ft,  P= 59.939,   phi= 0.835   P*phi= 50.064 kip
Mom= 140.235 kip-ft,  P= 28.813,   phi= 0.869   P*phi= 25.034 kip
Mom= 134.727 kip-ft,  P= 11.405,   phi= 0.888   P*phi= 10.124 kip
Mom= 130.887 kip-ft,  P= 0.000,   phi= 0.900   P*phi= 0.000 kip
Mom= 128.291 kip-ft,  P= -5.184,   phi= 0.900   P*phi= -4.665 kip
Mom= 97.824 kip-ft,  P= -65.504,   phi= 0.900   P*phi= -58.953 kip
Mom= 57.585 kip-ft,  P= -144.767,   phi= 0.900   P*phi= -130.291 kip
Mom= 0.000 kip-ft,  P= -240.000,   phi= 0.900   P*phi= -216.000 kip

For the Second Condition:

Vertical reinforcing ration   (A_st) / (A_g) = 3.16/324.00 = 0.00975

CONCRETE TIE COLUMNS -- DESIGN FOR PURE COMPRESSION

f'c =4.00 ksi  Fy =60.00 ksi.  width =18.00 in   depth =18.00 in
Clear column height = 10.00 ft.
Vertical bar size =  8   tie size =  3
(P)u =200.00 kip,   (M)u =120.00 ft-kip
Ec =4031 ksi  eu =0.003 in/in   Es =29000.0 ksi
Block stress profile, Beta1 =0.85
number of rows of steel reinforcements= 2
row(0)  area = 1.580 in^2  & dist= 15.500 in
row(1)  area = 1.580 in^2  & dist=  2.500 in

Column width reduced to accommodate the low V-bar ratio with new width
=17.56 in
Ag =316.00 in^2    Ixx =8532.0 in^4    Iyy =8115.9 in^4
(A_st) / (A_g) = 3.16/316.00 = 1.000%       ß----- Program made this

Mom= 0.000 kip-ft,  P= 1024.365,   phi= 0.700   P*phi= 717.055 kip
Mom= 84.612 kip-ft,  P= 1024.364,   phi= 0.700   P*phi= 717.055 kip
Mom= 29.553 kip-ft,  P= 1024.364,   phi= 0.700   P*phi= 717.055 kip
Mom= 0.000 kip-ft,  P= 1024.364,   phi= 0.700   P*phi= 717.055 kip
Mom= 17.973 kip-ft,  P= 1024.364,   phi= 0.700   P*phi= 717.055 kip
Mom= 8.986 kip-ft,  P= 1024.364,   phi= 0.700   P*phi= 717.055 kip
Mom= 96.756 kip-ft,  P= 1024.363,   phi= 0.700   P*phi= 717.054 kip
Mom= 119.327 kip-ft,  P= 961.868,   phi= 0.700   P*phi= 673.308 kip
Mom= 144.578 kip-ft,  P= 875.829,   phi= 0.700   P*phi= 613.080 kip
Mom= 162.367 kip-ft,  P= 801.566,   phi= 0.700   P*phi= 561.096 kip
Mom= 175.194 kip-ft,  P= 736.482,   phi= 0.700   P*phi= 515.537 kip
Mom= 184.652 kip-ft,  P= 678.690,   phi= 0.700   P*phi= 475.083 kip
Mom= 191.790 kip-ft,  P= 626.788,   phi= 0.700   P*phi= 438.751 kip
Mom= 197.314 kip-ft,  P= 579.711,   phi= 0.700   P*phi= 405.798 kip
Mom= 205.307 kip-ft,  P= 496.922,   phi= 0.700   P*phi= 347.845 kip
Mom= 208.351 kip-ft,  P= 460.049,   phi= 0.700   P*phi= 322.034 kip
Mom= 205.284 kip-ft,  P= 424.923,   phi= 0.700   P*phi= 297.446 kip
Mom= 201.335 kip-ft,  P= 393.809,   phi= 0.700   P*phi= 275.667 kip
Mom= 196.324 kip-ft,  P= 364.515,   phi= 0.700   P*phi= 255.161 kip
Mom= 191.233 kip-ft,  P= 338.450,   phi= 0.700   P*phi= 236.915 kip
Mom= 186.168 kip-ft,  P= 315.053,   phi= 0.700   P*phi= 220.537 kip
Mom= 181.190 kip-ft,  P= 293.884,   phi= 0.700   P*phi= 205.719 kip
Mom= 176.336 kip-ft,  P= 274.597,   phi= 0.700   P*phi= 192.218 kip
Mom= 171.627 kip-ft,  P= 256.913,   phi= 0.700   P*phi= 179.839 kip
Mom= 167.072 kip-ft,  P= 240.606,   phi= 0.700   P*phi= 168.424 kip
Mom= 162.672 kip-ft,  P= 225.489,   phi= 0.700   P*phi= 157.842 kip
Mom= 155.688 kip-ft,  P= 202.557,   phi= 0.700   P*phi= 141.790 kip
Mom= 149.089 kip-ft,  P= 181.889,   phi= 0.700   P*phi= 127.322 kip
Mom= 146.816 kip-ft,  P= 163.182,   phi= 0.719   P*phi= 117.370 kip
Mom= 144.508 kip-ft,  P= 146.042,   phi= 0.738   P*phi= 107.815 kip
Mom= 141.934 kip-ft,  P= 130.169,   phi= 0.756   P*phi= 98.385 kip
Mom= 139.176 kip-ft,  P= 115.453,   phi= 0.772   P*phi= 89.144 kip
Mom= 134.775 kip-ft,  P= 95.090,   phi= 0.795   P*phi= 75.566 kip
Mom= 130.157 kip-ft,  P= 76.433,   phi= 0.815   P*phi= 62.319 kip
Mom= 122.150 kip-ft,  P= 48.401,   phi= 0.846   P*phi= 40.966 kip
Mom= 117.314 kip-ft,  P= 33.217,   phi= 0.863   P*phi= 28.674 kip
Mom= 112.420 kip-ft,  P= 18.831,   phi= 0.879   P*phi= 16.555 kip
Mom= 105.530 kip-ft,  P= 0.000,   phi= 0.900   P*phi= 0.000 kip
Mom= 88.869 kip-ft,  P= -32.826,   phi= 0.900   P*phi= -29.544 kip
Mom= 54.869 kip-ft,  P= -99.373,   phi= 0.900   P*phi= -89.436 kip
Mom= 0.000 kip-ft,  P= -189.600,   phi= 0.900   P*phi= -170.640 kip

```