{"text_format":"1","workbook":"xlsx","n_sheets":5,"sheets":["Example 3.1","Example 3.2","Example 3.3","Example 3.4","Example 3.5"],"not_rendered":{"charts":1,"images":9,"macros":1,"external_links":0,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Example 3.1","index":0,"n_rows":63,"n_cols":23,"rows_kept":63,"cut":false,"hidden":false,"merged":[]}
["A Beginner's Guide to ACI318-14",null,null,null,null,null,"Last modified:","2017-12-04"]
["Example Problem 3.1",null,null,null,null,null,"by:","TBQ"]
[]
[]
[]
[]
[]
[null,"fy",60,"ksi",null,null,"X-X","Y-Y"]
[null,"f'c",5,"ksi","bar","Area","Axis","Axis"]
[null,"Beta 1",{"$f":"MAX(MIN(0.85-(C9-4)*0.05,0.85),0.65)","v":0.79999999999999993},null,null,"(in^2)","(in)","(in)"]
[null,null,null,null,1,1,15,-3]
[null,null,null,null,2,1,15,0]
[null,null,null,null,3,1,15,3]
[null,null,null,null,4,1,0,-9]
[null,null,null,null,5,1,0,0]
[null,null,null,null,6,1,0,9]
[null,null,null,null,7,1,-15,-9]
[null,null,null,null,8,1,-15,9]
[null,null,null,null,"coordinate measured from center of area"]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Strong Axis Bending"]
[null,"c =",25,"in","a =",{"$f":"+C10*C29","v":20},"in., measured from compression face"]
[]
[null,"Concrete Area and Centroid Computations",null,null,null,null,null,null,null,null,null,null,null,null,"Computation of Interaction Curve"]
[null,null,"Width","Height","Area","Ycf","Ycf*A","XCA","X*A",null,null,null,null,null,"c","Pn","Mnx"]
[null,null,"(in)","(in)","(in2)","(in)","(in3)","(in)","(in3)",null,null,null,null,null,"(in)","(k)","(ft-k)"]
[null,"A1",12,{"$f":"IF(F29<=12,F29,12)","v":12},{"$f":"+C34*D34","v":144},{"$f":"MIN(F29/2,6)","v":6},{"$f":"+F34*E34","v":864},0,{"$f":"+E34*H34","v":0},"Top third of  section",null,null,null,null,1E-3,479.95920000000001,-74.938801359999999,null,null,null,null,{"$f":"+Q34","v":-74.938801359999999},{"$f":"-P34","v":-479.95920000000001}]
[null,"A2",24,{"$f":"IF(F29<=24,MAX(0,F29-12),12)","v":8},{"$f":"+C35*D35","v":192},{"$f":"IF(F29<=24,MAX(0,F29-12)/2+12,18)","v":16},3072,0,{"$f":"+E35*H35","v":0},"Middle third of section",null,null,null,null,1.8,400.56,38.253600000000006,null,null,null,null,{"$f":"+Q35","v":38.253600000000006},{"$f":"-P35","v":-400.56}]
[null,"A3",12,{"$f":"IF(F29<=36,MAX(0,F29-24),12)","v":0},{"$f":"+C36*D36","v":0},{"$f":"IF(F29<=36,MAX(0,F29-24)/2+24,30)","v":24},0,0,0,"Bottom third of section",null,null,null,null,2.1800000000000002,309.23031192660551,154.23484609174315,null,null,null,null,154.23484609174315,-309.23031192660551]
[null,"As1",null,null,{"$f":"IF(F37<F$29,-F11,0)","v":-1},{"$f":"18-G11","v":3},-3,{"$f":"+H11","v":-3},3,null,null,null,null,null,3.31,140.50789123867071,368.2268399516617,null,null,null,null,368.2268399516617,-140.50789123867071]
[null,"As2",null,null,-1,3,-3,0,0,null,null,null,null,null,5.0599999999999996,4.5083003952584022E-2,541.73475024505922,null,null,null,null,541.73475024505922,-4.5083003952584022E-2]
[null,"As3",null,null,-1,3,-3,3,-3,null,null,null,null,null,8.1199999999999992,-183.11742857142843,747.05000171428571,null,null,null,null,747.05000171428571,183.11742857142843]
[null,"As4",null,null,-1,18,-18,-9,9,null,null,null,null,null,11.28,-351.98463829787227,876.35427600000003,null,null,null,null,876.35427600000003,351.98463829787227]
[null,"As5",null,null,-1,18,-18,0,0,null,null,null,null,null,13.64,-520.33384750733148,940.80304399999989,null,null,null,null,940.80304399999989,520.33384750733148]
[null,"As6",null,null,-1,18,-18,9,-9,null,null,null,null,null,15.82,-690.19613400758521,1002.6895719999999,null,null,null,null,1002.6895719999999,690.19613400758521]
[null,"As7",null,null,0,33,0,-9,0,null,null,null,null,null,17.53,-858.70028180262398,1056.8760519999998,null,null,null,null,1056.8760519999998,858.70028180262398]
[null,"As8",null,null,0,33,0,9,0,null,null,null,null,null,19.3,-1027.7103108808294,1096.2097000000001,null,null,null,null,1096.2097000000001,1027.7103108808294]
[null,"Total",null,null,{"$f":"SUM(E34:E44)","v":330},null,{"$f":"SUM(G34:G44)","v":3873},null,{"$f":"SUM(I34:I44)","v":0},null,null,null,null,null,20.91,-1197.2233601147773,1092.9428829210908,null,null,null,null,1092.9428829210908,1197.2233601147773]
[null,"Ac =",{"$f":"+E45","v":330},"in^2",null,null,null,null,null,null,null,null,null,null,22.53,-1352.5658428761653,1075.1352850226365,null,null,null,null,1075.1352850226365,1352.5658428761653]
[null,"Ycf =",{"$f":"+G45/C46","v":11.736363636363636},"in (center of area measured from the compression face)",null,null,null,null,null,null,null,null,null,null,24.21,-1521.809234200744,1045.0773494869889,null,null,null,null,1045.0773494869889,1521.809234200744]
[null,"Y =",{"$f":"18-C47","v":6.2636363636363637},"in (Y location of center of area measured from centroidal X axis)",null,null,null,null,null,null,null,null,null,null,25.93,-1690.7655549556498,1001.3649029679908,null,null,null,null,1001.3649029679908,1690.7655549556498]
[null,"X =",{"$f":"+I45/E45","v":0},"in (X location of center of area measured from centroidal Y axis)",null,null,null,null,null,null,null,null,null,null,27.7,-1860.9246931407943,942.1292234657044,null,null,null,null,942.1292234657044,1860.9246931407943]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,29.5,-2030.8016949152538,866.58758474576314,null,null,null,null,866.58758474576314,2030.8016949152538]
[null,null,"Area","Ycf","strain","stress","Force","y arm","Mnx",null,"x arm","Mny",null,null,32.4,-2201.197777777777,768.29667777777752,null,null,null,null,768.29667777777752,2201.197777777777]
[null,null,"(in^2)","(in)",null,"(ksi)","(k)","(in)","(in-k)",null,"(in)","(in-k)",null,null,35.799999999999997,-2370.5198882681557,639.98092681564265,null,null,null,null,639.98092681564265,2370.5198882681557]
[null,"Conc",{"$f":"+C46","v":330},{"$f":"+C47","v":11.736363636363636},"----",{"$f":"-0.85*C9","v":-4.25},{"$f":"+C53*F53","v":-1402.5},{"$f":"+D53-18","v":-6.2636363636363637},{"$f":"+G53*H53","v":8784.75},null,{"$f":"+C49","v":0},{"$f":"+G53*K53","v":0},null,null,40,-2572.4999999999995,443.00000000000063,null,null,null,null,443.00000000000063,2572.4999999999995]
[null,"Bar 1",{"$f":"F11","v":1},{"$f":"+F37","v":3},{"$f":"0.003*(D54-C$29)/C$29","v":-2.64E-3},{"$f":"MIN(MAX(E54*29000,-C$8),C$8)","v":-60},-60,{"$f":"-G11","v":-15},{"$f":"+G54*H54","v":900},null,{"$f":"+H11","v":-3},{"$f":"+G54*K54","v":180},null,null,42.5,-2681.3529411764703,315.56985294117641,null,null,null,null,315.56985294117641,2681.3529411764703]
[null,"Bar 2",1,3,-2.64E-3,-60,-60,-15,{"$f":"+G55*H55","v":900},null,0,{"$f":"+G55*K55","v":0},null,null,107,-2894,69.687500000000227,null,null,null,null,69.687500000000227,2894]
[null,"Bar 3",1,3,-2.64E-3,-60,-60,-15,{"$f":"+G56*H56","v":900},null,3,{"$f":"+G56*K56","v":-180}]
[null,"Bar 4",1,18,-8.4000000000000003E-4,-24.36,-24.36,0,{"$f":"+G57*H57","v":0},null,-9,{"$f":"+G57*K57","v":219.24}]
[null,"Bar 5",1,18,-8.4000000000000003E-4,-24.36,-24.36,0,{"$f":"+G58*H58","v":0},null,0,{"$f":"+G58*K58","v":0}]
[null,"Bar 6",1,18,-8.4000000000000003E-4,-24.36,-24.36,0,0,null,9,-219.24]
[null,"Bar 7",1,33,9.6000000000000002E-4,27.84,27.84,15,417.6,null,-9,-250.56]
[null,"Bar 8",1,33,9.6000000000000002E-4,27.84,27.84,15,417.6,null,9,250.56]
[null,null,null,null,null,"Pn =",{"$f":"SUM(G53:G61)","v":-1599.8999999999999},"k",{"$f":"SUM(I53:I61)","v":12319.95},"in-k",null,{"$f":"SUM(L53:L61)","v":0},"in-k"]
[null,null,null,null,null,null,null,"Mnx =",{"$f":"+I62/12","v":1026.6625000000001},"ft-k","Mny =",{"$f":"+L62/12","v":0},"ft-k"]

{"sheet":"Example 3.2","index":1,"n_rows":52,"n_cols":14,"rows_kept":52,"cut":false,"hidden":false,"merged":[]}
["A Beginner's Guide to ACI318-14",null,null,null,null,null,"Last modified:","2017-12-04"]
["Example Problem 3.2",null,null,null,null,null,"by:","TBQ"]
[]
[]
[]
[]
[null,"fy",60,"ksi","bar","Area","x","y"]
[null,"f'c",6,"ksi",null,"(in^2)",null,"(in)"]
[null,"b",36,"in",1,1.127,{"$f":"-36+6+13.2","v":-16.8},{"$f":"13.2-6","v":7.1999999999999993}]
[null,"h",36,"in",2,1.127,{"$f":"13.2-6","v":7.1999999999999993},{"$f":"+H9","v":7.1999999999999993}]
[null,null,null,null,3,1.127,{"$f":"+G10","v":7.1999999999999993},{"$f":"13.2-36+6","v":-16.8}]
[null,null,null,null,"coordinate measured from center of area"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Solution:"]
[]
[null,"b1",{"$f":"MAX(MIN(0.85-(C8-4)*0.05,0.85),0.65)","v":0.75}]
[]
[null,"c",100,"in  <-- Note that you cannot enter \"0\", so put in a small number (i.e. 0.0001) for zero"]
[null,"a",{"$f":"+C27*C25","v":75},"in"]
[]
[null,"Concrete Area and Centroid Computations"]
[null,null,"Width","Height","Area","Ycf","Ycf*A","XCA","X*A"]
[null,null,"(in)","(in)","(in2)","(in)","(in3)","(in)","(in3)"]
[null,"A1",36,{"$f":"MIN(12,C28)","v":12},{"$f":"+C33*D33","v":432},{"$f":"+D33/2","v":6},{"$f":"+F33*E33","v":2592},{"$f":"13.2-36/2","v":-4.8000000000000007},{"$f":"+E33*H33","v":-2073.6000000000004}]
[null,"A2",12,{"$f":"MAX(0,MIN(24,C28-12))","v":24},{"$f":"+C34*D34","v":288},{"$f":"+D34/2+12","v":24},6912,{"$f":"13.2-6","v":7.1999999999999993},{"$f":"+E34*H34","v":2073.6}]
[null,"AS1",null,null,{"$f":"IF(13.2-H9<=C28,-F9,0)","v":-1.127},{"$f":"13.2-H9","v":6},-6.7620000000000005,{"$f":"+G9","v":-16.8},{"$f":"+E35*H35","v":18.933600000000002}]
[null,"AS2",null,null,{"$f":"IF(13.2-H10<=C28,-F10,0)","v":-1.127},{"$f":"13.2-H10","v":6},-6.7620000000000005,{"$f":"+G10","v":7.1999999999999993},{"$f":"+E36*H36","v":-8.1143999999999998}]
[null,"AS3",null,null,{"$f":"IF(13.2-H11<=C28,-F11,0)","v":-1.127},30,-33.81,{"$f":"+G11","v":7.1999999999999993},{"$f":"+E37*H37","v":-8.1143999999999998}]
[null,null,null,null,{"$f":"SUM(E33:E37)","v":716.61900000000014},null,{"$f":"SUM(G33:G37)","v":9456.6659999999993},null,{"$f":"SUM(I33:I37)","v":2.7047999999995476}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"2*G48","v":-135.24}]
[null,"Ac =",{"$f":"+E38","v":716.61900000000014},"in^2"]
[null,"Ycf =",{"$f":"+G38/C40","v":13.196225609424252},"in (center of area measured from the compression face)"]
[null,"Y =",{"$f":"13.2-C41","v":3.7743905757476881E-3},"in (Y location of center of area measured from centroidal X axis)"]
[null,"X =",{"$f":"+I38/C40","v":3.7743905757446385E-3},"in (X location of center of area measured from centroidal Y axis)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"2*I48","v":973.72799999999995}]
[null,null,"Area","Ycf","strain","stress","Force","y arm","Mnx",null,"x arm","Mny"]
[null,null,"(in^2)","(in)",null,"(ksi)","(k)","(in)","(in-k)",null,"(in)","(in-k)"]
[null,"Conc",{"$f":"+C40","v":716.61900000000014},{"$f":"+C41","v":13.196225609424252},"----",{"$f":"-0.85*C8","v":-5.0999999999999996},{"$f":"+C47*F47","v":-3654.7569000000003},{"$f":"+D47-13.2","v":-3.7743905757476881E-3},{"$f":"+G47*H47","v":13.794480000008837},null,{"$f":"+C43","v":3.7743905757446385E-3},{"$f":"+G47*K47","v":-13.794479999997691}]
[null,"Bar 1",{"$f":"+F9","v":1.127},{"$f":"+F35","v":6},{"$f":"0.003*(D48-C$27)/C$27","v":-2.8200000000000005E-3},{"$f":"MIN(MAX(E48*29000,-C$7),C$7)","v":-60},-67.62,{"$f":"-H9","v":-7.1999999999999993},{"$f":"+G48*H48","v":486.86399999999998},null,{"$f":"+H35","v":-16.8},{"$f":"-G48*K48","v":-1136.0160000000001}]
[null,"Bar 2",{"$f":"+F10","v":1.127},{"$f":"+F36","v":6},{"$f":"0.003*(D49-C$27)/C$27","v":-2.8200000000000005E-3},{"$f":"MIN(MAX(E49*29000,-C$7),C$7)","v":-60},{"$f":"+C49*F49","v":-67.62},{"$f":"-H10","v":-7.1999999999999993},{"$f":"+G49*H49","v":486.86399999999998},null,{"$f":"+H36","v":7.1999999999999993},{"$f":"-G49*K49","v":486.86399999999998}]
[null,"Bar 3",1.127,30,-2.0999999999999999E-3,{"$f":"MIN(MAX(E50*29000,-C$7),C$7)","v":-60},-67.62,16.8,{"$f":"+G50*H50","v":-1136.0160000000001},null,{"$f":"+H37","v":7.1999999999999993},{"$f":"-G50*K50","v":486.86399999999998}]
[null,null,null,null,null,"Pn =",{"$f":"SUM(G47:G50)","v":-3857.6169},"k",{"$f":"SUM(I47:I50)","v":-148.49351999999135},"in-k",null,{"$f":"SUM(L47:L50)","v":-176.08247999999782},"in-k"]
[null,null,null,null,null,null,null,"Mnx =",{"$f":"+I51/12","v":-12.37445999999928},"ft-k","Mny =",{"$f":"+L51/12","v":-14.673539999999818},"ft-k"]

{"sheet":"Example 3.3","index":2,"n_rows":42,"n_cols":8,"rows_kept":42,"cut":false,"hidden":false,"merged":[]}
["A Beginner's Guide to ACI318-14",null,null,null,null,null,"Last modified:","2017-12-05"]
["Example Problem 3.3",null,null,null,null,null,"by:","TBQ"]
[]
[]
[]
[]
[]
[null,"fy",60,"ksi","b",12,"in"]
[null,"f'c",3,"ksi","d",21,"in"]
[null,"Beta 1",{"$f":"MAX(MIN(0.85-(C9-4)*0.05,0.85),0.65)","v":0.85},null,"# bars",5]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"cb =",{"$f":"0.003*F9/(0.003+C8/29000)","v":12.428571428571427},"in"]
[]
[null,"Case 1","Case 2","Case 3"]
["Ab",0.31,0.79,1.27,"in2"]
["As",{"$f":"+B22*$F10","v":1.55},{"$f":"+C22*$F10","v":3.95},{"$f":"+D22*$F10","v":6.35},"in2"]
["a",{"$f":"+B23*$C8/(0.85*$C9*$F8)","v":3.0392156862745101},{"$f":"+C23*$C8/(0.85*$C9*$F8)","v":7.7450980392156872},{"$f":"+D23*$C8/(0.85*$C9*$F8)","v":12.450980392156863},"in"]
["c",{"$f":"+B24/$C10","v":3.575547866205306},{"$f":"+C24/$C10","v":9.1118800461361023},{"$f":"+D24/$C10","v":14.648212226066898},"in"]
[null,{"$f":"IF(B25<=$C19,\"Stl Yields\",\"No yielding\")","v":"Stl Yields"},{"$f":"IF(C25<=$C19,\"Stl Yields\",\"No yielding\")","v":"Stl Yields"},"No yielding"]
["T = C =",{"$f":"+B23*$C8","v":93},{"$f":"+C23*$C8","v":237}]
["d - a/2",{"$f":"+$F9-B24/2","v":19.480392156862745},{"$f":"+$F9-C24/2","v":17.127450980392155}]
["Mnx",{"$f":"IF(B25<=C19,B27*B28,\"---\")","v":1811.6764705882354},{"$f":"IF(C25<=D19,C27*C28,\"---\")","v":4059.2058823529405},null,"in-k"]
["Mnx",{"$f":"+B29/12","v":150.97303921568627},{"$f":"+C29/12","v":338.26715686274503},null,"ft-k  <--- answers"]
[]
["quadratic a",null,null,{"$f":"0.85*C9*F8*C10","v":26.009999999999998}]
["quadratic b",null,null,{"$f":"0.003*29000*D23","v":552.44999999999993}]
["quadratic c",null,null,{"$f":"-0.003*29000*D23*F9","v":-11601.449999999999}]
["sqrt(b2 - 4ac)",null,null,{"$f":"SQRT(D33^2-4*D32*D34)","v":1229.7218630649777}]
["c = quad. X =",null,null,{"$f":"(-D33+D35)/2/D32","v":13.019451423778889},"in"]
["Stl Strain",null,null,{"$f":"0.003*F9/D36-0.003","v":1.8389135570594023E-3}]
["Stl stress",null,null,{"$f":"29000*D37","v":53.328493154722665},"ksi"]
["T = C =",null,null,{"$f":"+D38*D23","v":338.63593153248888},"k"]
["d - a/2",null,null,{"$f":"+F9-C10*D36/2","v":15.466733144893972},"in"]
["Mnx",null,null,{"$f":"+D39*D40","v":5237.5915862855918},"in-k"]
["Mnx",null,null,{"$f":"+D41/12","v":436.4659655237993},"ft-k <--- answer"]

{"sheet":"Example 3.4","index":3,"n_rows":53,"n_cols":13,"rows_kept":53,"cut":false,"hidden":false,"merged":[[47,2,47,8],[48,2,49,2],[48,3,49,3],[48,4,48,5],[48,6,48,7],[48,8,49,8]]}
["A Beginner's Guide to ACI318-14",null,null,null,null,null,"Last modified:","2017-12-04"]
["Example Problem 3.4",null,null,null,null,null,"by:","TBQ"]
[]
[]
[]
[]
[null,"fy",60,"ksi","bar set","Ab","Number","Area","d"]
[null,"f'c",3,"ksi",null,"(in2)",null,"(in2)","(in)"]
[null,"b",12,"in",1,0.31,5,{"$f":"+F9*G9","v":1.55},3]
[null,"h",24,"in",2,{"$f":"+F9","v":0.31},5,{"$f":"+G10*F10","v":1.55},21]
[null,"beta1",{"$f":"MAX(MIN(0.85-(C8-4)*0.05,0.85),0.65)","v":0.85}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Solution:"]
[]
[]
[]
[null,"Strong Axis Bending"]
[null,"c =",3.2205359090420793,"in","a =",{"$f":"+C11*C26","v":2.7374555226857673},"in., measured from compression face"]
[]
[null,"Concrete Area and Centroid Computations"]
[null,null,"Width","Height","Area","Ycf","Ycf*A","XCA","X*A"]
[null,null,"(in)","(in)","(in2)","(in)","(in3)","(in)","(in3)"]
[null,"Acg",12,{"$f":"MIN(F26,C10)","v":2.7374555226857673},{"$f":"+C31*D31","v":32.849466272229208},{"$f":"F26/2","v":1.3687277613428837},{"$f":"+F31*E31","v":44.961976432096847},0,{"$f":"+E31*H31","v":0}]
[null,"As1",null,null,{"$f":"IF(F32<F$26,-H9,0)","v":0},{"$f":"+I9","v":3},0,{"$f":"+H14","v":0},{"$f":"+E32*H32","v":0}]
[null,"As2",null,null,{"$f":"IF(F33<F$26,-H10,0)","v":0},{"$f":"+I10","v":21},0,{"$f":"+H15","v":0},{"$f":"+E33*H33","v":0}]
[null,"Total",null,null,{"$f":"SUM(E31:E33)","v":32.849466272229208},null,{"$f":"SUM(G31:G33)","v":44.961976432096847},null,{"$f":"SUM(I31:I33)","v":0}]
[null,"Ac =",{"$f":"+E34","v":32.849466272229208},"in^2"]
[null,"Ycf =",{"$f":"+G34/C35","v":1.3687277613428837},"in (center of area measured from the compression face)"]
[null,"Y =",{"$f":"18-C36","v":16.631272238657118},"in (Y location of center of area measured from centroidal X axis)"]
[null,"X =",{"$f":"+I34/E34","v":0},"in (X location of center of area measured from centroidal Y axis)"]
[]
[null,null,"Area","Ycf","strain","stress","Force","y arm","Mnx",null,"x arm","Mny"]
[null,null,"(in^2)","(in)",null,"(ksi)","(k)","(in)","(in-k)",null,"(in)","(in-k)"]
[null,"Conc",{"$f":"+C35","v":32.849466272229208},{"$f":"+C36","v":1.3687277613428837},"----",{"$f":"-0.85*C8","v":-2.5499999999999998},{"$f":"+C42*F42","v":-83.766138994184473},{"$f":"C36-C10/2","v":-10.631272238657116},{"$f":"+G42*H42","v":890.54062802836677},null,{"$f":"+C38","v":0},{"$f":"+G42*K42","v":0}]
[null,"Bar 1",{"$f":"H9","v":1.55},{"$f":"+F32","v":3},{"$f":"0.003*(D43-C$26)/C$26","v":-2.0543404756602371E-4},{"$f":"MIN(MAX(E43*29000,-C$7),C$7)","v":-5.9575873794146874},-9.2342604380927664,{"$f":"D43-C10/2","v":-9},{"$f":"+G43*H43","v":83.108343942834892},null,{"$f":"+H14","v":0},{"$f":"+G43*K43","v":0}]
[null,"Bar 2",{"$f":"H10","v":1.55},{"$f":"+F33","v":21},{"$f":"0.003*(D44-C$26)/C$26","v":1.6561961667037831E-2},{"$f":"MIN(MAX(E44*29000,-C$7),C$7)","v":60},93,{"$f":"+D44-C10/2","v":9},{"$f":"+G44*H44","v":837},null,{"$f":"+H15","v":0},{"$f":"+G44*K44","v":0}]
[null,null,null,null,null,"Pn =",{"$f":"SUM(G42:G44)","v":-3.9943227723426844E-4},"k",{"$f":"SUM(I42:I44)","v":1810.6489719712017},"in-k",null,{"$f":"SUM(L42:L44)","v":0},"in-k"]
[null,null,null,null,null,null,null,"Mnx =",{"$f":"+I45/12","v":150.88741433093347},"ft-k","Mny =",{"$f":"+L45/12","v":0},"ft-k"]
[]
[null,null,"Table 3.6.4.1"]
[null,null,"Case","Rebar Size","Singly Reinforced",null,"Doubly Reinforced",null,"Strength Increase"]
[null,null,null,null,"Mnx (ft-k)","c (in)","Mnx (ft-k)","c (in)"]
[null,null,"a","#5",151,3.58,151,3.22,{"$f":"+G51/E51-1","v":0}]
[null,null,"b","#8",338,9.11,336,4.71,{"$f":"+G52/E52-1","v":-5.9171597633136397E-3}]
[null,null,"c","#10",436,13.02,579,5.53,0.32798165137614688]

{"sheet":"Example 3.5","index":4,"n_rows":99,"n_cols":13,"rows_kept":99,"cut":false,"hidden":false,"merged":[]}
["A Beginner's Guide to ACI318-14",null,null,null,null,null,"Last modified:","2017-12-04"]
["Example Problem 3.5",null,null,null,null,null,"by:","TBQ"]
[]
[]
[]
[]
[null,"fy",60,"ksi","bar","Ab","X","Y"]
[null,"f'c",8,"ksi",null,"(in2)","(in)","(in)"]
[null,"b",12,"in",1,0.31,-4,4]
[null,"h",12,"in",2,{"$f":"+F9","v":0.31},4,4]
[null,"beta1",{"$f":"MAX(MIN(0.85-(C8-4)*0.05,0.85),0.65)","v":0.65},null,3,{"$f":"+F10","v":0.31},-4,-4]
[null,"0.85*f'c",null,"ksi",4,{"$f":"+F11","v":0.31},4,-4]
[]
[null,"Axis rotation angle:",null,30,"degrees"]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Solution Summary"]
[null,"Case","Pn","Mnx","Mny"]
[null,null,"(k)","(ft-k)","(ft-k)"]
[null,"a",{"$f":"+G54","v":-6.637062499999999},{"$f":"+I55","v":31.714624999999995},{"$f":"+L55","v":-27.518145833333332}]
[null,"b",{"$f":"+G67","v":-349.96107000000006},{"$f":"+I68","v":108.33764333333335},{"$f":"+L68","v":-53.638643333333334}]
[null,"c ",{"$f":"+G82","v":-943.32553500000017},{"$f":"+I83","v":3.447613333333333},{"$f":"+L83","v":-1.8743633333333332}]
[null,"d",{"$f":"+G98","v":896.36800000000005},{"$f":"+I99","v":0},{"$f":"+L99","v":0}]
[]
["Solution:"]
[null,"Depths to rebar from compression face"]
[null,"Bar 1",2.75,"in"]
[null,"Bar 2",6.625,"in"]
[null,"Bar 3",8.375,"in"]
[null,"Bar 4",13.69,"in"]
[]
[null,"Case dependent values"]
[null,"Case","a","b","c","d"]
[null,"c ",4,10,20,100,"in"]
[null,"a",{"$f":"+C40*$C11","v":2.6},{"$f":"+D40*$C11","v":6.5},{"$f":"+E40*$C11","v":13},{"$f":"+F40*$C11","v":65},"in"]
[null,"Ac",7.81,48.52,130.71,144,"in2"]
[null,"X",-4.25,{"$f":"-1-11/16","v":-1.6875},{"$f":"-3/8","v":-0.375},0,"in"]
[null,"Y",{"$f":"5+1/16","v":5.0625},{"$f":"3+9/16","v":3.5625},{"$f":"9/16","v":0.5625},0,"in"]
[]
[null,"Case (a)","No steel located in the compression area"]
[null,null,"Area","dcf","strain","stress","Force","y arm","Mnx",null,"x arm","Mny"]
[null,null,"(in2)","(in)",null,"(ksi)","(k)","(in)","(in-k)",null,"(in)","(in-k)"]
[null,"Concrete",7.81,null,null,{"$f":"-0.85*C8","v":-6.8},{"$f":"C49*$F49","v":-53.107999999999997},{"$f":"+C44","v":5.0625},{"$f":"-G49*H49","v":268.85924999999997},null,{"$f":"+C43","v":-4.25},{"$f":"-G49*K49","v":-225.70899999999997}]
[null,"Bar 1",{"$f":"+F9","v":0.31},{"$f":"+C33","v":2.75},{"$f":"0.003*(D50-C$40)/C$40","v":-9.3749999999999997E-4},{"$f":"MIN(MAX(E50*29000,-C$7), C$7)","v":-27.1875},{"$f":"+F50*C50","v":-8.4281249999999996},{"$f":"+H9","v":4},{"$f":"-G50*H50","v":33.712499999999999},null,{"$f":"+G9","v":-4},{"$f":"-G50*K50","v":-33.712499999999999}]
[null,"Bar 2",{"$f":"+F10","v":0.31},{"$f":"+C34","v":6.625},{"$f":"0.003*(D51-C$40)/C$40","v":1.96875E-3},{"$f":"MIN(MAX(E51*29000,-C$7), C$7)","v":57.09375},{"$f":"+F51*C51","v":17.6990625},{"$f":"+H10","v":4},{"$f":"-G51*H51","v":-70.796250000000001},null,{"$f":"+G10","v":4},-70.796250000000001]
[null,"Bar 3",0.31,8.375,3.2812499999999999E-3,{"$f":"MIN(MAX(E52*29000,-C$7), C$7)","v":60},18.600000000000001,-4,74.400000000000006,null,-4,74.400000000000006]
[null,"Bar 4",0.31,13.69,7.2674999999999997E-3,{"$f":"MIN(MAX(E53*29000,-C$7), C$7)","v":60},18.600000000000001,-4,74.400000000000006,null,4,-74.400000000000006]
[null,null,null,null,null,"Pn =",{"$f":"SUM(G49:G53)","v":-6.637062499999999},"kips",{"$f":"SUM(I49:I53)","v":380.57549999999992},null,null,{"$f":"SUM(L49:L53)","v":-330.21774999999997}]
[null,null,null,null,null,null,null,"Mnx =",{"$f":"+I54/12","v":31.714624999999995},"ft-k","Mny =",{"$f":"+L54/12","v":-27.518145833333332},"ft-k"]
[]
[]
[null,"Case (b)","One bar in compression area"]
[null,null,"Area","dcf","strain","stress","Force","y arm","Mnx",null,"x arm","Mny"]
[null,null,"(in2)","(in)",null,"(ksi)","(k)","(in)","(in-k)",null,"(in)","(in-k)"]
[null,"Concrete",{"$f":"+D42","v":48.52},null,null,{"$f":"+F49","v":-6.8},{"$f":"C61*$F61","v":-329.93600000000004},{"$f":"+D44","v":3.5625},{"$f":"-G61*H61","v":1175.3970000000002},null,{"$f":"+D43","v":-1.6875},{"$f":"-G61*K61","v":-556.76700000000005}]
[null,"Hole-Bar1",{"$f":"F9","v":0.31},{"$f":"+D63","v":2.75},null,{"$f":"-F61","v":6.8},{"$f":"+C62*F62","v":2.1080000000000001},{"$f":"+H63","v":4},{"$f":"-G62*H62","v":-8.4320000000000004},null,{"$f":"+K63","v":-4},{"$f":"-G62*K62","v":8.4320000000000004}]
[null,"Bar 1",{"$f":"+F9","v":0.31},{"$f":"+D50","v":2.75},{"$f":"0.003*(D63-D$40)/D$40","v":-2.1750000000000003E-3},{"$f":"MIN(MAX(E63*29000,-C$7), C$7)","v":-60},{"$f":"+F63*C63","v":-18.600000000000001},{"$f":"+H50","v":4},{"$f":"-G63*H63","v":74.400000000000006},null,{"$f":"+K50","v":-4},-74.400000000000006]
[null,"Bar 2",{"$f":"+F10","v":0.31},{"$f":"+D51","v":6.625},{"$f":"0.003*(D64-D$40)/D$40","v":-1.0124999999999999E-3},{"$f":"MIN(MAX(E64*29000,-C$7), C$7)","v":-29.362499999999997},{"$f":"+F64*C64","v":-9.1023749999999986},{"$f":"+H51","v":4},{"$f":"-G64*H64","v":36.409499999999994},null,{"$f":"+K51","v":4},36.409499999999994]
[null,"Bar 3",0.31,8.375,-4.8749999999999998E-4,{"$f":"MIN(MAX(E65*29000,-C$7), C$7)","v":-14.137499999999999},-4.382625,-4,-17.5305,null,-4,-17.5305]
[null,"Bar 4",0.31,13.69,1.1069999999999999E-3,{"$f":"MIN(MAX(E66*29000,-C$7), C$7)","v":32.102999999999994},9.9519299999999991,-4,39.807719999999996,null,4,{"$f":"-G66*K66","v":-39.807719999999996}]
[null,null,null,null,null,"Pn =",{"$f":"SUM(G61:G66)","v":-349.96107000000006},"kips",{"$f":"SUM(I61:I66)","v":1300.0517200000002},null,null,{"$f":"SUM(L61:L66)","v":-643.66372000000001}]
[null,null,null,null,null,null,null,"Mnx =",{"$f":"+I67/12","v":108.33764333333335},"ft-k","Mny =",{"$f":"+L67/12","v":-53.638643333333334},"ft-k"]
[]
[]
[null,"Case (c)","Three bars in compression area"]
[null,null,"Area","dcf","strain","stress","Force","y arm","Mnx",null,"x arm","Mny"]
[null,null,"(in2)","(in)",null,"(ksi)","(k)","(in)","(in-k)",null,"(in)","(in-k)"]
[null,"Concrete",{"$f":"+E42","v":130.71},null,null,{"$f":"+F61","v":-6.8},{"$f":"C74*$F74","v":-888.82799999999997},{"$f":"+D56","v":0},{"$f":"-G74*H74","v":0},null,{"$f":"+D55","v":0},{"$f":"-G74*K74","v":0}]
[null,"Hole-Bar1",{"$f":"+F9","v":0.31},{"$f":"+D78","v":2.75},null,{"$f":"-F74","v":6.8},{"$f":"+C75*F75","v":2.1080000000000001},{"$f":"+H78","v":4},{"$f":"-G75*H75","v":-8.4320000000000004},null,{"$f":"+K78","v":-4},{"$f":"-G75*K75","v":8.4320000000000004}]
[null,"Hole-Bar2",{"$f":"+F10","v":0.31},{"$f":"+D79","v":6.625},null,{"$f":"-F74","v":6.8},{"$f":"+C76*F76","v":2.1080000000000001},{"$f":"+H79","v":4},{"$f":"-G76*H76","v":-8.4320000000000004},null,{"$f":"+K79","v":4},{"$f":"-G76*K76","v":-8.4320000000000004}]
[null,"Hole-Bar3",0.31,8.375,null,{"$f":"-F74","v":6.8},2.1080000000000001,-4,8.4320000000000004,null,-4,8.4320000000000004]
[null,"Bar 1",{"$f":"+F9","v":0.31},{"$f":"+D63","v":2.75},{"$f":"0.003*(D78-E$40)/E$40","v":-2.5875000000000004E-3},{"$f":"MIN(MAX(E78*29000,-C$7), C$7)","v":-60},{"$f":"+F78*C78","v":-18.600000000000001},{"$f":"+H63","v":4},{"$f":"-G78*H78","v":74.400000000000006},null,{"$f":"+K63","v":-4},{"$f":"-G78*K78","v":-74.400000000000006}]
[null,"Bar 2",{"$f":"+F10","v":0.31},{"$f":"+D64","v":6.625},{"$f":"0.003*(D79-E$40)/E$40","v":-2.0062500000000002E-3},{"$f":"MIN(MAX(E79*29000,-C$7), C$7)","v":-58.181250000000006},{"$f":"+F79*C79","v":-18.0361875},{"$f":"+H64","v":4},{"$f":"-G79*H79","v":72.144750000000002},null,{"$f":"+K64","v":4},{"$f":"-G79*K79","v":72.144750000000002}]
[null,"Bar 3",0.31,{"$f":"+D65","v":8.375},-1.7437500000000001E-3,{"$f":"MIN(MAX(E80*29000,-C$7), C$7)","v":-50.568750000000001},-15.6763125,{"$f":"+H65","v":-4},-62.705249999999999,null,{"$f":"+K65","v":-4},{"$f":"-G80*K80","v":-62.705249999999999}]
[null,"Bar 4",0.31,{"$f":"+D66","v":13.69},-9.4650000000000008E-4,{"$f":"MIN(MAX(E81*29000,-C$7), C$7)","v":-27.448500000000003},-8.5090350000000008,{"$f":"+H66","v":-4},-34.036140000000003,null,{"$f":"+K66","v":4},{"$f":"-G81*K81","v":34.036140000000003}]
[null,null,null,null,null,"Pn =",{"$f":"SUM(G74:G81)","v":-943.32553500000017},"kips",{"$f":"SUM(I74:I81)","v":41.371359999999996},null,null,{"$f":"SUM(L74:L81)","v":-22.492359999999998}]
[null,null,null,null,null,null,null,"Mnx =",{"$f":"+I82/12","v":3.447613333333333},"ft-k","Mny =",{"$f":"+L82/12","v":-1.8743633333333332},"ft-k"]
[]
[]
[null,"Case (d)","four bars in compression area"]
[null,null,"Area","dcf","strain","stress","Force","y arm","Mnx",null,"x arm","Mny"]
[null,null,"(in2)","(in)",null,"(ksi)","(k)","(in)","(in-k)",null,"(in)","(in-k)"]
[null,"Concrete",{"$f":"+F42","v":144},null,null,{"$f":"+F77","v":6.8},{"$f":"C89*$F89","v":979.19999999999993},{"$f":"+D71","v":0},{"$f":"-G89*H89","v":0},null,{"$f":"+D70","v":0},{"$f":"-G89*K89","v":0}]
[null,"Hole-Bar1",{"$f":"+F9","v":0.31},{"$f":"+D94","v":2.75},null,{"$f":"-F89","v":-6.8},{"$f":"+C90*F90","v":-2.1080000000000001},{"$f":"+H94","v":4},{"$f":"-G90*H90","v":8.4320000000000004},null,{"$f":"+K94","v":-4},{"$f":"-G90*K90","v":-8.4320000000000004}]
[null,"Hole-Bar2",{"$f":"+F10","v":0.31},{"$f":"+D95","v":6.625},null,{"$f":"-F89","v":-6.8},{"$f":"+C91*F91","v":-2.1080000000000001},{"$f":"+H95","v":4},{"$f":"-G91*H91","v":8.4320000000000004},null,{"$f":"+K95","v":4},8.4320000000000004]
[null,"Hole-Bar3",0.31,8.375,null,{"$f":"-F89","v":-6.8},-2.1080000000000001,-4,-8.4320000000000004,null,-4,-8.4320000000000004]
[null,"Hole-Bar4",0.31,13.69,null,{"$f":"-F89","v":-6.8},{"$f":"+C93*F93","v":-2.1080000000000001},-4,{"$f":"-G93*H93","v":-8.4320000000000004},null,4,{"$f":"-G93*K93","v":8.4320000000000004}]
[null,"Bar 1",{"$f":"+F9","v":0.31},{"$f":"+D78","v":2.75},{"$f":"0.003*(D94-F$40)/F$40","v":-2.9175E-3},{"$f":"MIN(MAX(E94*29000,-C$7), C$7)","v":-60},{"$f":"+F94*C94","v":-18.600000000000001},{"$f":"+H78","v":4},{"$f":"-G94*H94","v":74.400000000000006},null,{"$f":"+K78","v":-4},{"$f":"-G94*K94","v":-74.400000000000006}]
[null,"Bar 2",{"$f":"+F10","v":0.31},{"$f":"+D79","v":6.625},{"$f":"0.003*(D95-F$40)/F$40","v":-2.8012499999999999E-3},{"$f":"MIN(MAX(E95*29000,-C$7), C$7)","v":-60},{"$f":"+F95*C95","v":-18.600000000000001},{"$f":"+H79","v":4},{"$f":"-G95*H95","v":74.400000000000006},null,{"$f":"+K79","v":4},{"$f":"-G95*K95","v":74.400000000000006}]
[null,"Bar 3",0.31,{"$f":"+D80","v":8.375},-2.7487499999999999E-3,{"$f":"MIN(MAX(E96*29000,-C$7), C$7)","v":-60},-18.600000000000001,{"$f":"+H80","v":-4},-74.400000000000006,null,{"$f":"+K80","v":-4},{"$f":"-G96*K96","v":-74.400000000000006}]
[null,"Bar 4",0.31,{"$f":"+D81","v":13.69},-2.5893000000000001E-3,{"$f":"MIN(MAX(E97*29000,-C$7), C$7)","v":-60},-18.600000000000001,{"$f":"+H81","v":-4},-74.400000000000006,null,{"$f":"+K81","v":4},{"$f":"-G97*K97","v":74.400000000000006}]
[null,null,null,null,null,"Pn =",{"$f":"SUM(G89:G97)","v":896.36800000000005},"kips",{"$f":"SUM(I89:I97)","v":0},null,null,{"$f":"SUM(L89:L97)","v":0}]
[null,null,null,null,null,null,null,"Mnx =",{"$f":"+I98/12","v":0},"ft-k","Mny =",{"$f":"+L98/12","v":0},"ft-k"]