Post on 10-Nov-2015
Lecture Chp-9&10 Columns
Lecture GoalsDefinitions for short columnsColumns
Analysis and Design of Short ColumnsGeneral InformationVertical Structural membersTransmits axial compressive loads with or without momenttransmit loads from the floor & roof to the foundationColumn:
Analysis and Design of Short ColumnsGeneral InformationColumn Types:TiedSpiralCompositeCombinationSteel pipe
Analysis and Design of Short ColumnsTie spacing h (except for seismic)tie support long bars (reduce buckling)ties provide negligible restraint to lateral expose of coreTied Columns - 95% of all columns in buildings are tied
Analysis and Design of Short ColumnsPitch = 1.375 in. to 3.375 in.spiral restrains lateral (Poissons effect)axial load delays failure (ductile) Spiral Columns
Analysis and Design of Short ColumnsElastic Behavior An elastic analysis using the transformed section method would be:For concentrated load, Puniform stress over sectionn = Es / EcAc = concrete areaAs = steel area
Analysis and Design of Short ColumnsElastic Behavior The change in concrete strain with respect to time will effect the concrete and steel stresses as follows:Concrete stressSteel stress
Analysis and Design of Short ColumnsElastic Behavior An elastic analysis does not work, because creep and shrinkage affect the acting concrete compression strain as follows:
Analysis and Design of Short ColumnsElastic Behavior Concrete creeps and shrinks, therefore we can not calculate the stresses in the steel and concrete due to acting loads using an elastic analysis.
Analysis and Design of Short ColumnsElastic Behavior Therefore, we are not able to calculate the real stresses in the reinforced concrete column under acting loads over time. As a result, an allowable stress design procedure using an elastic analysis was found to be unacceptable. Reinforced concrete columns have been designed by a strength method since the 1940s. Creep and shrinkage do not affect the strength of the member.Note:
Behavior, Nominal Capacity and Design under Concentric Axial loadsInitial Behavior up to Nominal Load - Tied and spiral columns. 1.
Behavior, Nominal Capacity and Design under Concentric Axial loads
Behavior, Nominal Capacity and Design under Concentric Axial loadsFactor due to less than ideal consolidation and curing conditions for column as compared to a cylinder. It is not related to Whitneys stress block.Let Ag = Gross Area = b*h Ast = area of long steel fc = concrete compressive strength fy = steel yield strength
Behavior, Nominal Capacity and Design under Concentric Axial loadsMaximum Nominal Capacity for Design Pn (max) 2.r = Reduction factor to account for accidents/bendingr = 0.80 ( tied )r = 0.85 ( spiral )ACI 10.3.6.3
Behavior, Nominal Capacity and Design under Concentric Axial loadsReinforcement Requirements (Longitudinal Steel Ast) 3.- ACI Code 10.9.1 requires Let
Behavior, Nominal Capacity and Design under Concentric Axial loads3.- Minimum # of Bars ACI Code 10.9.2 min. of 6 bars in circular arrangement w/min. spiral reinforcement.min. of 4 bars in rectangular arrangementmin. of 3 bars in triangular ties Reinforcement Requirements (Longitudinal Steel Ast)
Behavior, Nominal Capacity and Design under Concentric Axial loads3.ACI Code 7.10.5.1 Reinforcement Requirements (Lateral Ties) # 3 bar if longitudinal bar # 10 bar # 4 bar if longitudinal bar # 11 bar # 4 bar if longitudinal bars are bundledsize
Behavior, Nominal Capacity and Design under Concentric Axial loads3.Reinforcement Requirements (Lateral Ties) Vertical spacing: (ACI 7.10.5.2)
Behavior, Nominal Capacity and Design under Concentric Axial loadsArrangement Vertical spacing: (ACI 7.10.5.3)
Behavior, Nominal Capacity and Design under Concentric Axial loadsExamples of lateral ties.
Behavior, Nominal Capacity and Design under Concentric Axial loadsACI Code 7.10.4 Reinforcement Requirements (Spirals ) 3/8 dia. (3/8 f smooth bar, #3 bar dll or wll wire)sizeclear spacing between spirals 3 in.ACI 7.10.4.31 in.
Behavior, Nominal Capacity and Design under Concentric Axial loadsReinforcement Requirements (Spiral) Spiral Reinforcement Ratio, rs
Behavior, Nominal Capacity and Design under Concentric Axial loadsReinforcement Requirements (Spiral) ACI Eqn. 10-5where
Behavior, Nominal Capacity and Design under Concentric Axial loads4.Design for Concentric Axial Loads (a) Load CombinationGravity:Gravity + Wind:andetc.Check for tension
Behavior, Nominal Capacity and Design under Concentric Axial loads4.Design for Concentric Axial Loads (b) General Strength Requirementf = 0.65 for tied columnsf = 0.7 for spiral columnswhere,
Behavior, Nominal Capacity and Design under Concentric Axial loads4.Design for Concentric Axial Loads (c) Expression for Designdefined:
Behavior, Nominal Capacity and Design under Concentric Axial loadsor
Behavior, Nominal Capacity and Design under Concentric Axial loads* when rg is known or assumed:* when Ag is known or assumed:
Example: Design Tied Column for Concentric Axial Load
Example: Design Tied Column for Concentric Axial LoadDesign tied column for concentric axial loadPdl = 150 k; Pll = 300 k; Pw = 50 k fc = 4500 psi fy = 60 ksiDesign a square column aim for rg = 0.03. Select longitudinal transverse reinforcement.
Example: Design Tied Column for Concentric Axial LoadDetermine the loadingCheck the compression or tension in the column
Example: Design Tied Column for Concentric Axial LoadFor a square column r = 0.80 and f = 0.65 and r = 0.03
Example: Design Tied Column for Concentric Axial LoadFor a square column, As=rAg= 0.03(15.2 in.)2 =6.93 in2Use 8 #8 bars Ast = 8(0.79 in2) = 6.32 in2
Example: Design Tied Column for Concentric Axial LoadCheck P0
Example: Design Tied Column for Concentric Axial LoadUse #3 ties compute the spacing < 6 in. No cross-ties needed
Example: Design Tied Column for Concentric Axial LoadStirrup design Use #3 stirrups with 16 in. spacing in the column
Behavior under Combined Bending and Axial LoadsUsually moment is represented by axial load times eccentricity, i.e.
Behavior under Combined Bending and Axial LoadsInteraction Diagram Between Axial Load and Moment ( Failure Envelope )Concrete crushes before steel yieldsSteel yields before concrete crushesAny combination of P and M outside the envelope will cause failure.Note:
Behavior under Combined Bending and Axial LoadsAxial Load and Moment Interaction Diagram General
Behavior under Combined Bending and Axial LoadsResultant Forces action at Centroid( h/2 in this case )Moment about geometric center
Columns in Pure TensionSection is completely cracked (no concrete axial capacity)Uniform Strain
ColumnsStrength Reduction Factor, f (ACI Code 9.3.2)Axial tension, and axial tension with flexure. f = 0.9Axial compression and axial compression with flexure. Members with spiral reinforcement confirming to 10.9.3 f = 0.70Other reinforced members f = 0.65(a)(b)
ColumnsExcept for low values of axial compression, f may be increased as follows:when and reinforcement is symmetricand
ds = distance from extreme tension fiber to centroid of tension reinforcement.Then f may be increased linearly to 0.9 as fPn decreases from 0.10fc Ag to zero.
Column
ColumnsCommentary:Other sections:f may be increased linearly to 0.9 as the strain es increase in the tension steel. fPb
Design for Combined Bending and Axial Load (Short Column)Design - select cross-section and reinforcement to resist axial load and moment.
Design for Combined Bending and Axial Load (Short Column)Column TypesSpiral Column - more efficient for e/h < 0.1, but forming and spiral expensiveTied Column - Bars in four faces used when e/h < 0.2 and for biaxial bending
1)2)
General ProcedureThe interaction diagram for a column is constructed using a series of values for Pn and Mn. The plot shows the outside envelope of the problem.
General Procedure for Construction of IDCompute P0 and determine maximum Pn in compressionSelect a c value (multiple values)Calculate the stress in the steel components.Calculate the forces in the steel and concrete,Cc, Cs1 and Ts.Determine Pn value.Compute the Mn about the center.Compute moment arm,e = Mn / Pn.
General Procedure for Construction of IDRepeat with series of c values (10) to obtain a series of values.Obtain the maximum tension value.Plot Pn verse Mn.Determine fPn and fMn.Find the maximum compression level.Find the f will vary linearly from 0.65 to 0.9 for the strain values The tension component will be f = 0.9
Example: Axial Load vs. Moment Interaction DiagramConsider an square column (20 in x 20 in.) with 8 #10 (r = 0.0254) and fc = 4 ksi and fy = 60 ksi. Draw the interaction diagram.
Example: Axial Load vs. Moment Interaction DiagramGiven 8 # 10 (1.27 in2) and fc = 4 ksi and fy = 60 ksi
Example: Axial Load vs. Moment Interaction DiagramGiven 8 # 10 (1.27 in2) and fc = 4 ksi and fy = 60 ksi[ Point 1 ]
Example: Axial Load vs. Moment Interaction DiagramDetermine where the balance point, cb.
Example: Axial Load vs. Moment Interaction DiagramDetermine where the balance point, cb. Using similar triangles, where d = 20 in. 2.5 in. = 17.5 in., one can find cb
Example: Axial Load vs. Moment Interaction DiagramDetermine the strain of the steel
Example: Axial Load vs. Moment Interaction DiagramDetermine the stress in the steel
Example: Axial Load vs. Moment Interaction DiagramCompute the forces in the column
Example: Axial Load vs. Moment Interaction DiagramCompute the forces in the column
Example: Axial Load vs. Moment Interaction DiagramCompute the moment about the center
Example: Axial Load vs. Moment Interaction DiagramA single point from interaction diagram, (585.6 k, 556.9 k-ft). The eccentricity of the point is defined as
[ Point 2 ]
Example: Axial Load vs. Moment Interaction DiagramNow select a series of additional points by selecting values of c. Select c = 17.5 in. Determine the strain of the steel. (c is at the location of the tension steel)
Example: Axial Load vs. Moment Interaction DiagramCompute the forces in the column
Example: Axial Load vs. Moment Interaction DiagramCompute the forces in the column
Example: Axial Load vs. Moment Interaction DiagramCompute the moment about the center
Example: Axial Load vs. Moment Interaction DiagramA single point from interaction diagram, (1314 k, 351.1 k-ft). The eccentricity of the point is defined as
[ Point 3 ]
Example: Axial Load vs. Moment Interaction DiagramSelect c = 6 in. Determine the strain of the steel, c =6 in.
Example: Axial Load vs. Moment Interaction DiagramCompute the forces in the column
Example: Axial Load vs. Moment Interaction DiagramCompute the forces in the column
Example: Axial Load vs. Moment Interaction DiagramCompute the moment about the center
Example: Axial Load Vs. Moment Interaction DiagramA single point from interaction diagram, (151 k, 471 k-ft). The eccentricity of the point is defined as
[ Point 4 ]
Example: Axial Load vs. Moment Interaction DiagramSelect point of straight tension. The maximum tension in the column is
[ Point 5 ]
Example: Axial Load vs. Moment Interaction Diagram
Example: Axial Load vs. Moment Interaction DiagramUse a series of c values to obtain the Pn verses Mn.
Chart1
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13.466
37.6081052632
60.781
83.1231428571
104.7478181818
125.7486086957
151.2835
185.99
219.1383076923
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310.846
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1867.9062021639
M (k-ft)
P (k)
Column Analysis
Sheet1
Concrete Column Analysis
fy60ksiEs29000ksi
fc4ksir1
400f0.7
Ast13.81b10.85
Ast22.54
Ast33.81
h20in
b20in
Strain of the Steel
c (in)S1S2S3CcCs1Cs2TPMMPe
2-0.00075-0.012-0.02325115.6-21.75-60-60-82.8675-152.4-228.6-348.26752150.73375179.2278125-348.2675-6.1755224073106.6882118339-207.3117798883
2.25-0.0003333333-0.0103333333-0.0203333333130.05-9.6666666667-60-60-36.83-152.4-228.6-287.782614.4146875217.867890625-287.78-9.0847685298141.2203326939-186.53683765
2.50-0.009-0.018144.50-60-60-12.954-152.4-228.6-249.4542908.81375242.4011458333-249.454-11.6607220169165.2515877464-170.0597141485
2.750.0002727273-0.0079090909-0.0160909091158.957.9090909091-60-6017.1796363636-152.4-228.6-204.87036363643247.0744602273270.5895383523-204.8703636364-15.8494103422195.0242795384-147.6579446133
30.0005-0.007-0.0145173.414.5-60-6042.291-152.4-228.6-165.3093544.5975295.383125-165.309-21.4422535978223.1190096157-124.8669177041
3.250.0006923077-0.0062307692-0.0131538462187.8520.0769230769-60-6063.5390769231-152.4-228.6-129.61092307693810.0752644231317.5062720353-129.6109230769-29.3962512879249.7473989557-101.950713311
3.50.0008571429-0.0055714286-0.012202.324.8571428571-60-6081.7517142857-152.4-228.6-96.94828571434049.7166071429337.4763839286-96.9482857143-41.7719259016275.1007082562-79.0293583028
3.750.001-0.005-0.011216.7529-60-6097.536-152.4-228.6-66.7144268.0746875355.672890625-66.714-63.9756975672299.3432854905-56.1481869285
40.001125-0.0045-0.010125231.232.625-60-60111.34725-152.4-228.6-38.452754468.564375372.3803645833-38.45275-116.2092275585322.6131601938-33.3136877653
4.250.0012352941-0.0040588235-0.0093529412245.6535.8235294118-60-60123.5336470588-152.4-228.6-11.81635294124653.7970404412387.8164200368-11.8163529412-393.8437742685345.0250242995-10.5125447248
0-6100-549
4.50.0013333333-0.0036666667-0.0086666667260.138.6666666667-60-60134.366-152.4-228.613.4664825.80375402.150312513.466358.3695046785357.196844655411.9607334885
4.750.0014210526-0.0033157895-0.0080526316274.5541.2105263158-60-60144.0581052632-152.4-228.637.60810526324986.1879769737415.515664747837.6081052632132.582802087360.29068602232.609721353
50.0015-0.003-0.007528943.5-60-60152.781-152.4-228.660.7815136.2325428.01937560.78184.5039156973362.453922572151.4703612841
5.250.0015714286-0.0027142857-0.007303.4545.5714285714-60-60160.6731428571-152.4-228.683.12314285715276.9757589286439.747979910783.123142857163.4838334734363.789102033868.7650538028
5.50.0016363636-0.0024545455-0.0065454545317.947.4545454545-60-60167.8478181818-152.4-228.6104.74781818185409.2673863636450.772282197104.747818181851.6408597359364.379817552484.6724441265
5.750.0016956522-0.0022173913-0.0061304348332.3549.1739130435-60-60174.3986086957-152.4-228.6125.74860869575533.8092527174461.1507710598125.748608695744.0069223041364.295259576699.3376243108
60.00175-0.002-0.00575346.850.75-58-60180.4035-147.32-228.6151.28355651.18625470.9321875151.283537.3549412196361.5002328608116.1292897993
6.250.0018-0.0018-0.0054361.2552.2-52.2-60185.928-132.588-228.6185.995761.8896875480.1574739583185.9930.9795671138354.0002990537137.1227549125
6.50.0018461538-0.0016153846-0.0050769231375.753.5384615385-46.8461538462-60191.0275384615-118.9892307692-228.6219.13830769235866.3352884615488.8612740385219.138307692326.7700127387346.2379433817155.2055787621
6.750.0018888889-0.0014444444-0.0047777778390.1554.7777777778-41.8888888889-60195.7493333333-106.3977777778-228.6250.90155555565964.8771875497.0730989583250.901555555623.7737752334347.9511692708175.6310888889
70.0019285714-0.0012857143-0.0045404.655.9285714286-37.2857142857-60200.1338571429-94.7057142857-228.6281.42814285716057.8189285714504.8182440476281.428142857121.5252777035353.3727708333196.9997
7.250.0019655172-0.001137931-0.0042413793419.0557-33-60204.216-83.82-228.6310.8466145.4221875512.118515625310.84619.769989601358.4829609375217.5922
7.50.002-0.001-0.004433.558-29-60208.026-73.66-228.6339.2666227.91375518.9928125339.26618.3570229554363.29496875237.4862
7.750.0020322581-0.0008709677-0.0037741935447.9558.935483871-25.2580645161-60211.5901935484-64.155483871-228.6366.78470967746305.4911391129525.4575949261366.784709677417.1912595393367.8203164483256.7492967742
80.0020625-0.00075-0.0035625462.459.8125-21.75-60214.931625-55.245-228.6393.4866256378.3271875531.527265625393.48662516.2097687247372.0690859375275.4406375
8.250.0020909091-0.0006363636-0.0033636364476.8560-18.4545454545-60215.646-46.8745454545-228.6417.02145454556428.3896875535.699140625417.021454545515.4150095095374.9893984375291.9150181818
8.50.0021176471-0.0005294118-0.0031764706491.360-15.3529411765-60215.646-38.9964705882-228.6439.34952941186470.02375539.1686458333439.349529411814.7263700468377.4180520833307.5446705882
8.750.0021428571-0.0004285714-0.003505.7560-12.4285714286-60215.646-31.5685714286-228.6461.22742857146508.5871875542.382265625461.227428571414.1114486787379.6675859375322.8592
90.0021666667-0.0003333333-0.0028333333520.260-9.6666666667-60215.646-24.5533333333-228.6482.69266666676544.08545.34482.692666666713.5574464911381.738337.8848666667
9.250.0021891892-0.0002432432-0.0026756757534.6560-7.0540540541-60215.646-17.9172972973-228.6503.77870270276576.5021875548.0418489583503.778702702713.0543473795383.6292942708352.6450918919
9.50.0022105263-0.0001578947-0.0025263158549.160-4.5789473684-60215.646-11.6305263158-228.6524.51547368426605.85375550.4878125524.515473684212.5942018519385.34146875367.1608315789
9.750.0022307692-0.0000769231-0.0023846154563.5560-2.2307692308-60215.646-5.6661538462-228.6544.92984615386632.1346875552.677890625544.929846153812.1706211071386.8745234375381.4508923077
100.002250-0.00225578600-60215.646-8.636-228.6556.416655.345554.6120833333556.4111.9612246365388.2284583333389.487
10.250.00226829270.0000731707-0.0021219512592.45602.1219512195-60215.646-3.2462439024-228.6576.24975609766675.4846875556.290390625576.249756097611.5843601092389.4032734375403.3748292683
10.360.00227606180.0001042471-0.0020675676598.808603.0231660232-59.9594594595215.646-0.9571583012-228.4455405405585.05130115836682.2149300541556.8512441712585.051301158311.421588016389.7958709198409.5359108108
10.50.00228571430.0001428571-0.002606.9604.1428571429-58215.6461.8868571429-220.98603.45285714296635.40375552.9503125603.452857142910.9957284508387.06521875422.417
10.750.00230232560.0002093023-0.0018837209621.35606.0697674419-54.6279069767215.6466.7812093023-208.1323255814635.64488372096553.0446293605546.0870524467635.644883720910.3092855731382.2609367127444.9514186047
110.00231818180.0002727273-0.0017727273635.8607.9090909091-51.4090909091215.64611.4530909091-195.8686363636667.03045454556471.9947727273539.3328977273667.03045454559.7026975734377.5330284091466.9213181818
11.250.00233333330.0003333333-0.0016666667650.25609.6666666667-48.3333333333215.64615.9173333333-184.15697.66333333336391.9621875532.663515625697.66333333339.1619580421372.8644609375488.3643333333
11.50.00234782610.0003913043-0.0015652174664.76011.347826087-45.3913043478215.64620.1874782609-172.9408695652727.59260869576312.6802717391526.0566893116727.59260869578.6761192957368.2396825181509.314826087
11.750.00236170210.0004468085-0.0014680851679.156012.9574468085-42.5744680851215.64624.2759148936-162.2087234043756.86319148946233.9051130319519.4920927527756.86319148948.2365018977363.6444649269529.8042340426
120.0023750.0005-0.001375693.66014.5-39.875215.64628.194-151.92375785.516256155.413125512.95109375785.516257.8361372219359.065765625549.861375
12.250.00238775510.0005510204-0.0012857143708.056015.9795918367-37.2857142857215.64631.9521632653-142.0585714286813.58959183676076.9989732143506.4165811012813.58959183677.4693666613354.4916067708569.5127142857
12.50.00240.0006-0.0012722.56017.4-34.8215.64635.56-132.588841.1185998.47375499.8728125841.1187.1315484272349.91096875588.7826
12.750.00241176470.0006470588-0.0011176471736.956018.7647058824-32.4117647059215.64639.0263529412-123.4888235294868.13352941185919.6633639706493.3052803309868.13352941186.818839687345.3136962316607.6934705882
130.00242307690.0006923077-0.0010384615751.46020.0769230769-30.1153846154215.64642.3593846154-114.7396153846894.66576923085840.4071153846486.7005929487894.66576923086.5280323851340.6904150641626.2660384615
13.250.00243396230.0007358491-0.0009622642765.856021.3396226415-27.9056603774215.64645.5666415094-106.3205660377920.74207547175760.556432783480.0463693986920.74207547176.2564279251336.032458579644.5194528302
13.50.00244444440.0007777778-0.0008888889780.36022.5555555556-25.7777777778215.64648.6551111111-98.2133333333946.38777777785679.97375473.3311458333946.38777777786.0017403895331.3318020833662.4714444444
13.750.00245454550.0008181818-0.0008181818794.756023.7272727273-23.7272727273215.64651.6312727273-90.4009090909971.62636363645598.5315056818466.5442921402971.62636363645.7620209941326.5810044981680.1384545455
140.00246428570.0008571429-0.00075809.26024.8571428571-21.75215.64654.5011428571-82.8675996.47964285715516.11125459.6759375996.47964285715.5355985338321.77315625697.53575
14.250.00247368420.0008947368-0.0006842105823.656025.9473684211-19.8421052632215.64657.2703157895-75.59842105261020.96789473685432.6028453947452.71690378291020.96789473685.3210320064316.901832648714.6775263158
14.50.00248275860.0009310345-0.0006206897838.16027-18215.64659.944-68.581045.115347.90375445.65864583331045.115.1170726048311.9610520833731.577
14.750.00249152540.0009661017-0.000559322852.556028.0169491525-16.2203389831215.64662.5270508475-61.79949152541068.9235593225261.9183739407438.49319782841068.9235593224.9226329872306.9452384799748.2464915254
150.00250.001-0.00058676029-14.5215.64665.024-55.2451092.4255174.5575431.2131251092.4254.7367622491301.8491875764.6975
15.250.00250819670.0010327869-0.000442623881.456029.9508196721-12.8360655738215.64667.4390819672-48.90540983611115.62967213125085.7377612705423.81148010591115.62967213124.5586254008296.6680360741780.9407704918
15.50.0025161290.0010645161-0.0003870968895.96030.8709677419-11.2258064516215.64669.7762580645-42.77032258061138.55193548394995.3811693548416.28176411291138.55193548394.3874864323291.397234879796.9863548387
15.750.00252380950.0010952381-0.0003333333910.356031.7619047619-9.6666666667215.64672.0392380952-36.831161.20523809524903.4146875408.6178906251161.20523809524.2226942548286.0325234375812.8436666667
160.002531250.001125-0.00028125924.86032.625-8.15625215.64674.2315-31.07531251183.60218754809.76984375400.81415364581183.60218754.0636709652280.5699075521828.52153125
16.250.00253846150.0011538462-0.0002307692939.256033.4615384615-6.6923076923215.64676.3563076923-25.49769230771205.75461538464714.3823798077392.86519831731205.75461538463.909901998275.0056388221844.0282307692
16.50.00254545450.0011818182-0.0001818182953.76034.2727272727-5.2727272727215.64678.4167272727-20.08909090911227.67363636364617.1919318182384.76599431821227.67363636363.7609278191269.3361960227859.3715454545
16.750.00255223880.0012089552-0.0001343284968.156035.0597014925-3.8955223881215.64680.415641791-14.84194029851249.36970149254518.1417397388376.51181164491249.36970149253.6163368892263.5582681514874.5587910448
170.00255882350.0012352941-0.0000882353982.66035.8235294118-2.5588235294215.64682.3557647059-9.74911764711270.85264705884417.1783823529368.09819852941270.85264705883.4757596741257.6687389706889.5968529412
17.250.00256521740.0012608696-0.0000434783997.056036.5652173913-1.2608695652215.64684.2396521739-4.80391304351292.13173913044314.2515353261359.52096127721292.13173913043.3388635266251.664672894904.4922173913
17.50.00257142860.001285714301011.56037.28571428570215.64686.069714285701313.21571428574209.31375350.77614583331313.21571428573.2053482944245.5433020833919.251
17.750.00257746480.00130985920.00004225351025.956037.9859154931.2253521127215.64687.8482253521-8.28540845071321.15881690144199.4752508803349.95627090671321.15881690143.1786301519244.9693896347924.811171831
180.00258333330.00133333330.00008333331040.46038.66666666672.4166666667215.64689.5773333333-3.74651341.87683333334090.38375340.86531251341.87683333333.0482557329238.60571875939.3137833333
18.250.00258904110.00135616440.00012328771054.856039.32876712333.5753424658215.64691.25906849320.66805479451362.42312328773979.1542765411331.59618971181362.42312328772.9206449953232.1173327982953.6961863014
18.50.00259459460.00137837840.00016216221069.36039.9729729734.7027027027215.64692.89535135144.96329729731382.80464864863865.7490202703322.14575168921382.80464864862.7955857858225.5020261824967.9632540541
18.750.00260.00140.00021083.756040.65.8215.64694.4889.1441403.0283750.1321875312.5110156251403.0282.6728847803218.7577109375982.1196
190.00260526320.00142105260.00023684211098.26041.21052631586.8684210526215.64696.038736842113.21468421051423.09942105263632.269868421302.68915570181423.09942105262.5523655021211.8824089912996.1695947368
19.250.00261038960.00144155840.00027272731112.656041.80519480527.9090909091215.64697.549194805217.17963636361443.02483116883512.1299147727292.67749289771443.02483116882.4338665828204.87424502841010.1173818182
19.50.00261538460.00146153850.00030769231127.16042.38461538468.9230769231215.64699.020923076921.04292307691462.80984615383389.6818269231282.47348557691462.80984615382.3172402318197.73143990381023.9668923077
19.750.00262025320.00148101270.00034177221141.556042.94936708869.9113924051215.646100.455392405124.80840506331482.45979746843264.8966495253272.07472079381482.45979746842.2023508867190.45230455561037.7218582278
200.0026250.00150.00037511566043.510.875215.646101.85428.479751501.979753137.746875261.478906251501.979752.0890740205183.0352343751051.385825
20.250.00262962960.00151851850.00040740741170.456044.03703703711.8148148148215.646103.218074074132.06044444441521.37451851853008.2063541667250.68386284721521.37451851851.9772950825175.47870399311064.962162963
20.50.00263414630.00153658540.00043902441184.96044.560975609812.7317073171215.646104.548878048835.5538048781540.64868292682876.2502134146239.68751778461540.64868292681.8669085595167.78126244921078.4540780488
20.750.00263855420.00155421690.00046987951199.356045.072289156613.6265060241215.646105.847614457838.96298795181559.80660240962741.8547778614228.48789815511559.80660240961.7578171381159.94152870861084
210.00264285710.00157142860.00051213.86045.571428571414.5215.646107.115428571442.2911578.85242857142604.9975217.0831251578.85242857141.649930958151.95818751084
21.250.00264705880.00158823530.00052941181228.256046.058823529415.3529411765215.646108.353411764745.54070588241597.79011764712465.6568933824205.47140778191597.79011764711.5431669442143.82998544731084
21.50.00265116280.00160465120.00055813951242.76046.534883720916.1860465116215.646109.562604651248.71483720931616.62344186052323.8124709302193.65103924421616.62344186051.4374482089135.55572747091084
21.750.00265517240.00162068970.00058620691257.15604717215.646110.74451.8161635.3562179.4446875181.6203906251635.3561.3327035138127.13427343751084
220.00265909090.00163636360.00061363641271.66047.454545454517.7954545455215.646111.898545454554.84668181821653.99122727272032.5348863636169.3779071971653.99122727271.2288667877118.56453503791084
22.250.00266292130.00165168540.00064044941286.056047.898876404518.5730337079215.646113.027146067457.8092584271672.53240449441883.0652492978156.92210410811672.53240449441.1258766911109.84547287571084
22.50.00266666670.00166666670.00066666671300.56048.333333333319.3333333333215.646114.130666666760.7061690.98266666671731.01875144.25156251690.98266666671.0236762234100.976093751084
22.750.00267032970.00168131870.00069230771314.956048.758241758220.0769230769215.646115.209934065963.53907692311709.3450109891576.3791105769131.36492588141709.3450109890.922212368291.9554481171084
230.0026739130.00169565220.00071739131329.46049.173913043520.8043478261215.646116.265739130466.31056521741727.62230434781419.1307608696118.26089673911727.62230434780.821435771882.78262771741084
23.250.00267741940.00170967740.00074193551343.856049.580645161321.5161290323215.646117.298838709769.02245161291745.81729032261259.2588004032104.93823336691745.81729032260.721300451973.45676335691084
23.50.00268085110.00172340430.00076595741358.36049.978723404322.2127659574215.646118.309957446871.67663829791763.93259574471096.74896276691.39574689721763.93259574470.62176353363.9770228281084
23.750.00268421050.00173684210.00078947371372.756050.368421052622.8947368421215.646119.299789473774.27494736841781.9707368421931.587582236877.63229851971781.97073684210.522785005954.34260896381084
240.00268750.001750.00081251387.26050.7523.5625215.646120.26976.8191251799.934125763.761562563.6467968751799.9341250.424327508444.55275781251084
24.250.00269072160.00176288660.00083505151401.656051.123711340224.2164948454215.646121.218226804179.31084536081817.825072165593.258347293849.43819560781817.8250721650.326356125434.60673692551084
24.50.00269387760.00177551020.00085714291416.16051.489795918424.8571428571215.646122.148081632781.75171428571835.6457959184420.065892857135.00549107141835.64579591840.228838207124.503843751084
24.750.00269696970.00178787880.00087878791430.556051.848484848525.4848484848215.646123.059151515284.14327272731853.3984242424244.172642045520.34772017051853.39842424240.131743201514.24340411931084
24.9550.0026994590.00179783610.00089621321442.3996052.137247044725.9901823282215.646123.792607493586.06859467041867.906202163997.9170458478.15975382061867.90620216390.0524207515.71182767441084
Sheet1
M (k-ft)
P (k)
Column Analysis
Sheet2
fMn (k-ft)
fPn (k)
Column Analysis
Sheet3
Factored
Unfactored
Mn (k-ft)
Pn (k)
Column Analysis
Example: Axial Load vs. Moment Interaction DiagramCb
Chart2
-549
11.9607334885
32.609721353
51.4703612841
68.7650538028
84.6724441265
99.3376243108
116.1292897993
137.1227549125
155.2055787621
175.6310888889
196.9997
217.5922
237.4862
256.7492967742
275.4406375
291.9150181818
307.5446705882
322.8592
337.8848666667
352.6450918919
367.1608315789
381.4508923077
389.487
403.3748292683
409.5359108108
422.417
444.9514186047
466.9213181818
488.3643333333
509.314826087
529.8042340426
549.861375
569.5127142857
588.7826
607.6934705882
626.2660384615
644.5194528302
662.4714444444
680.1384545455
697.53575
714.6775263158
731.577
748.2464915254
764.6975
780.9407704918
796.9863548387
812.8436666667
828.52153125
844.0282307692
859.3715454545
874.5587910448
889.5968529412
904.4922173913
919.251
924.811171831
939.3137833333
953.6961863014
967.9632540541
982.1196
996.1695947368
1010.1173818182
1023.9668923077
1037.7218582278
1051.385825
1064.962162963
1078.4540780488
1084
1084
1084
1084
1084
1084
1084
1084
1084
1084
1084
1084
1084
1084
1084
1084
1084
1084
fMn (k-ft)
fPn (k)
Column Analysis
Sheet1
Concrete Column Analysis
fy60ksiEs29000ksi
fc4ksir1
400f0.7
Ast13.81b10.85
Ast22.54
Ast33.81
h20in
b20in
Strain of the Steel
c (in)S1S2S3CcCs1Cs2TPMMPe
2-0.00075-0.012-0.02325115.6-21.75-60-60-82.8675-152.4-228.6-348.26752150.73375179.2278125-348.2675-6.1755224073106.6882118339-207.3117798883
2.25-0.0003333333-0.0103333333-0.0203333333130.05-9.6666666667-60-60-36.83-152.4-228.6-287.782614.4146875217.867890625-287.78-9.0847685298141.2203326939-186.53683765
2.50-0.009-0.018144.50-60-60-12.954-152.4-228.6-249.4542908.81375242.4011458333-249.454-11.6607220169165.2515877464-170.0597141485
2.750.0002727273-0.0079090909-0.0160909091158.957.9090909091-60-6017.1796363636-152.4-228.6-204.87036363643247.0744602273270.5895383523-204.8703636364-15.8494103422195.0242795384-147.6579446133
30.0005-0.007-0.0145173.414.5-60-6042.291-152.4-228.6-165.3093544.5975295.383125-165.309-21.4422535978223.1190096157-124.8669177041
3.250.0006923077-0.0062307692-0.0131538462187.8520.0769230769-60-6063.5390769231-152.4-228.6-129.61092307693810.0752644231317.5062720353-129.6109230769-29.3962512879249.7473989557-101.950713311
3.50.0008571429-0.0055714286-0.012202.324.8571428571-60-6081.7517142857-152.4-228.6-96.94828571434049.7166071429337.4763839286-96.9482857143-41.7719259016275.1007082562-79.0293583028
3.750.001-0.005-0.011216.7529-60-6097.536-152.4-228.6-66.7144268.0746875355.672890625-66.714-63.9756975672299.3432854905-56.1481869285
40.001125-0.0045-0.010125231.232.625-60-60111.34725-152.4-228.6-38.452754468.564375372.3803645833-38.45275-116.2092275585322.6131601938-33.3136877653
4.250.0012352941-0.0040588235-0.0093529412245.6535.8235294118-60-60123.5336470588-152.4-228.6-11.81635294124653.7970404412387.8164200368-11.8163529412-393.8437742685345.0250242995-10.5125447248
0-6100-549
4.50.0013333333-0.0036666667-0.0086666667260.138.6666666667-60-60134.366-152.4-228.613.4664825.80375402.150312513.466358.3695046785357.196844655411.9607334885
4.750.0014210526-0.0033157895-0.0080526316274.5541.2105263158-60-60144.0581052632-152.4-228.637.60810526324986.1879769737415.515664747837.6081052632132.582802087360.29068602232.609721353
50.0015-0.003-0.007528943.5-60-60152.781-152.4-228.660.7815136.2325428.01937560.78184.5039156973362.453922572151.4703612841
5.250.0015714286-0.0027142857-0.007303.4545.5714285714-60-60160.6731428571-152.4-228.683.12314285715276.9757589286439.747979910783.123142857163.4838334734363.789102033868.7650538028
5.50.0016363636-0.0024545455-0.0065454545317.947.4545454545-60-60167.8478181818-152.4-228.6104.74781818185409.2673863636450.772282197104.747818181851.6408597359364.379817552484.6724441265
5.750.0016956522-0.0022173913-0.0061304348332.3549.1739130435-60-60174.3986086957-152.4-228.6125.74860869575533.8092527174461.1507710598125.748608695744.0069223041364.295259576699.3376243108
60.00175-0.002-0.00575346.850.75-58-60180.4035-147.32-228.6151.28355651.18625470.9321875151.283537.3549412196361.5002328608116.1292897993
6.250.0018-0.0018-0.0054361.2552.2-52.2-60185.928-132.588-228.6185.995761.8896875480.1574739583185.9930.9795671138354.0002990537137.1227549125
6.50.0018461538-0.0016153846-0.0050769231375.753.5384615385-46.8461538462-60191.0275384615-118.9892307692-228.6219.13830769235866.3352884615488.8612740385219.138307692326.7700127387346.2379433817155.2055787621
6.750.0018888889-0.0014444444-0.0047777778390.1554.7777777778-41.8888888889-60195.7493333333-106.3977777778-228.6250.90155555565964.8771875497.0730989583250.901555555623.7737752334347.9511692708175.6310888889
70.0019285714-0.0012857143-0.0045404.655.9285714286-37.2857142857-60200.1338571429-94.7057142857-228.6281.42814285716057.8189285714504.8182440476281.428142857121.5252777035353.3727708333196.9997
7.250.0019655172-0.001137931-0.0042413793419.0557-33-60204.216-83.82-228.6310.8466145.4221875512.118515625310.84619.769989601358.4829609375217.5922
7.50.002-0.001-0.004433.558-29-60208.026-73.66-228.6339.2666227.91375518.9928125339.26618.3570229554363.29496875237.4862
7.750.0020322581-0.0008709677-0.0037741935447.9558.935483871-25.2580645161-60211.5901935484-64.155483871-228.6366.78470967746305.4911391129525.4575949261366.784709677417.1912595393367.8203164483256.7492967742
80.0020625-0.00075-0.0035625462.459.8125-21.75-60214.931625-55.245-228.6393.4866256378.3271875531.527265625393.48662516.2097687247372.0690859375275.4406375
8.250.0020909091-0.0006363636-0.0033636364476.8560-18.4545454545-60215.646-46.8745454545-228.6417.02145454556428.3896875535.699140625417.021454545515.4150095095374.9893984375291.9150181818
8.50.0021176471-0.0005294118-0.0031764706491.360-15.3529411765-60215.646-38.9964705882-228.6439.34952941186470.02375539.1686458333439.349529411814.7263700468377.4180520833307.5446705882
8.750.0021428571-0.0004285714-0.003505.7560-12.4285714286-60215.646-31.5685714286-228.6461.22742857146508.5871875542.382265625461.227428571414.1114486787379.6675859375322.8592
90.0021666667-0.0003333333-0.0028333333520.260-9.6666666667-60215.646-24.5533333333-228.6482.69266666676544.08545.34482.692666666713.5574464911381.738337.8848666667
9.250.0021891892-0.0002432432-0.0026756757534.6560-7.0540540541-60215.646-17.9172972973-228.6503.77870270276576.5021875548.0418489583503.778702702713.0543473795383.6292942708352.6450918919
9.50.0022105263-0.0001578947-0.0025263158549.160-4.5789473684-60215.646-11.6305263158-228.6524.51547368426605.85375550.4878125524.515473684212.5942018519385.34146875367.1608315789
9.750.0022307692-0.0000769231-0.0023846154563.5560-2.2307692308-60215.646-5.6661538462-228.6544.92984615386632.1346875552.677890625544.929846153812.1706211071386.8745234375381.4508923077
100.002250-0.00225578600-60215.646-8.636-228.6556.416655.345554.6120833333556.4111.9612246365388.2284583333389.487
10.250.00226829270.0000731707-0.0021219512592.45602.1219512195-60215.646-3.2462439024-228.6576.24975609766675.4846875556.290390625576.249756097611.5843601092389.4032734375403.3748292683
10.360.00227606180.0001042471-0.0020675676598.808603.0231660232-59.9594594595215.646-0.9571583012-228.4455405405585.05130115836682.2149300541556.8512441712585.051301158311.421588016389.7958709198409.5359108108
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19.250.00261038960.00144155840.00027272731112.656041.80519480527.9090909091215.64697.549194805217.17963636361443.02483116883512.1299147727292.67749289771443.02483116882.4338665828204.87424502841010.1173818182
19.50.00261538460.00146153850.00030769231127.16042.38461538468.9230769231215.64699.020923076921.04292307691462.80984615383389.6818269231282.47348557691462.80984615382.3172402318197.73143990381023.9668923077
19.750.00262025320.00148101270.00034177221141.556042.94936708869.9113924051215.646100.455392405124.80840506331482.45979746843264.8966495253272.07472079381482.45979746842.2023508867190.45230455561037.7218582278
200.0026250.00150.00037511566043.510.875215.646101.85428.479751501.979753137.746875261.478906251501.979752.0890740205183.0352343751051.385825
20.250.00262962960.00151851850.00040740741170.456044.03703703711.8148148148215.646103.218074074132.06044444441521.37451851853008.2063541667250.68386284721521.37451851851.9772950825175.47870399311064.962162963
20.50.00263414630.00153658540.00043902441184.96044.560975609812.7317073171215.646104.548878048835.5538048781540.64868292682876.2502134146239.68751778461540.64868292681.8669085595167.78126244921078.4540780488
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21.250.00264705880.00158823530.00052941181228.256046.058823529415.3529411765215.646108.353411764745.54070588241597.79011764712465.6568933824205.47140778191597.79011764711.5431669442143.82998544731084
21.50.00265116280.00160465120.00055813951242.76046.534883720916.1860465116215.646109.562604651248.71483720931616.62344186052323.8124709302193.65103924421616.62344186051.4374482089135.55572747091084
21.750.00265517240.00162068970.00058620691257.15604717215.646110.74451.8161635.3562179.4446875181.6203906251635.3561.3327035138127.13427343751084
220.00265909090.00163636360.00061363641271.66047.454545454517.7954545455215.646111.898545454554.84668181821653.99122727272032.5348863636169.3779071971653.99122727271.2288667877118.56453503791084
22.250.00266292130.00165168540.00064044941286.056047.898876404518.5730337079215.646113.027146067457.8092584271672.53240449441883.0652492978156.92210410811672.53240449441.1258766911109.84547287571084
22.50.00266666670.00166666670.00066666671300.56048.333333333319.3333333333215.646114.130666666760.7061690.98266666671731.01875144.25156251690.98266666671.0236762234100.976093751084
22.750.00267032970.00168131870.00069230771314.956048.758241758220.0769230769215.646115.209934065963.53907692311709.3450109891576.3791105769131.36492588141709.3450109890.922212368291.9554481171084
230.0026739130.00169565220.00071739131329.46049.173913043520.8043478261215.646116.265739130466.31056521741727.62230434781419.1307608696118.26089673911727.62230434780.821435771882.78262771741084
23.250.00267741940.00170967740.00074193551343.856049.580645161321.5161290323215.646117.298838709769.02245161291745.81729032261259.2588004032104.93823336691745.81729032260.721300451973.45676335691084
23.50.00268085110.00172340430.00076595741358.36049.978723404322.2127659574215.646118.309957446871.67663829791763.93259574471096.74896276691.39574689721763.93259574470.62176353363.9770228281084
23.750.00268421050.00173684210.00078947371372.756050.368421052622.8947368421215.646119.299789473774.27494736841781.9707368421931.587582236877.63229851971781.97073684210.522785005954.34260896381084
240.00268750.001750.00081251387.26050.7523.5625215.646120.26976.8191251799.934125763.761562563.6467968751799.9341250.424327508444.55275781251084
24.250.00269072160.00176288660.00083505151401.656051.123711340224.2164948454215.646121.218226804179.31084536081817.825072165593.258347293849.43819560781817.8250721650.326356125434.60673692551084
24.50.00269387760.00177551020.00085714291416.16051.489795918424.8571428571215.646122.148081632781.75171428571835.6457959184420.065892857135.00549107141835.64579591840.228838207124.503843751084
24.750.00269696970.00178787880.00087878791430.556051.848484848525.4848484848215.646123.059151515284.14327272731853.3984242424244.172642045520.34772017051853.39842424240.131743201514.24340411931084
24.9550.0026994590.00179783610.00089621321442.3996052.137247044725.9901823282215.646123.792607493586.06859467041867.906202163997.9170458478.15975382061867.90620216390.0524207515.71182767441084
Sheet1
M (k-ft)
P (k)
Column Analysis
Sheet2
fMn (k-ft)
fPn (k)
Column Analysis
Sheet3
Factored
Unfactored
Mn (k-ft)
Pn (k)
Column Analysis