Shear Wall Design

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Session No.(20): Analysis and Design of rectangular tied column (unixially loading). Purpose : Draw design interaction diagram. Disclaimer

Problem title :

column C11- comb4

b(mm) h(mm) fc(Mpa) fy(Mpa) Cover(mm) db(mm) d tie(mm)

500 6000

30

360

40

25

10

suggested (b)= 1250 (For Design) Pu(KN) Mu(KN.m) suggested (h)= 1874 (For Design)

26139

25282.0

1.00 270.0 (In case of slender column) Mox= 107.5 (In case of biaxial loading)

# bars/ layer

5

Distance

100.0

928.6 1757.1

2585.7

3414.3

4242.9

5071.4

5900.0

0.00654498 Not good ro<0.01 Magnified moment ===> d _b= d _b* Mu =

Equivalent uniaxial moment ===>

d₁ d₂ d₃ d₄ d₅ d₆ d₇ d₈ r_o= d₃ d₂ 0 10000 20000 30000 40000 50000 0 5000 10000 15000 20000 25000 30000 35000 40000 45000

50000

Design Interaction diagram for tied column

Design interaction diagram

The applied loading condition Mu (KN.m)

P

u

(

K

N

)

d_tie d_b h

Note: h is dimension resisting applied moment.

b

d₁

(2)

(3)

Calculations:

3687.5

3000000 0.85

Design Process:

rg =

0.02 assumed

Ag =

1561470

h =

1249.588

e =

967.2137

e/h =

0.774026

b =

1249.588

h =

1874.382

values for nominal interaction diagram:

2454.36926 2454.36926 2454.36926 2454.36926 2454.36926

c

_b

(mm)

_{Ag ( mm}2 ₎

b

₁ As₁ As₂ As₃ As₄ As₅

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Page 4

2454.36926 2454.36926 2454.36926

As

19634.9541 As₆ As₇ As₈

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c(mm)

2.5

6000 360 360 360 341.428571

2.4

6000 360 360 360 341.428571

2.3

6000 360 360 360 341.428571

2.2

6000 360 360 360 341.428571

2.1

6000 360 360 360 341.428571

2

6000 360 360 360 341.428571

1.9

6000 360 360 360 341.428571

1.8

6000 360 360 360 341.428571

1.7

6000 360 360 360 341.428571

1.6

5900 360 360 360 337.046005

1.5

5531.25 360 360 360 319.515738

1.4

5162.5 360 360 360 299.481148

1.3

4793.75 360 360 360 276.364314

1.2

4425 360 360 360 249.394673

1.1

4056.25 360 360 340.083645 217.521462

1

3687.5 360 360 314.09201 179.273608

0.9

3318.75 360 360 282.324455 132.526231

0.85

3134.375 360 360 263.637658 105.027774

0.8

2950 360 360 242.615012 74.0920097

Values for Design interaction diagram

0.75

2765.625 360 360 218.789346 39.031477

0.7

2581.25 360 360 191.560014 1.03770322

0.65

2396.875 360 360 160.141553 47.2713727

0.6

2212.5 360 348.184019 123.486683 101.210654

0.55

2028.125 360 325.291657 80.1672903 164.957077

0.5

1843.75 360 297.820823 28.1840194 241.452785

0.45

1659.375 360 264.245359 35.3510896 334.947538

0.4

1475 360 222.276029 114.769976 360

c /c

_b fs₁ fs₂ fs₃ fs₄

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Page 6

0.35

1290.625 360 168.315462 216.879972 360

0.3

1106.25 360 96.3680387 353.026634 360

0.25

921.875 360 4.35835351 360 360

0.2

737.5 360 155.447942 360 360

0.15

553.125 360 360 360 360

0.1

368.75 360 360 360 360

0.05

184.375 274.576271 360 360 360

0.059

217.5625 324.217179 360 360 360

0.058

213.875 319.462303 360 360 360

0.057

210.1875 314.540589 360 360 360

0.056

206.5 309.443099 360 360 360

0.055

202.8125 304.160247 360 360 360

0.054

199.125 298.681733 360 360 360

0.053

195.4375 292.996482 360 360 360

0.052

191.75 287.092568 360 360 360

0.051

188.0625 280.957129 360 360 360

0.05

184.375 274.576271 360 360 360

0.049

180.6875 267.934971 360 360 360

0.001

100 0 360 360 360

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stresses:(Mpa)

Forces:(KN)

c (mm) 258.571429 175.714286 92.8571429 10 6000 820.986518 820.986518 820.986518 775.405374 572.04335 368.681325 165.319301 258.571429 175.714286 92.8571429 10 6000 820.986518 820.986518 820.986518 775.405374 572.04335 368.681325 165.319301 258.571429 175.714286 92.8571429 10 6000 820.986518 820.986518 820.986518 775.405374 572.04335 368.681325 165.319301 258.571429 175.714286 92.8571429 10 6000 820.986518 820.986518 820.986518 775.405374 572.04335 368.681325 165.319301 258.571429 175.714286 92.8571429 10 6000 820.986518 820.986518 820.986518 775.405374 572.04335 368.681325 165.319301 258.571429 175.714286 92.8571429 10 6000 820.986518 820.986518 820.986518 775.405374 572.04335 368.681325 165.319301 258.571429 175.714286 92.8571429 10 6000 820.986518 820.986518 820.986518 775.405374 572.04335 368.681325 165.319301 258.571429 175.714286 92.8571429 10 6000 820.986518 820.986518 820.986518 775.405374 572.04335 368.681325 165.319301 258.571429 175.714286 92.8571429 10 6000 820.986518 820.986518 820.986518 775.405374 572.04335 368.681325 165.319301 252.784504 168.523002 84.2615012 0 5900 820.986518 820.986518 820.986518 764.648938 557.840099 351.031261 144.222422 229.636804 139.757869 49.8789346 40 5531.25 820.986518 820.986518 820.986518 721.623191 501.027096 280.431002 59.8349077 203.18229 106.883431 10.5845728 85.7142857 5162.5 820.986518 820.986518 820.986518 672.450909 436.09795 199.744992 -36.607966 172.657851 68.9513876 34.7550754 138.461538 4793.75 820.986518 820.986518 820.986518 615.71366 361.179705 106.64575 -85.301789 137.046005 24.6973366 87.6513317 200 4425 820.986518 820.986518 820.986518 549.520203 273.775085 -1.9700325 -215.12873 94.959278 27.6029056 150.165089 272.727273 4056.25 820.986518 820.986518 772.104429 471.291573 170.478717 -67.747723 -368.56058 44.4552058 90.3631961 225.181598 360 3687.5 820.986518 820.986518 708.311357 377.417216 46.5230745 -221.78465 -552.67879 17.2719935 167.070218 316.868442 360 3318.75 820.986518 820.986518 630.342048 262.681891 -42.39185 -410.05201 -777.71216 53.5821108 212.191995 360 360 3134.375 820.986518 820.986518 584.477749 195.190523 -131.51029 -520.79751 -883.57293 94.4309927 262.953995 360 360 2950 820.986518 820.986518 532.880412 119.262735 -231.76853 -645.3862 -883.57293 140.726392 320.484262 360 360 2765.625 820.986518 820.986518 474.40343 33.2112412 -345.39453 -786.58672 -883.57293 193.63542 360 360 360 2581.25 820.986518 820.986518 407.572593 -2.5469069 -475.25282 -883.57293 -883.57293 254.684299 360 360 360 2396.875 820.986518 820.986518 330.46009 -116.0214 -625.08931 -883.57293 -883.57293 325.90799 360 360 360 2212.5 820.986518 791.985738 240.495502 -248.40832 -799.89855 -883.57293 -883.57293 360 360 360 360 2028.125 820.986518 735.799429 134.173717 -404.86558 -883.57293 -883.57293 -883.57293 360 360 360 360 1843.75 820.986518 668.375858 6.58757464 -592.61429 -883.57293 -883.57293 -883.57293 360 360 360 360 1659.375 820.986518 585.969271 -86.764628 -822.08494 -883.57293 -883.57293 -883.57293 360 360 360 360 1475 820.986518 482.961037 -281.6879 -883.57293 -883.57293 -883.57293 -883.57293 fs₅ fs₆ fs₇ fs₈ F₁ F₂ F₃ F₄ F₅ F₆ F₇

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360 360 360 360 1290.625 820.986518 350.521879 -532.30354 -883.57293 -883.57293 -883.57293 -883.57293 360 360 360 360 1106.25 820.986518 173.936336 -866.45772 -883.57293 -883.57293 -883.57293 -883.57293 360 360 360 360 921.875 820.986518 -10.697009 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 360 360 360 360 737.5 820.986518 -381.52665 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 360 360 360 360 553.125 820.986518 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 360 360 360 360 368.75 820.986518 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 360 360 360 360 184.375 611.325144 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 360 360 360 360 217.5625 733.162262 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 360 360 360 360 213.875 721.49204 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 360 360 360 360 210.1875 709.412336 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 360 360 360 360 206.5 696.901215 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 360 360 360 360 202.8125 683.935143 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 360 360 360 360 199.125 670.488847 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 360 360 360 360 195.4375 656.535143 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 360 360 360 360 191.75 642.044759 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 360 360 360 360 188.0625 626.986124 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 360 360 360 360 184.375 611.325144 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 360 360 360 360 180.6875 595.02494 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 360 360 360 360 100 0 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293 -883.57293

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Mn(KN.m) Pn(KN) Mu(KN.m) Pu(KN) Mu(KN.m) Pu(KN) Cc 0 83067.8921 9000 0 58147.524 0 46518.0196 -38.042724 65025 33757.0033 69331.3662 23629.9 48531.956 0 46518.0196 820.986518 65025 31265.8185 70190.3954 21886.07 49133.277 0 46518.0196 820.986518 65025 31265.8185 70190.3954 21886.07 49133.277 0 46518.0196 820.986518 65025 31265.8185 70190.3954 21886.07 49133.277 0 46518.0196 820.986518 65025 31265.8185 70190.3954 21886.07 49133.277 0 46518.0196 820.986518 65025 31265.8185 70190.3954 21886.07 49133.277 0 46518.0196 820.986518 65025 31265.8185 70190.3954 21886.07 49133.277 0 46518.0196 820.986518 65025 31265.8185 70190.3954 21886.07 49133.277 0 46518.0196 820.986518 65025 31265.8185 70190.3954 21886.07 49133.277 0 46518.0196 0 63941.25 35943.5602 68221.9523 25160.49 47755.367 0 46518.0196 -98.17477 59944.9219 43922.8293 63872.6229 30745.98 44710.836 30745.98049 44710.836 -210.37451 55948.5938 50728.4946 59472.8647 35509.95 41631.005 35509.94621 41631.00528 -339.83574 51952.2656 56249.1426 55073.6268 39374.4 38551.539 39374.39979 38551.53873 -490.87385 47955.9375 60768.366 50534.2197 42537.86 35373.954 42537.85623 35373.95381 -669.37343 43959.6094 64051.1272 45909.7754 44835.79 32136.843 44835.78904 32136.84277 -883.57293 39963.2813 66341.6221 41079.4696 46439.14 28755.629 46439.13546 28755.62869 -883.57293 35966.9531 66844.8574 36388.2211 46791.4 25471.755 46791.40016 25471.7548 -883.57293 33968.7891 66639.3671 33970.9767 46647.56 23779.684 46647.55698 23779.68369 -883.57293 31970.625 65912.6438 31620.4406 46138.85 22134.308 46138.85065 22134.30841 -883.57293 29972.4609 64886.2104 29222.9215 45420.35 20456.045 45420.34725 20456.04507 -883.57293 27974.2969 63508.8531 26895.324 44456.2 18826.727 44456.19715 18826.72678 -883.57293 25976.1328 61661.1073 24556.7364 43162.78 17189.715 43162.77508 17189.71549 -883.57293 23977.9688 59426.676 22132.4108 41598.67 15492.688 41598.67323 15492.68759 -883.57293 21979.8047 56754.7246 19731.607 39728.31 13812.125 39728.30724 13812.12493 -883.57293 19981.6406 53672.289 17350.6845 37570.6 12145.479 37570.6023 12145.47918 -883.57293 17983.4766 50270.9304 14947.291 35189.65 10463.104 35189.65131 10463.10373 -883.57293 15985.3125 46457.1018 12589.7075 32713.24 8865.1698 32713.23769 8865.169754

max. (0.1f`cAg ;f*Pn

_b F₈

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Page 10

-883.57293 13987.1484 42225.4152 10208.4886 31297.53 7566.5449 31297.53212 7566.54492 -883.57293 11988.9844 37485.3063 7699.58484 29247.11 6007.4369 29247.11105 6007.436918 -883.57293 9990.82031 32809.4113 5499.67222 26721.61 4479.2055 26721.61005 4479.205526 -883.57293 7992.65625 27455.946 3130.67851 23373.26 2665.1484 23373.26209 2665.148361 -883.57293 5994.49219 21517.525 630.468168 19154.74 561.23817 19154.74404 561.2381721 -883.57293 3996.32812 16305.9072 -1367.6959 14675.32 -1230.926 14675.31651 -1230.9263 -883.57293 1998.16406 10173.1217 -3575.5213 9155.81 -3217.969 9155.809552 -3217.9692 -883.57293 2357.83359 11544.018 -3094.0147 10389.62 -2784.613 10389.61618 -2784.61321 -883.57293 2317.87031 11397.6122 -3145.6482 10257.85 -2831.083 10257.85097 -2831.08337 -883.57293 2277.90703 11249.8937 -3197.6912 10124.9 -2877.922 10124.90429 -2877.92205 -883.57293 2237.94375 11100.7987 -3250.1656 9990.719 -2925.149 9990.718868 -2925.14901 -883.57293 2197.98047 10950.2592 -3303.0949 9855.233 -2972.785 9855.233295 -2972.78543 -883.57293 2158.01719 10798.2018 -3356.5045 9718.382 -3020.854 9718.381601 -3020.85405 -883.57293 2118.05391 10644.5476 -3410.4215 9580.093 -3069.379 9580.09284 -3069.37934 -883.57293 2078.09063 10489.2118 -3464.8752 9440.291 -3118.388 9440.290607 -3118.38764 -883.57293 2038.12734 10332.1028 -3519.8971 9298.893 -3167.907 9298.892507 -3167.90736 -883.57293 1998.16406 10173.1217 -3575.5213 9155.81 -3217.969 9155.809552 -3217.9692 -883.57293 1958.20078 10012.1617 -3631.7848 9010.945 -3268.606 9010.945489 -3268.60633 -883.57293 1083.75 5767.55213 -5101.2605 5190.797 -4591.134 5190.79692 -4591.13448

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0

2

4

6

8 10 12

0

2

4

6

8

10

12

Column BE

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Session No.(20): Analysis and Design of rectangular tied column. Purpose : Check slenderness

Problem title : column C11- comb4

Type of frame : 1

K= 2

dimensions: at top at bottom

Columns Col.(AB) 6000 500 3 3 300 300

Top col. 0 0 0 150 150

bott.col 450 450 8.6 120 120

top beams No.1 600 300 8 60 60

No.2 600 300 8

bot.beams No.1 600 300 8

No.2 600 300 8

Design as short column with:

Pu= 675 KN

Mc= 270.0 KN.m

Comments :

1) User shall determine the correct sign for the moments at TOP ;

Service loading on col.(AB)

h(mm) b(mm) L(m) Lu(m) P_D(KN) P_L(KN) M_D(KN.m) M_L(KN.m) d_b Mu =

For (ONLY) double curvature, both M_D and M_L at TOP shall have MINUS signs. 2) The magnified moment (db Mu) must be used in column design .

3) The magnification factor (ds) is not calculated.

L Lu

top col

bott.col.

top beam No.1 top beam

No.2 botomt.beam No.1 bottom beam No.2. A B Enter: ( 1) for braced , ( 0) for unbraced

Enter: (value of K) : In case of K is already known.

or ( 0) : The program calculates K ,

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Calculations: Ec= 25742.9602 Mpa Pu(KN) Mu(KN.m) top 420 255 675 270 168 bottom 420 255 675 270 168 270 KN.m 270 KN.m **For columns: col(AB) Ig = 9E+12 mm4

r = 1732.051 mm tob col. Ig= 0 mm4

bottom col. Ig= 3417187500 mm4 **For beams: tob: 5.4E+09 mm4 5.4E+09 mm4 bottom: 5.4E+09 mm4 5.4E+09 mm4 4444.44444

Infinity for hinge 4445.03311 10 for footing 4444.44444 0 for fixed Pu_d(KN) Pu_L(KN) Mu_D(kN.m) M_2b= M_1b= Ig₁ = Ig₂ = Ig_{1 =} Ig₂ = y_A= y = y_B= y_min=

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Page 16

K(eqn.) 1 K 2 Kl/r 3.4641016151 22 0.62222222 EI 5.712821E+16 N/mm2 Pc ### KN 1 `ok` Cm

1

5.7464E-05 1.000057 1.00005747 Not calculated 34-12(M_1b/M_2b)= b_d C_m Pu/fPc= dd = ds =

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Session No. (20): Analysis and Design of rectangular tied column.

Determine equivalent uniaxial moment.

Problem title : column C11- comb4

INPUT DATA

Pu(KN) Mux(KN.m)Muy(KN.m)

X

5000

100

150

Equivalent unaxail loading :

Pu =

5000

Calculation for biaxially column:

Mox=

108

0.6 e0y= 21.5 30.0 20.0 M0x= 108 Purpose :

Mu =

a

=

e

_x

(mm)

e

_y

(mm)

Y

b h Mx My

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Page 18

Problem title :column C11- comb4

fy =

400 Mpa

fc =

30 Mpa

20 mm

Compresion Tension Condition Clase 560 0<fs<0.5fy

A

913

1/2 of bars are spliced

1):0<fs<0.5fy

B

1187

>1/2of bars are splicd 2):0.5fy<fs<fy

Comments:

Assumed uncoated bar and normal weight concrete . Session No.(20): The lap splices

Purpose : Compute required length of lab splices.

d

_b