Lattice Girder_fair Rock

do - Tunnel Radius - 3.5 m - Angle of Internal friction - 30 Degreec - Cohesive Strength - 0.1 MpaGSI - - 60 - Unit weight of Rock mass - 26 kN / cu mH - Height of over burden - 100 mdo - Tunnel radius - 5 mPo - In-situ Stress

- H- 2.6 Mpa

Pi - Internal Support Pressure- 1.2 Mpa (Figure-1)

ci - Lab Uniaxial compressive strength-- 1.1017 Mpa

cm - Rock mass Strength/In situ Uniaxial compressive strength- 2c cos /(1-sin)- 0.35 Mpa

dp - Plastic zone radiusi - Tunnel Sidewall deformation/Tunnel closurek - (1+sin )/(1-sin ) or cm/Po - Rock mass Strength/In situ Stress

- 0.13Pi/Po - 0.46dp/do - 1.20i/do - 0.005Strain of the tunnel

- i /do

dp - 4.19 mi - 0.02 m

critical support pressure pcr,

0.019 e 0.05 GSI/ cm

1/ 3

Failure of the rock masssurrounding the tunnel occurs when the internal pressure pi is less than a critical supportpressure pcr , which is defined by:

Pcr - 2 Po - cm1+k

- #VALUE!

1 - Axial stress at which failure occurs3 - Confining stress

When the internal support pressure pi is less than the critical support pressure pcr, failure

surrounding the tunnel occurs when the internal pressure pi is less than a critical support

When the internal support pressure pi is less than the critical support pressure pcr, failure

Definitions of Dimensions:b = 2000 mmt = 600 mm

b 1 = 700 mmb 2 = 500 mmt 2 = 50 mmd 1 = 26 mmd 2 = 34 mm = 30 Degree

Cover = 50 mmh g = 500 mmbg = 300 mmLo = 2000 mmd 3 = 6 mm @ 100 mm c/c

Lo Rock Bolts

ELEV

bb 1

d 1

t

t 2 d 3d 2

b 2PLAN

500

300Lattice Girder

-1500 -1000 -500 0 500 1000 1500-2000

0

2000

4000

6000

8000

10000

12000

14000

16000

Column E

h = t + t 2= 650 mm

d g = h g - 0.5(d 1 + d 2)= 453 mm

Definitions of Material Properties:

f cd = 20 Mpafyd = 415 Mpa = 0.85

A st 1 = 1061 Sq mmA st 2 = 907 Sq mmA st 3 = 28 Sq mmA c = b t + 0.5 t 2 b 2 - A st 1 - A st 2

= 759682 Sq mmb ef = 0.2 (b-b 2) + 0.24 L o+b 2

= 1280 mm

A s11 == 1423 Sq mm (only in tension)

h cm == 305.07 mm (Calculation of center of mass)

Eight Strain conditions to derive M-N envelope:1 Pure axial force2 Zero strain in tensioned bars (positive Moment)3 Equilibrium (Max strain in shotcrete and yielding in rebars at the same time - Positive Moment)4 Pure moment (Positive)5 Pure tension6 Pure Moment (Negative)7 Equilibrium (Max strain in shotcrete and yielding in rebars at the same time - Negative Moment)8 Zero strain in tensioned bars (Negative Moment)

Pure axial forceNd = f cd A c + f yd (A st1 + A st2)

= 13732 kN

Pure tensionN tog = f yd (A s11 +A st2)

= 967 kN

Equilibrium (Max strain in shotcrete and yielding in rebars at the same time - Positive Moment) cu = 0.0035 syd = 0.0021d = t+t2-co-co

= 550 mmX bal = cu d

= cu + syd= 344 mm

0.8 X bal < t0.8 X bal = 275 mm

< 600 mm

f c = f cd 0.8 X bal b eff -f s1 = f yd A st1 -f s2 = f yd A st2 -N ud = f c + f s1 - f s2 -M ud = f c (h cm -0.4 X bal) + f s1 (h cm - 0.5 d1) + f s2 (d - h cm)

= 1039.15 kN m

Zero strain in tensioned bars (positive Moment)h c3 = 0.8 d - 440 mm

A c3 = t b ef + (0.5 b2 t2= 704117 sq mm

Center mass of compression zone

h cm2 = + 0.5((2(h-hc3)/tan + b2)) (t + 0.5(hc3+co-t))(hc3+co -t)b eff t+ 0.5((2(h-hc3)/tan + b2)) (hc3+co -t)

= 230400000 + 614 -x 59950714240

= 271.067075 mm

f c3 = f cd A c3= 11969981.51

N ud3 = f c3 + f s1= 12410 kN

M ud3 = f c3 (d - h cm2) + f s1 (d -0.5 d1) - Nud3 (d-hcm)= 412 kN m

Pure moment (Positive)x = f yd A st2

= f cd 0.8 b eff= 21.63 mm

Mu = f yd A st2 (d -0.4 x)

- (h - h c3)2 / tan )

0.5 b ef t 2

= 203.87 kN m

Pure Moment (Negative)d 1 = h -0.5 d 1 -co

= 587 mm

h c = Sqrt ((A s11 f yd tan )/ f cd)= 141.62 mm

M u2 = f yd A s 11 (d 1 - 0.67 hc)= 290.63 kN m

Equilibrium (Max strain in shotcrete and yielding in rebars at the same time - Negative Moment)X bal2 = cu d

= cu + syd= 367 mm

h c2 = 0.8 X bal2= 294 mm

f c2 = - 2536447f s11 = f yd A s 11 - 590565f s2 = f yd A st2 - 376596N ud2 = f c2 + f s2 - f s11 - 2322M ud2 = f c2 (h-h cm -0.67 h c2) + f s1 (d-h cm ) + f s2 (h cm - 0.5d1)

= 641 kN m

Zero strain in tensioned bars (Negative Moment)h c4 = 0.8 d1

= 469.6 mmA c4 = 549588 Sq mm

f c4 = 9342996 N

N ud4 = 9720 kN

h cm3 = Center mass of compression zone

= (h c4 -t2)b ef (h -h c4 + 0.5(h c4 - t2)) + (0.5 t2 b2 (t + 0.33 t2))((h c4 -t2)b ef ) + (0.5 t2 b2)

= 395.3508281 mm

M ud4 = f c4 (h cm3 -0.5 d1) + fs2 (d1 - co - 0.5 d2) - N ud4 (h cm - 0.5 d1)

= 1034.951147 kN m

f cd (h c2)2/tan

0 0M ud3 412M ud 1039.15M u 203.87

Moment = 0 = 0 kN m-M u2 -290.63

-M ud2 -641-M ud4 -1034.951

0 0M 271

N d 13732N ud3 12410N ud 6048

0 0Nforce = -N tog = -967 kN

0 0N ud2 2322N ud4 9720

N d 13732N 837

Shear checkPermissible Stress in Steel in = 230Condition : Shear < Shear resistance (concrete + steel)

Shear resistance by steel = 12999.6 N

N/mm2 (grade fe 415)

-1500 -1000 -500 0 500 1000 1500-2000

0

2000

4000

6000

8000

10000

12000

14000

16000

Shear resistance by M20 concrete = 117600 NShear calculated = 72768 N

Shear resistance (concrete + steel) = 130599.6 >HENCE O.K.

-1500 -1000 -500 0 500 1000 1500-2000

0

2000

4000

6000

8000

10000

12000

14000

16000

Column E

Equilibrium (Max strain in shotcrete and yielding in rebars at the same time - Positive Moment)

Equilibrium (Max strain in shotcrete and yielding in rebars at the same time - Negative Moment)

Equilibrium (Max strain in shotcrete and yielding in rebars at the same time - Positive Moment)

5984000 N440448 N376596 N

6048 kNf c (h cm -0.4 X bal) + f s1 (h cm - 0.5 d1) + f s2 (d - h cm)

+ 0.5((2(h-hc3)/tan + b2)) (t + 0.5(hc3+co-t))(hc3+co -t)b eff t+ 0.5((2(h-hc3)/tan + b2)) (hc3+co -t)

- (h - h c3)2 / tan )

Equilibrium (Max strain in shotcrete and yielding in rebars at the same time - Negative Moment)

NNNkN

f c2 (h-h cm -0.67 h c2) + f s1 (d-h cm ) + f s2 (h cm - 0.5d1)

(h c4 -t2)b ef (h -h c4 + 0.5(h c4 - t2)) + (0.5 t2 b2 (t + 0.33 t2))((h c4 -t2)b ef ) + (0.5 t2 b2)

f c4 (h cm3 -0.5 d1) + fs2 (d1 - co - 0.5 d2) - N ud4 (h cm - 0.5 d1)

Shear resistance (concrete + steel)

-1500 -1000 -500 0 500 1000 1500-2000

0

2000

4000

6000

8000

10000

12000

14000

16000

72768 N

M(kNm)GOOD ROCK 80FAIR ROCK

N(kN)281

1.00 m0.03 0.15 m

0.10 m0.030.15 m

Compression Load @ Moderate eccentricity

No. Types

Wire Spacing Wire Diameter Sheet Weight per

Main mm Cross mm Main mm Cross mm Dimensions/m sheet kg/pc

1 A98 200 200 5 5

2.15 X 5.00

16.7

2 A142 200 200 6 6 24.1

3 A193 200 200 7 7 32.8

4 A252 200 200 8 8 43

5 A393 200 200 10 10 67.1

6 B503 100 200 8 8 64.7

7 B785 100 200 10 8 89.1

8 A98* 200 200 5 5

1.80 X 3.00

8.3

9 A142* 200 200 6 6 12

10 A252* 200 200 8 8

1.75 X 3.00

21

11 A393* 200 200 10 10 32.9

12 Q92 150 150 4.2 4.2

2.15 X 5.00

15.9

13 Q131 150 150 5 5 22.5

14 Q188 150 150 6 6 32.4

15 Q257 150 150 7/5() 7 39.7

16 R92 150 250 4.2 4.2 12.8

TABLE I - STANDARD

MESH FABRIC FOR

CONCRETE REINFORCEME

NT

STAAD PLANESTART JOB INFORMATIONENGINEER DATE 02-Jan-12END JOB INFORMATIONINPUT WIDTH 79UNIT METER KNJOINT COORDINATES2 7.5 0 0; 4 7.5 3.75 0; 15 3.75 7.5 0; 25 4.33663 7.45383 7.1839e-017;26 4.90881 7.31646 1.41909e-016; 27 5.45246 7.09127 2.08485e-016;28 5.9542 6.78381 2.69927e-016; 29 6.40165 6.40165 3.24723e-016;30 6.78381 5.9542 3.71523e-016; 31 7.09127 5.45246 4.09175e-016;32 7.31646 4.90881 4.36751e-016; 33 7.45383 4.33663 4.53574e-016;39 7.5 0.625 0; 40 7.5 1.25 0; 41 7.5 1.875 0; 42 7.5 2.5 0; 43 7.5 3.125 0;MEMBER INCIDENCES3 2 39; 34 15 25; 35 25 26; 36 26 27; 37 27 28; 38 28 29; 39 29 30; 40 30 31;41 31 32; 42 32 33; 43 33 4; 49 39 40; 50 40 41; 51 41 42; 52 42 43; 53 43 4;DEFINE MATERIAL STARTISOTROPIC CONCRETEE 2.17185e+007POISSON 0.17DENSITY 25ALPHA 1e-005DAMP 0.05END DEFINE MATERIALMEMBER PROPERTY AMERICAN3 34 TO 43 49 TO 53 PRIS YD 0.45 ZD 0.75 YB 0.2 ZB 0.25CONSTANTSBETA 180 MEMB 3 49 TO 53MATERIAL CONCRETE ALLSUPPORTS25 INC REF 4.3366 7.4538 0 FIXED BUT FZ MX MY MZ KFX 470.4 KFY 156.826 INC REF 4.9088 7.3165 0 FIXED BUT FZ MX MY MZ KFX 470.4 KFY 156.827 INC REF 5.4525 7.0913 0 FIXED BUT FZ MX MY MZ KFX 470.4 KFY 156.828 INC REF 5.9542 6.7838 0 FIXED BUT FZ MX MY MZ KFX 470.4 KFY 156.829 INC REF 6.4016 6.4016 0 FIXED BUT FZ MX MY MZ KFX 470.4 KFY 156.830 INC REF 6.7838 5.9542 0 FIXED BUT FZ MX MY MZ KFX 470.4 KFY 156.831 INC REF 7.0913 5.4525 0 FIXED BUT FZ MX MY MZ KFX 470.4 KFY 156.832 INC REF 7.3165 4.9088 0 FIXED BUT FZ MX MY MZ KFX 470.4 KFY 156.833 INC REF 7.4538 4.3366 0 FIXED BUT FZ MX MY MZ KFX 470.4 KFY 156.839 TO 43 FIXED BUT FY MY MZ KFX 5002 PINNED4 FIXED BUT FY MY MZ KFX 485.215 FIXED BUT FYSPRING COMPRESSION25 TO 33 KFX KFY

39 TO 43 KFX4 KFXLOAD 1 LOADTYPE None TITLE SELF WEIGHTSELFWEIGHT Y -1 LIST 3 34 TO 43 49 TO 53LOAD 2 LOADTYPE None TITLE ROCK LOADMEMBER LOAD34 TO 38 UNI GY -91.1253 39 TO 43 49 TO 53 UNI GX -45.5625LOAD COMB 3 SELF WEIGHT+ROCK LOAD1 1.0 2 0.5PERFORM ANALYSISPRINT ANALYSIS RESULTSFINISH

Sheet7

Page 35

Beam L/C Node Fx kN Fy kN1 3 SELF WEIGHT+ 1 274.685 76.894

4 -267.617 -49.3943 3 SELF WEIGHT+ 4 267.617 49.394

5 -260.548 -21.8944 3 SELF WEIGHT+ 5 260.548 21.894

6 -253.48 5.6065 3 SELF WEIGHT+ 6 253.48 -5.606

7 -246.411 33.1066 3 SELF WEIGHT+ 7 246.411 -35.565

2 -239.343 63.0657 3 SELF WEIGHT+ 2 246.415 -49.324

25 -241.998 80.8078 3 SELF WEIGHT+ 25 260.826 -13.892

26 -263.525 45.5689 3 SELF WEIGHT+ 26 261.176 13.701

27 -270.856 16.58110 3 SELF WEIGHT+ 27 264.543 35.1

28 -280.719 -7.73211 3 SELF WEIGHT+ 28 277.011 64.939

29 -240.038 -6.09612 3 SELF WEIGHT+ 29 234.379 60.496

30 -211.426 5.09913 3 SELF WEIGHT+ 30 205.383 46.793

24 -197.602 22.264

Sheet7

Page 36

Fz kN Mx kNm My kNm Mz kNm0 0 0 00 0 0 63.1440 0 0 -63.1440 0 0 98.7890 0 0 -98.7890 0 0 106.9330 0 0 -106.9330 0 0 87.5780 0 0 -87.5780 0 0 38.2630 0 0 -38.2630 0 0 -34.5880 0 0 34.5880 0 0 -67.8750 0 0 67.8750 0 0 -69.4870 0 0 69.4870 0 0 -45.5090 0 0 45.5090 0 0 -5.7420 0 0 5.7420 0 0 25.2710 0 0 -25.2710 0 0 39.002

MOI of 3bars

Page 37

for finding MOI of 3bars with coordinates as below:-42 25042 250

0 0

x= -22287.72 + 22287.72 + 01968.78

therefore,x = 0

y= 132665 + 132665 + 01968.78

therefore,x = 134.77

therefore, centroid coord = ( 0 , 134.77 )Ig= ( 44840.77 + 7046232.58 ) + (= 3.08E+007 mm4

1352 11561061.32 907.46

1968.78

Err:512

1st bar coord:2nd bar coord:3rd bar coord:

MOI of 3bars

Page 38

44840.77 + 7046232.58 ) + ( 131127.97 +

1713

220

MOI of 3bars

Page 39

16481845.06 )

Sheet9

Page 40

Finished diameter of Tunnel = 10Thickness of Lining = 600Axial force 'T' =Moment 'M' =Grade of Conc. = M-20Cover To R/F = 50Permissible Stress in Concrete = 2.8Permissible Stress in Steel in = 230direct tension and flexural tension (Clause: B - 2.2, IS 456 : 2000)

As per Carranza -Torres article Mechanical analysis of circular lines with particular reference to composite supports (Page 10-12)-Tunnel underground space technology(2009)r = 5b = 1 ms = 1 mn=b/s= = 1

For steel= 200000 Mpa= 0.00197 m2= 0.25= 1.26E-005 m4= 420266666.67= 420.27 MN

= 2696533.333

= 2.697 MN/m2

For shotcrete= 0.4= 22360= 0.15= 0.19803= 0.0026540267= 4529872941.18= 4529.87= 60710011.53

= 60.71

D1 = E1A1/(1-v12)

K1 = E1 I1/(1-v12)

E1A1v1I1D1

K1

t2E2v2A2 = (1/n) x bt2 A1I2 = (1/n) x bt23 /12 I1D2 =E2A2/(1-v2

2)

K2 = E2I2/(1-v22)

Sheet9

Page 41

= 0.392= 12626= 5396

= 0.043= 0.957

From staad output

Beam L/C Node Fx kN1.00 3 SELF WEIGHT+ROCK LOAD 1.00 6.0272

4.00 -926.693.00 3 SELF WEIGHT+ROCK LOAD 4.00 926.72







27.00 -861.4910.003 SELF WEIGHT+ROCK LOAD 27.00 846.49




24.00 -576.92

teq = sqrt (12(K1+K2)/(D1+D2))Eeq=n(D1+D2)/(bteq)G= Eeq/2(1+v)

K1/n(K1+K2)K2/n(K1+K2)

Sheet9

Page 42

y= 166.67A= 1970 mm2I= 51300000 mm4

fy= 230 N/mm2M= 11519430.51 knmF= 77343.06 N

IS 800:1984, Cl 7.1.2

0.284 + 0.247 =

Page -8

FS = 0.67A = 392056.8

= 40 Mpa= 2.5 Mpa= 23406373.6 -= 1462898.3 -

N Q -Q-60000000.0 29456112.3 -29456112.3-55000000.0 28559558.6 -28559558.6-45000000.0 26676207.7 -26676207.7-40000000.0 25682793.8 -25682793.8-36100000.0 4941916.0 -4941916.0-36100000.0 4941916.0 -4941916.0-30000000.0 4522881.2 -4522881.2-10000000.0 2730002.4 -2730002.4-2000000.0 1500498.9 -1500498.9-1800000.0 1456523.8 -1456523.8-1200000.0 1315809.8 -1315809.8-1000000.0 1265432.7 -1265432.7-500000.0 1129704.1 -1129704.1

0.0 975265.6 -975265.6500000.0 791236.0 -791236.0

1000000.0 548603.6 -548603.6

t/0.6fy + bt/0.66fy

N = cA/FS 9Q2FS/4cA

mm2ctN (by c)N (by t)

-70000000.0 -60000000.0 -50000000.0 -40000000.0 -30000000.0 -20000000.0 -10000000.0 0.0 10000000.0

-40000000.0

-30000000.0

-20000000.0

-10000000.0

0.0

10000000.0

20000000.0

30000000.0

40000000.0

N (in N)

Q (in N)

Sheet9

Page 43

1500000.0 Err:502 Err:502

N= 522500 - 4.30622010E-006N= 8360000 - 2.69138756E-007

N Q522500 0

0 348333.3333331000000 594607.7138192000000 765363.0220723000000 904435.0600114000000 1024804.859475000000 1132451.863096000000 1230719.07617

0 1000000 2000000 3000000 4000000 5000000 6000000 70000000

200000

400000

600000

800000

1000000

1200000

1400000

Column B

-70000000.0 -60000000.0 -50000000.0 -40000000.0 -30000000.0 -20000000.0 -10000000.0 0.0 10000000.0

-40000000.0

-30000000.0

-20000000.0

-10000000.0

0.0

10000000.0

20000000.0

30000000.0

40000000.0

N (in N)

Q (in N)

Sheet9

Page 44

mmm (= D)kNkNm

mm

(Clause: B - 2.2, IS 456 : 2000)

As per Carranza -Torres article Mechanical analysis of circular lines with particular reference to composite supports (Page 10-12)

40 2.5

M 0.2 500000 -Mpa 30000 8000000 -

0.15 Qm2 0.095 577350.27m4 0.000311 333333.33

149071.20MN 210818.51

258198.89MN/m2 298142.40

N/mm2N/mm2 (grade fe 415)

0.00 2000000.00 4000000.00 6000000.00 8000000.00

-2000000

0

2000000

4000000

6000000

8000000

10000000

Column J

Sheet9

Page 45

m 7589466.38MpaMpa

-0.119464 -0.04951

Fy kN Mz kNm-0.26904 -0.099023 -0.004 -0.09 0.51-162.73 12.63 0.537 12.09 -78.78162.73 -12.63 -0.537 -12.09 78.79-75.23 131.62 5.597 126.02 -77.3475.23 -131.62 -5.597 -126.02 77.3512.27 163.10 6.936 156.16 -75.16-12.27 -163.10 -6.936 -156.16 75.1799.77 107.08 4.554 102.53 -72.24-99.77 -107.08 -4.554 -102.53 72.25187.27 -36.43 -1.549 -34.88 -68.58-95.23 36.43 1.549 34.88 69.94196.20 -199.58 -8.488 -191.09 -66.76-12.10 199.58 8.488 191.09 68.78115.24 -270.87 -11.519 -259.35 -68.3472.77 270.87 11.519 259.35 68.7427.38 -245.46 -10.439 -235.02 -71.06

164.77 245.46 10.439 235.02 69.79-72.64 -112.55 -4.787 -107.77 -74.85269.86 112.55 4.787 107.77 71.62-76.60 81.40 3.462 77.94 -62.95238.67 -81.40 -3.462 -77.94 59.94-23.22 228.02 9.697 218.32 -54.78161.81 -228.02 -9.697 -218.32 53.0865.00 282.21 12.002 270.21 -51.37

-11.519 -77.34

M1(kNm) = MK1/n(K1+K2)

M2(kNm) = MK2/n(K1+K2)

Fx1 = {FxD1/(n(D1+D2))} +{M(D2K1D1K2)/(nR(D1+D2)(K1+K2))}

Sheet9

Page 46

0.531

Sheet9

Page 47

Q2 SIG TQ2 SIG C

0 1000000 2000000 3000000 4000000 5000000 6000000 70000000

200000

400000

600000

800000

1000000

1200000

1400000

Column B

-70000000.0 -60000000.0 -50000000.0 -40000000.0 -30000000.0 -20000000.0 -10000000.0 0.0 10000000.0

-40000000.0

-30000000.0

-20000000.0

-10000000.0

0.0

10000000.0

20000000.0

30000000.0

40000000.0

N (in N)

Q (in N)

Sheet9

Page 48

0.0000045 Q2 SIG T2.8125E-007 Q2 SIG C

N-1000000

0400000300000200000100000

0.00 2000000.00 4000000.00 6000000.00 8000000.00

-2000000

0

2000000

4000000

6000000

8000000

10000000

Column J

Sheet9

Page 49

8200000

0.51 5.51-78.78 -847.9178.79 847.93-77.34 -820.5177.35 820.55-75.16 -793.8775.17 793.92-72.24 -767.9872.25 768.04-68.58 -742.8569.94 757.44-66.76 -739.4868.78 761.30-68.34 -763.6068.74 767.98-71.06 -790.4369.79 776.71-74.85 -818.0671.62 783.19-62.95 -670.4259.94 637.97-54.78 -567.7453.08 549.40-51.37 -525.55-77.34

= {FxD1/(n(D1+D2))} +D1K2)/(nR(D1+D2)

))}

Fx2 = {FxD2/(n(D1+D2))} -{M(D2K1D1K2)/(nR(D1+D2)(K1+K2))}

Sheet9

Page 50

-70000000.0 -60000000.0 -50000000.0 -40000000.0 -30000000.0 -20000000.0 -10000000.0 0.0 10000000.0

-40000000.0

-30000000.0

-20000000.0

-10000000.0

0.0

10000000.0

20000000.0

30000000.0

40000000.0

N (in N)

Q (in N)

Sheet9

Page 51

0 1000000 2000000 3000000 4000000 5000000 6000000 70000000

200000

400000

600000

800000

1000000

1200000

1400000

Column B

-70000000.0 -60000000.0 -50000000.0 -40000000.0 -30000000.0 -20000000.0 -10000000.0 0.0 10000000.0

-40000000.0

-30000000.0

-20000000.0

-10000000.0

0.0

10000000.0

20000000.0

30000000.0

40000000.0

N (in N)

Q (in N)

Sheet10

Page 52

Liner Elements on Excavation

Start_Node End_Node Start_Node_X Start_Node_Y End_Node_X23 24 10 -50 1024 25 10 -49.5 1025 26 10 -49 1026 27 10 -48.5 1027 28 10 -48 1028 29 10 -47.5 1029 30 10 -47 1030 31 10 -46.5 1031 32 10 -46 1032 33 10 -45.5 1033 34 10 -45 9.937534 35 9.9375 -44.4435 9.87535 36 9.875 -43.887 9.6936 37 9.69 -43.359 9.50537 38 9.505 -42.831 9.20738 39 9.207 -42.357 8.90939 40 8.909 -41.883 8.51340 41 8.513 -41.487 8.11741 42 8.117 -41.091 7.64342 43 7.643 -40.793 7.16943 44 7.169 -40.495 6.64144 45 6.641 -40.31 6.11345 46 6.113 -40.125 5.556546 47 5.5565 -40.0625 547 48 5 -40 4.443548 49 4.4435 -40.0625 3.88749 50 3.887 -40.125 3.35950 51 3.359 -40.31 2.83151 52 2.831 -40.495 2.35752 53 2.357 -40.793 1.88353 54 1.883 -41.091 1.48754 55 1.487 -41.487 1.09155 56 1.091 -41.883 0.79356 57 0.793 -42.357 0.49557 58 0.495 -42.831 0.3158 59 0.31 -43.359 0.12559 60 0.125 -43.887 0.062560 61 0.0625 -44.4435 0

Sheet10

Page 53

61 62 0 -45 062 63 0 -45.5 063 64 0 -46 064 65 0 -46.5 065 66 0 -47 066 67 0 -47.5 067 68 0 -48 068 69 0 -48.5 069 70 0 -49 070 71 0 -49.5 0

Sheet10

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End_Node_Y Distance Axial_force Moment_1 Moment_Mid Moment_2-49.5 8.25 3.581 0.091251 0.16675 0.244815-49 8.75 3.8534 0.244815 0.24874 0.259035

-48.5 9.25 4.0887 0.259035 0.26697 0.26253-48 9.75 4.1248 0.26253 0.25466 0.245745

-47.5 10.25 4.2099 0.245745 0.23316 0.2184-47 10.75 4.2268 0.2184 0.20169 0.18361

-46.5 11.25 4.23 0.18361 0.16422 0.144425-46 11.75 4.2142 0.144425 0.12605 0.107461

-45.5 12.25 4.2387 0.107461 0.085131 0.058621-45 12.75 4.2581 0.058621 0.021678 -0.00225675

-44.4435 13.28 4.4526 -0.00225675 0.012384 0.027057-43.887 13.84 4.8424 0.027057 -0.014732 -0.054594-43.359 14.4 5.4767 -0.054594 -0.0028141 0.047944-42.831 14.959 6.0119 0.047944 -0.0068747 -0.064463-42.357 15.519 6.5208 -0.064463 -0.010979 0.044355-41.883 16.079 6.9085 0.044355 -0.017708 -0.080461-41.487 16.639 7.1464 -0.080461 -0.016958 0.048735-41.091 17.199 7.2078 0.048735 -0.012548 -0.077531-40.793 17.759 6.9711 -0.077531 -0.0237 0.022849-40.495 18.319 6.5526 0.022849 -0.06348 -0.157225-40.31 18.878 5.8011 -0.157225 -0.13869 -0.10642

-40.125 19.438 5.5757 -0.10642 -0.13555 -0.13514-40.0625 19.998 3.9233 -0.13514 -0.054254 0

-40 20.558 3.5035 0 -0.038409 -0.0753135-40.0625 21.118 3.5899 -0.0753135 -0.036905 0.0104615-40.125 21.678 4.2564 0.0104615 -0.037767 -0.119464-40.31 22.237 6.0272 -0.119464 -0.099023 -0.04951

-40.495 22.797 6.2712 -0.04951 -0.082327 -0.11105-40.793 23.356 7.028 -0.11105 -0.029538 0.04721-41.091 23.916 7.2987 0.04721 -0.0072948 -0.0670315-41.487 24.476 7.4503 -0.0670315 -0.0032486 0.059166-41.883 25.036 7.3847 0.059166 -0.0090304 -0.076486-42.357 25.596 7.148 -0.076486 -0.013845 0.0483-42.831 26.156 6.7558 0.0483 -0.010384 -0.0670075-43.359 26.716 6.2441 -0.0670075 -0.0087046 0.0470005-43.887 27.275 5.7173 0.0470005 -0.006796 -0.061789

-44.4435 27.835 5.0912 -0.061789 -0.020324 0.0249265-45 28.395 4.7314 0.0249265 0.011988 0.00287065

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-45.5 28.925 4.4532 0.00287065 0.032717 0.065157-46 29.425 4.4562 0.065157 0.086262 0.108947

-46.5 29.925 4.5093 0.108947 0.12987 0.150325-47 30.425 4.5244 0.150325 0.16988 0.188095

-47.5 30.925 4.5134 0.188095 0.20426 0.219795-48 31.425 4.4707 0.219795 0.23431 0.247375

-48.5 31.925 4.3995 0.247375 0.257 0.26174-49 32.425 4.3358 0.26174 0.2614 0.25942

-49.5 32.925 4.0735 0.25942 0.25903 0.25935-50 33.425 3.9773 0.25935 0.18245 0.10616

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Shear_force Yielded-0.52305 Yes

-0.009341 Yes0.0070889 No0.030899 No0.05628 No

0.069795 No0.078938 No0.069171 No0.095053 No0.16734 No

-0.089219 No0.26005 No-0.30712 No0.34658 No-0.34089 No0.38545 No-0.39562 No0.3898 Yes

-0.34521 Yes0.47692 Yes-0.21794 Yes0.1623 Yes

-0.33975 Yes0.22666 Yes-0.23546 Yes0.35337 Yes-0.26904 Yes0.24072 Yes-0.44148 Yes0.37059 Yes-0.39354 Yes0.41436 Yes-0.39045 Yes0.35713 No-0.3542 No0.32381 No-0.27318 No0.086772 No

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-0.17277 No-0.094236 No-0.08203 No

-0.075814 No-0.061542 No-0.054497 No-0.030656 No0.0045701 Yes-0.0064226 Yes

0.52857 No

Sheet1M-N ENVELOPESheet3Sheet2Sheet4Sheet5Sheet7MOI of 3barsSheet9Sheet10

Lattice Girder_fair Rock

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Transcript of Lattice Girder_fair Rock