Prestress Concrete - Inner Beams - After Check

Position 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

35.57 677.38 1322.83 1904.82 2398.34 2833.75 3192.11 3471.41 3671.19 3803.7 3845.89 3738.83 3569.69 3325.77 3015.63 2613.95 2142.89 1611.14 997.12 320.33 31.73

Max 22.76 695.33 1320.14 1919.84 2405.92 2832.25 3186.97 3470.02 3672.17 3816.63 3859.98 3750.21 3578.4 3328.56 2999.11 2618.68 2148.09 1616.81 977.01 299.48 14.43

4.31 685.27 1342.32 1918.97 2415.82 2831.09 3185.35 3468.71 3672.16 3817.98 3856.93 3744.85 3569.38 3317.64 3013.63 2606.04 2133.71 1600.69 978.85 301.5 7.04

17.84 672.95 1351.59 2068.58 2498.25 2881.5 3178.58 3460.53 3665.02 3803.06 3845.41 3737.98 3565.48 3323.87 3009.87 2607 2134.98 1602.28 979.3 300.85 9.43

-28.09 398.77 780.98 1121 1406.42 1655.64 1851.4 2002.39 2100.05 2157.42 2172.85 2130.34 2052.47 1923.89 1755.21 1531.25 1258.63 951.32 587.95 187.82 -12.93

Min -31.83 410.25 781.17 1132.64 1415.07 1659.44 1851.03 2001.96 2099.68 2161.07 2176.39 2134.04 2056.36 1926.82 1749.82 1538.89 1265.2 956.81 577.31 175.85 -7.83

-4.05 404.29 794.36 1132.14 1420.83 1658.81 1850.16 2001.27 2099.68 2161.59 2175.42 2131.76 2052.11 1920.99 1757.66 1531.53 1256.84 947.46 578.41 177.04 -4.21

-34.24 396.15 790.16 1175.48 1407.41 1655.64 1844.04 1996.54 2097.21 2157.17 2172.69 2129.97 2050.46 1919.09 1752.06 1527.23 1254.06 946.2 577.4 176.32 -14.62

Des Max Des Min 35.57 -34.24 695.33 396.15 1351.59 780.98 2068.58 1121 2498.25 1406.42 2881.5 1655.64 3192.11 1844.04 3471.41 1996.54 3672.17 2097.21 3817.98 2157.17 3859.98 2172.69 3750.21 2129.97 3578.4 2050.46 3328.56 1919.09 3015.63 1749.82 2618.68 1527.23 2148.09 1254.06 1616.81 946.2 997.12 577.31 320.33 175.85 31.73 -14.62

kN.m

Bending Moments 4000 3750 3500 3250 3000 2750 2500 2250 2000 1750 1500 1250 1000 750 500 250 0 -250 0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Chainage Max

Column C

Column D

Column E

Min

Column G

Column H

Column I

Des Max

Des Min

17

18

19

20

Data Input 1 2

Concrete Class = K Value =

C45/55 45 Concrete Class 0.8 % Stress of Ultimate Tendon Stress

3

Element Class

=

Class 1 Allowable cracking to occur

4

System

=

Strength Class fctm (N/mm2) Ecm (kN/mm2) fcu (N/mm2)

35

Post - Tensioning System

C20/25 2.2

C25/30 2.6

C30/37 2.9

C35/45 3.2

C40/50 3.5

C45/55 3.8

C50/60 4.1

30

31

33

34

35

36

37

20

25

30

35

40

45

50

Design Section Properties 3 4

A Z1

= =

5 6

Z2 Y1

= =

7

Y2

=

700,250 mm2 1.50E+08 mm3 2.88E+08 mm3 832 mm 433 mm 1,265 mm 225 mm

Auto Dmax = 8 Tendon - cover =

Section Area Section Modulus for Top of Design Section

0.700 149.980

Section Modulus Bottom of Design Section From Bottom Edge to Centroid

288.270

From Top Edge to Centroid Total Section Depth Concrete Cover + Reinforcing + Cable Centroid

Design Concrete Stresses At Service Auto fa max

=

Auto fa min At transfer Auto fa maxt

=

= Auto fa mint = Tension Force - At Transfer Auto ƒ1 min = ƒ Auto 2 min =

14.9 MPa 0.0 MPa

33% f cu (Design Concrete Strength)

20.3 MPa -1.0 MPa

45% of f ci (Concrete Strength at Transfer) -1.000

40.2 MPa -7.5 MPa

Auto Pe min = 6167.6 kN Auto es max = 607.1 mm Tension Force - At Service Loading Auto ƒ1 max = 29.3 MPa Auto ƒ2 max Auto Pe min Auto es max

Class 1

Pre-stress Force Eccentricity

-6.1 MPa

=

4231.1 kN 825.7 mm

= =

Pre-stress Force Eccentricity

Bending Moments 9 Mmax

=

10 Mdn 11 Mmin

= =

3,860.0 kN/m 2,172.7 kN/m 0.0 kN/m

Maximum Bending Moments (without Dn) Bending moments due to own Dn Minimum Bending moments (without Dn)

Magnel Diagram Construction Auto emax TOP Auto emax BOT

=

400 mm

=

1,000 mm

Plotting: Upper Range Limit for Prestress Offset Plotting: Lower Range limit for prestress Offset

Magnel Diagram 150,000 125,000 100,000 75,000 50,000

1/Po

25,000 0 -25,000 -50,000 -75,000 -100,000 -125,000 -150,000 -175,000 -200,000 400

450

500

550

600

80 21

Pe

=

5200.0 kN

Max Negative Value -10 -9 -8 -7 -6 -5 -4 Min Pe -3 Min Pe -2 -1 Max Pe 0 Min Pe 1 2 3 4 5 6 7 8 650 700 750 800 850 900 950 1 9 000 10 e-offset Mx Positive Value Enter Pre-stress Force from Magnel Diagram at Max es

e values

Min Pe

Pe - Post Tensioning Force Max Pe Min Pe -150,152 112,260 40,857 24,973 17,982 14,049 11,528 9,774 8,483 7,493 6,711 6,076 5,551 5,109 4,733 4,408 4,125 3,876 3,655 3,459 3,282 3,122 2,978

400 427.27 454.55 481.82 509.09 536.36 563.64 590.91 618.18 645.45 672.73 700.00 727.27 754.55 781.82 809.09 836.36 863.64 890.91 918.18 945.45 972.73 1000

9,822 9,405 9,021 8,668 8,341 8,038 7,756 7,493 7,248 7,018 6,802 6,599 6,408 6,227 6,057 5,895 5,742 5,597 5,459 5,328 5,202 5,083 4,969

570

7,693

11,064

7,164 6,859 6,580 6,322 6,083 5,862 5,657 5,465 5,286 5,118 4,961 4,813 4,674 4,542 4,418 4,300 4,188 4,082 3,981 3,886 3,794 3,707 3,624

Min Pe -186,221 139,226 50,671 30,972 22,301 17,424 14,297 12,122 10,521 9,293 8,323 7,535 6,884 6,337 5,870 5,467 5,116 4,807 4,534 4,289 4,070 3,872 3,693

5,611

13,722

Class 2

Class 3

14.9 0.0

14.9 -2.4

14.9 -2.0

20.3 -1.0

20.3 -3.1

20.3 -3.0

Limiting Design Stress - Class 2 Sections System 30.0 Pre Post -

0 2.1 2.1

Concrete Grade (Mpa) 40.0 45.0 50.0 2.9 2.3 2.3

3.05 2.43 2.43

3.2 2.6 2.55

60.0 3.5 2.8 2.8

Bending Moments (kN.m) Chainage Mmin Mmax K Value fmax

=

fmin

= =

f'min

=

Zt

=

Zb

= =

A Emax Top Emax Bot

=

P (Mmax)

=

-34.24 396.15

35.57 695.33

461 543

363 446

-609 -450

-206 -47

2

780.98

1351.59

617

520

-292

111

3

1121

2068.58

683

585

-120

283

20.25 (N/mm ) Less than 0.45 x fcu for Upper Boundary Conditions -1.0 (N/mm2) Less than Zero for Lower Boundary Conditions 2.88E+08 mm3 Section Modulus of Top Beam Section

4

1406.42

2498.25

738

640

-17

386

5

1655.64

2881.5

785

688

75

478

6

1844.04

3192.11

822

724

150

553

1.50E+08 mm3 700250 mm2 -658 mm

Section Modulus of Bottom Section Section Area

7 8

1996.54 2097.21

3471.41 3672.17

851 870

754 773

217 265

620 669

Max Offset from Centroid to Top of Edge of Beam

9

2157.17

3817.98

882

785

300

704

607 mm 5,200,000 N

Max Offset from Centroid to Top of Edge of Beam Minimum Pre-stress Force

10

2172.69

3859.98

885

788

311

714

3750.21 3578.4 3328.56 3015.63 2618.68 2148.09 1616.81 997.12 320.33 31.73

877 861 836 804 761 708 649 578 501 464 461 885

779 764 739 706 664 611 552 481 404 367 363 788

284 243 183 108 12 -101 -229 -378 -540 -610 -610 311

687 646 586 511 415 302 174 26 -137 -207 -207 714

2

=

Po at Service Zt & Mmax Zb & Mmax

0 1

0.8 Factor % Stress of Ultimate Tendon Stress 14.85 (N/mm2) Calculated from concrete class 0.0 (N/mm2) Minimum is 0

=

f'max

11 2129.97 12 2050.46 13 1919.09 14 1749.82 15 1527.23 16 1254.06 17 946.2 18 577.31 19 175.85 20 -14.62 Minimum Values Maximum Values

Cable Zone

mm Offset

All values from previous sheet

Design Data from Pre-stress Calcs

Po at Transfer Zt & Mmin Zb - Mmin

900 800 700 600 500 400 300 200 100 0 -100 -200 -300 -400 -500 -600 -700 0

1

2

3

4

5

6

7

8

9

10

11

12

13

Beam Chainage

Po at Transfer

Column L

Po at Service

Column N

14

15

16

17

18

19

20

Data Input 1

Concrete Class =

Auto K Value

=

Auto Element Class

=

45 Concrete Class

C45/55

0.8 % Stress of Ultimate Tendon Stress Class 1 Allowable compressive Stress

Design Concrete Stresses At Service Auto fmax 3 fmin At Transfer 4 f'max 5

2 14.9 (N/mm ) 33% fcu 0.0 (N/mm2) 36% x √fcu

= =

20.3 (N/mm2) 80% of fa max -1.0 (N/mm2) 36% x √(80% fcu)

=

f'min

=

Design Section Properties 6

A

=

700,250 mm

7 8

Ztop Z bot Dmax

= =

1.50E+08 mm 2.88E+08 mm3 1,265 mm 225 mm

9 10

= Tendon - cover =

2

Section Area

3

Section Modulus for Top of Design Section Section Modulus Bottom of Design Section Maximum Section Depth

Bending Moments 11 Mmax 12 Mmin

=

3,860.0 kN/m

Maximum Bending Moments

=

2,172.7 kN/m

Minimum Bending moments

Magnel Diagram Construction Auto emax TOP

=

0 mm

Auto emax BOT Auto ZB/A Auto ZT/A

= =

950 mm 412 mm

=

-214 mm

Upper Range Limit for Prestress Offset Lower Range limit for prestress Offset e value for Magnel Construction

Magnel Diagram

106/Po - Post Tensioning Fo

400 350 300 250

1/Po

200 150 100 50 0 -50 -100 -150 0

100

200

300

400

3000 13 emax Auto Max Po Auto Min Po 14 emin Auto Max Po Auto Min Po Auto Pe

500

600

700

800

900

e-offset

Max Negative Value -10 -9 -8 -7 -6 -5 -4 Max Po -3 Max Po -2 -1 Min Po 0 Min Po 1 2 3 4 5 6 7 8 9 1000 10 Mx Positive Value

= = =

820 mm 3,917 kN 3,834 kN

Enter the Maximum e value within Area of 4 lines

= = = =

600 mm 5,290 kN 7,918 kN 5,200 kN

Enter the Minimum e value within Area of 4 lines

Safe Value for Post tensioning Force

e values

Max Po

0 43.18 86.36 129.55 172.73 215.91 259.09 302.27 345.45 388.64 431.82 475.00 518.18 561.36 604.55 647.73 690.91 734.09 777.27 820.45 863.64 906.82

-105 -84 -63 -41 -20 1 22 43 64 85 107 128 149 170 191 212 234 255 276 297 318 339

950

361

106/Po - Post Tensioning Force Max Po

Min Po

Min Po

20

85 94 103 112 121 130 139 148 157 166 175 184 193 202 211 220 229 237 246 255 264 273

-92 -74 -55 -36 -18 1 19 38 57 75 94 112 131 149 168 187 205 224 242 261 280 298

51 57 62 68 73 78 84 89 95 100 105 111 116 121 127 132 138 143 148 154 159 165

282

317

170

fctm Ecm fcu

Class 1 Class 2 Class 3 14.9 14.9 14.9

1,040

0.0

-2.4

-2.0

11.9

11.9

11.9

-1.0

-3.1

-3.0

Strength Class C20/25

C25/30

C30/37

C35/45

C40/50

C45/55

C50/60

(N/mm2)

2.2

2.6

2.9

3.2

3.5

3.8

4.1

(kN/mm2)

30

31

33

34

35

36

37

(N/mm )

20

25

30

35

40

45

50

2

Class Element Prestress Loss % Class 1 Class 2 0 Class 3 1 2 3 4 5 6 7 8 10 11 17 18 19

Design Data from Pre-stress Calcs K Value fmax

=

fmin

= =

0.8 Factor % Stress of Ultimate Tendon Stress 14.85 (N/mm2) Calculated from concrete class 0.0 (N/mm2) Minimum is 0 20.25 (N/mm2) Less than 0.45 x fcu for Upper Boundary Conditions -1.0 (N/mm2) Less than Zero for Lower Boundary Conditions

=

f'max f'min Zt

=

1.50E+08 mm3 2.88E+08 mm3 700250 mm2 5,200,000 N

= = = =

Zb A P (Mmax)

Section Modulus of Top Beam Section Section Modulus of Bottom Section Section Area Minimum Pre-stress Force

Po at Transfer Zt & Mmin Zb - Mmin

Po at Service Zt & Mmax Zb & Mmax Profile 1 offset

236 319

704 787

-313 -154

-403 -245

536 535

300 285

236 250

-300 -285

-64 -35

0 1

296 297

596 582

896 867

2

780.981

1351.593

393

861

4

-87

545

265

280

-265

15

2

287

552

817

3 4

1120.997 1406.415

2068.579 2498.246

459 513

926 981

176 279

86 189

555 585

220 180

335 405

-220 -180

115 225

3 4

277 247

497 427

717 607

5

1655.638

2881.503

561

1,029

371

281

630

165

465

-165

300

5

202

367

532

3192.113 3471.409 3672.167 3817.980 3859.982 3750.208 3578.399 3328.564 3015.631 2618.684 2148.093 1616.811 997.117 320.328 31.730

598 627 646 658 661 653 637 612 580 537 484 425 354 277 240 236 661

1,066 1,095 1,114 1,126 1,129 1,121 1,105 1,080 1,047 1,005 952 893 822 745 708 704 1,129

446 513 562 597 607 580 539 479 404 308 195 67 -82 -244 -314 -314 607

356 423 471 506 516 490 449 388 313 218 105 -23 -172 -335 -404 -404 516

660 670 670 670 680 670 670 670 660 630 585 555 545 535 536

145 130 110 100 100 100 110 130 145 165 180 220 265 285 300

515 540 560 570 580 570 560 540 515 465 405 335 280 250 236

-145 -130 -110 -100 -100 -100 -110 -130 -145 -165 -180 -220 -265 -285 -300

370 410 450 470 480 470 450 410 370 300 225 115 15 -35 -64

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

172 162 162 162 152 162 162 162 172 202 247 277 287 297 296

317 292 272 262 252 262 272 292 317 367 427 497 552 582 596

462 422 382 362 352 362 382 422 462 532 607 717 817 867 896

6 1844.041 7 1996.542 8 2097.214 9 2157.169 10 2172.692 11 2129.973 12 2050.456 13 1919.090 14 1749.816 15 1527.226 16 1254.058 17 946.196 18 577.311 19 175.850 20 -14.617 Minimum Values Maximum Values

mm Offset

700 500 300 100 -100 -300 Row 5

Row 6

Row 7

Row 8

Row 9

Row 10

Row 11

Row 12

Row 13

Row 14

Row 15

Row 16

Row 17

Row 18

Row 19

Row 20

Row 21

Row 22

Row 23

13

14

15

16

17

18

19

20

Beam Chainage

Zt & Mmin

Zb - Mmin

Zt & Mmax

Zb & Mmax

Cable Profiles 700 650 600 550 500 450 400 350 300 250 200 150 100 50 0 -50 -100 0

1

2

3

4

5

6

7

8

9

10

11

Beam Chainage

Column Q

Column O

Column S

Profile 3

35.570 695.330

900

Row 4

Distance from soffit Profile 1 Profile 2

Profile 3 Chainage

-34.244 396.146

1,100

-500 Row 3

Design Profile 2 offset

0 1

Cable Zone

mm Offset

All values from previous sheet

Bending Moments (kN.m) Chainage Mmin Mmax

12

All Auto values from previous sheets

Design Data from Pre-stress Calcs K Value fmax

=

fmin

=

f'max

=

f'min

=

Zt

=

Zb

= =

A P (Mmax) Md e fcu f'cu

=

= = = = =

% Stress of Ultimate Tendon Stress

20.25 N/mm2 -1 N/mm2

Less than 0.45 x fcu for Upper Boundary Conditions

Pre - Tensioning

5.33E-05

4.80E-05

4.80E-05

Less than Zero for Lower Boundary Conditions

Post - Tensioning

4.00E-05

3.60E-05

3.60E-05

4.00E-05

3.60E-05

Calculated from concrete class Minimum is 0

1.50E+08 mm3 2.88E+08 mm3 700250 mm2 5,200,000 N 2,173 kN.m 607 mm 45 MPa 36 MPa

ec

=

r ∂ ∆P(x)R + ∆P(x)w

= =

88 m #N/A

=

#N/A kN

i

=

ℓo Pℓo

=

P'jack ∆P(x)ws

Modulus of Elasticity for Concrete Moment of Inertia Perimeter of X-section

Number of cables Sheath inside Diameter Total Tendon Area 7-wire Strand Manufacturers specs Manufacturers specs Midspan or Span/2 Total depth of cable eccentricity (maxe + mine)

26 28 29.5 31

Losses due to friction caused by radius of duct and wobble

45

32

50 60

34 36

Wedge Slip in (From Manufacturers) Length of Tendon effected by wedge slip

= =

#N/A kN

Stressing at Anchor

Description

=

#N/A kN

Losses due to slip

High Tensile Steel Wire

205

7-wire Strand

195

High Tensile Alloy Steel Bars

165

=

Es

=

20.25 MPa 195.00 GPa

Ec

=

32 MPa

Loss Ecs

= =

62 MPa 3 kN

∆P1 P'

= =

Stress at ℓo

#N/A N #N/A kN

f'cu

=

Higher than 40 Mpa

fck

=

3.60E-05

0.4 x fcu

=

18.00 MPa

∆fck

= =

126 MPa 6.7 kN

P' - (∆P1 + ∆P2) =

Friction Coefficient

Total Short Term Losses Total After Short Term Losses

Strand or Wire in Steel Duct 0.25 Pulled through Oversized Duct with water-saluble oil0.17

Concrete Cube Strength at Transfer

0.55 0.33

Grease strand running in plastic sleeve

0.05

Manufacturers specs

0.18

Creep Coefficient Concrete Stress Stress x Creep Factor Losses due to Creep

1.40E-04 Shrinkage Strain 27 MPa 1 kN #N/A kN

Long term and Short term losses

Steel Relaxation

Wobble Factor Minimum Strong Rigid Sheath - no displacement

3.30E-03 1.70E-03

Greased Strands in Plastic sleeves

2.50E-03

Manufacturers specs

1.70E-03

Initial Jacking Force 70%

= =

80% Percentage of Ultimate Tendon Stressing Force - Pe 10% Relaxation % of Stressing force

75% 80%

=

#N/A kN

85%

Initial Prestress Force #N/A Plosses Pinitial

GPA

Lightly rusted Tendon, Unlined concrete Duct Lightly rusted Tendon, Lightly rusted Duct

Shrinkage: = = =

Modulus of Elasticity for Steel

Loss due to Elastic Shortening

Creep:

Po Factor Pu

Modulus of Elasticity (Gpa) 25

30 35 40

Elastic Shortening:

Shrinkage

Modulus of Elasticity for Concrete

Cube Strength (Mpa) 20

#N/A m #N/A kN

fcs

HUMID ATMOSPHERES (OUTSIDE: 80% RH)

Higher than 40 MPa

Shrinkage Coefficient Shrinkage per Unit length System Humidity Pre - Tensioning Post - Tensioning 80% - Coastal 1.80E-04 1.40E-04 60% - Mostly inland 3.10E-04 2.50E-04 35% - Low e.g. Windhoek 4.20E-04 3.50E-04

Radius of Tendon Curvature Stress Factor

Wedge Slip

cs

Lower than 40 MPa

25

Friction

6.5 mm

System used

Section Modulus of Bottom Section Section Area Minimum Pre-stress Force Max moments due to Own Weight Maximum Cable Offset from Section Sentroid Concrete Strength during Service Concrete Strength at Transfer

32 MPa = = 1.248E+11 Ixx = 6,515 mm = 80% - Coastal = Post - Tensioning = 3 no = 75 mm = 13254 mm2 = 195 kN/mm2 = 3.30E-01 Coefficient = #N/A Factor = 10000 mm 570 mm

DRY ATMOSPHERES (INSIDE: 50% RH)

Concrete Cube Strength at Transfer

Section Modulus of Top Beam Section

Ecm I U Humidity System No Diameter Ap Es µ k x

ε

CREEP COEFFICIENT OF CONCRETE - fck

0.8 Factor 14.85 N/mm2 0 N/mm2

=

#N/A kN

Total Losses

=

#N/A kN

Initial Stressing Force

90% 95% 100%

0 0 0