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(b) BEAM DETACHED FROM SUPPORTS

BEAM SUBJECT TO POST-TENSIONING. LOAD ONLY. A. B. C. D. TENDON. FORCE P. (a) THREE SPAN POST-TENSIONED BEAM. TENDON. DISPLACEMENT d. LINE OF SUPPORTS. (b) BEAM DETACHED FROM SUPPORTS. HYPERSTATIC (SECONDARY). REACTIONS AND MOMENTS. A. B. C. D. R. i. REACTION.

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(b) BEAM DETACHED FROM SUPPORTS

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  1. BEAM SUBJECT TO POST-TENSIONING LOAD ONLY A B C D TENDON FORCE P (a) THREE SPAN POST-TENSIONED BEAM TENDON DISPLACEMENT d LINE OF SUPPORTS (b) BEAM DETACHED FROM SUPPORTS

  2. HYPERSTATIC (SECONDARY) REACTIONS AND MOMENTS A B C D R i REACTION (a) REACTIONS AT SUPPORTS DUE TO PRESTRESSING (HYPERSTATIC REACTIONS) MOMENT (b) MOMENTS DUE TO PRESTRESSING SUPPORT REACTIONS (HYPERSTATIC MOMENTS)

  3. SECTIONAL ACTIONS DUE TO PRESTRESSING & THE CORRESPONDING INTERNAL DISTRIBUTION OF FORCES AT STRENGTH LIMIT STATE A B M HYP R V i HYP X i REACTION DUE TO POST-TENSIONING (a) RESULTANT MOMENT AND SHEAR AT A SECTION CONCRETE COMPRESSION A B C z T R i TENDON FORCE REACTION (b) ASSUMED INTERNAL FORCE DISTRIBUTION AT STRENGTH LIMIT STATE

  4. TN7-351 DL LL PT TENDON DL = DEAD LOAD LL = LIVE LOAD POST-TENSIONED FRAME UNDER LOADING

  5. TN7-150 JOINT i JOINT 1 M M t t 1 i PT R M M R 1 b b 1 i i SUPPORT REACTIONS DUE TO POST-TENSIONING

  6. TN7-143 M M t t 1 i PT R M M 1 b b 1 R i i X i X 1 ACTIONS CAUSING HYPERSTATIC MOMENTS AND SHEARS

  7. TN7-319 POST-TENSIONING M M t t i 1 M M M V R b b 1 R 1 i i X i X 1 HYPERSTATIC MOMENT (M) AND SHEAR (V) IN A SECTION

  8. TN7-503 0.90m 5.75m 8.20m 6.75m mm 1100 3.00m 1600 2.50m mm (a) PLAN 260mm 200mm 3.00m 300mm DROP CAP x 450mm 1600mm COLUMN x 1100mm 200mm x 200mm WALL (b) ELEVATION 235 130 235 163 130 1237.5kN 1650kN 25 25 25 EQ EQ EQ EQ EQ EQ (c) TENDON GEOMETRY (Y-SCALE EXAGGERATED) GEOMETRY OF THREE SPAN TWO-WAY SLAB

  9. TN7-505 1 2 3 4 5.75m 8.20m 6.75m 0.90m 9.834 18.870 8.983 -8.972 -9.015 9.005 (a) HYPERSTATIC ACTIONS AT SUPPORTS (UNITS IN kN AND kN-m) 60.78 51.65 25.82 41.91 41.82 41.87 225 mm FACE OF SUPPORT EQ EQ IN-SPAN (b) DISTRIBUTION OF HYPERSTATIC MOMENTS (UNITS kN-m) HYPERSTATIC ACTIONS OF THE TWO-WAY SLAB DESIGN STRIP

  10. TN7-514 -200 -100 0 MOMENT (kNm) 100 200 300 SPAN 1 SPAN 2 SPAN 3 CANT DISTRIBUTION OF POST-TENSIONING MOMENT

  11. TN7-456 1 2 3 0.3m 8.7m 6.7m A OPENING 9.7m 4.0m 600 DIA. B 4.0m DROP PANEL 7.7m 500mm SLAB 250 mm 600 X 600mm TYP. UNO. BELOW SLAB C 9.6m 0.3m STRUCTURE PLAN

  12. TN7-457 BANDED 2 3 1 TENDONS A 1T 4T 27T 5T 12T 12T 2T DISTRINUTED TENDONS B C TENDON CGS ABOVE SLAB SOFFIT NOTE: DISTRIBUTED TENDONS: 3 STRANDS EACH, UNO. 50mm AT LOW POINT 200mm AT HIGH POINT 12T MEANS 12 STRANDS 125mm AT SLAB EDGE STRESSING END DEAD END TENDON LAYOUT

  13. TN7-458 2 3 1 A Fz = 1.05 Fz = 20.3 Fz = 2.18 OPENING DROP CAP COLUMN B Fz = 38.8 Fz = 47.8 Fz = -140 Mx = 0.495 kNm My = 0 Fz = 8.61 Fz = -0.576 Fz = 21.6 C Y X SUPPORT REACTIONS DUE TO POST- TENSIONING ONLY (kN)

  14. TN7-459 1 2 3 A 0 0 0.926 kN -0.366 kN 0 0 0 10 10 10 10 10 20 361 kNm 20 0 0 30 10 10 -10 0 B -10 64.1 kN 40 -10 0 30 10 0 20 10 10 10 10 10 0 4.97 kN C 0 0 0 Y CONTOURS AT 10kN INTERVALS X CONTOUR PLOT OF HYPERSTATIC MOMENTS, My

  15. TN7-508 1 2 3 A -2.38kN/m COMPRESSION -173kN TENSION 349kN -69kN/m B -77kN/m 103kN/m -176kN -9.33kN/m C (a) DISTRIBUTION OF IN-PLANE COMPRESSION AT LINE 2 A 3 B 2 C 125mm 173kN 349kN 176kN (b) IN-PLANE ACTIONS AT LINE 2 HYPERSTATIC IN-PLANE FORCES AT LINE 2

  16. TN7-509 20 m 20 m POST-TENSIONING PRE-TENSIONING (a) COMPLETED STRUCTURE 300mm 80mm (b) INSTALLATION OF PRECAST GIRDERS (c) CLOSURE OF SPLICE 300mm 80mm 80mm 8.28m 300mm (d) APPLICATION OF POST-TENSIONING TWO SPAN SEGMENTAL CONSTRUCTION

  17. MOMENTS DUE TO POST-TENSIONING 262 kNm 344 kNm • DISTRIBUTION OF PRESTRESSING MOMENT IN THE COMPLETED STRUCTURE (b) DISTRIBUTION OF HYPERSTATIC MOMENT IN THE COMPLETED STRUCTURE

  18. 171 kNm (a) DISTRIBUTION OF MOMENT DUE TO SELF- WEIGHT SEGMENTAL CONSTRUCTION -172 kNm 99.8 kNm (b) DISTRIBUTION MOMENT DUE TO SELF WEIGHT ONE STAGE CONSTRUCTION

  19. A B w V A M b P P R V X b i AD66 (F3) 062389 BFL X dx a . . M (wdx)x + V a + R X A b i i M + M ; OR SEC P . M P e + M SEC b BALANCED MOMENT M AS SUM OF b PRIMARY AND SECONDARY MOMENTS

  20. A B w W V A M PRIMARY MOMENT P O P P COMPRESSION X V dx x a . M = (wdx)x + V a A P (a) FREE BODY DIAGRAM OF CUT BEAM AD62 (F3) 062089 BFL w W V A e-ECCENTRICITY P P V x X dx a . . . P e= (wdx)x + V a ; HENCE M = P e A P (b) FREE BODY DIAGRAM OF CUT TENDON ILLUSTRATION OF PRIMARY MOMENT (M ) AT P DISTANCE a ALONG THE MEMBER

  21. V W P B AD69B (F3) 062089 BFL P A FREE BODY DIAGRAM OF A TENDON SECTION BETWEEN ITS LOW POINT (A) AND POINT OF INFLEXION (B)

  22. A B C D W V V A D P P (a) FREE BODY DIAGRAM OF BEAM AFTER REMOVAL OF TENDON AD61 (F3) 062089 BFL W V V D A P P TENDON (b) FREE BODY DIAGRAM OF TENDON ILLUSTRATION OF FORCE SYSTEM BETWEEN TENDON AND BEAM

  23. AD80 (F4) 062089 BFL TENDON THREE SPAN POST-TENSIONED BEAM

  24. AD80 (F4) 062089 BFL TENDON THREE SPAN POST-TENSIONED BEAM

  25. A B C D W V V A D P P (a) FREE BODY DIAGRAM OF BEAM AFTER REMOVAL OF TENDON AD61 (F3) 062089 BFL W V V D A P P TENDON (b) FREE BODY DIAGRAM OF TENDON ILLUSTRATION OF FORCE SYSTEM BETWEEN TENDON AND BEAM

  26. V W P B AD69B (F3) 062089 BFL P A FREE BODY DIAGRAM OF A TENDON SECTION BETWEEN ITS LOW POINT (A) AND POINT OF INFLEXION (B)

  27. A B w W V A M PRIMARY MOMENT P O P P COMPRESSION X V dx x a (a) FREE BODY DIAGRAM OF CUT BEAM AD62 (F3) 062089 BFL w W V A e-ECCENTRICITY P P V x X dx a (b) FREE BODY DIAGRAM OF CUT TENDON ILLUSTRATION OF PRIMARY MOMENT (M ) AT P DISTANCE a ALONG THE MEMBER

  28. BEAM SUBJECT TO POST-TENSIONING LOAD ONLY A B C D TENDON FORCE P (a) THREE SPAN POST-TENSIONED BEAM TENDON DISPLACEMENT d LINE OF SUPPORTS (b) BEAM DETACHED FROM SUPPORTS

  29. HYPERSTATIC (SECONDARY) REACTIONS AND MOMENTS A B C D REACTION (a) REACTIONS AT SUPPORTS DUE TO PRESTRESSING (HYPERSTATIC REACTIONS) MOMENT (b) MOMENTS DUE TO PRESTRESSING SUPPORT REACTIONS (HYPERSTATIC MOMENTS)

  30. SECTIONAL ACTIONS DUE TO PRESTRESSING & THE CORRESPONDING INTERNAL DISTRIBUTION OF FORCES AT STRENGTH LIMIT STATE A B M SEC R V i SEC X i REACTION DUE TO POST-TENSIONING (a) RESULTANT MOMENT AND SHEAR AT A SECTION CONCRETE COMPRESSION A B C z T R i TENDON FORCE REACTION (b) ASSUMED INTERNAL FORCE DISTRIBUTION AT STRENGTH LIMIT STATE

  31. A B w V A M b P P R V X b i AD66 (F3) 062389 BFL X dx a OR BALANCED MOMENT M AS SUM OF b PRIMARY AND SECONDARY MOMENTS

  32. TN7-341 NA NA TENDON (a) w b P P m CENTROIDAL AXIS (b) BALANCED LOADING m P M =Pm P P (c) m P P (d) ACTIONS CAUSING AXIAL COMPRESSION w b M p (e) ACTIONS CAUSING FLEXURE OF MEMBERS (BALANCED ACTIONS) BALANCED LOADING AND CHANGES IN MEMBER THICKNESS

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