T-Beams...PRC_I

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Prepared by madam rafia firdous. She is a lecturer and instructor in subject of Plain and Reinforcement concrete at University of South Asia LAHORE,PAKISTAN.

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T-Beams...PRC_I

  1. 1. PLAIN & REINFORCED CONCRETE-1 TEE - BEAMS By Engr. Rafia Firdous 1
  2. 2. Plain & Reinforced Concrete-1 T & L Beams • With the exception of pre-cast systems, reinforced concrete floors, roofs, decks, etc., are almost always monolith. • Beam stirrups and bent bars extend up into the slab. • It is evident, therefore, that a part of the slab will act with the upper part of the beam to resist compression. • The slab forms the beam flange, while a part of the beam projecting below the slab forms what is called the “web” or “stem”. 2
  3. 3. Plain & Reinforced Concrete-1 T & L Beams (contd…) d h b or bf b hf bw b = Effective width bw = width of web/rib/stem hf = Thickness of flange hf 3
  4. 4. Plain & Reinforced Concrete-1 Effective With of T & L Beams T-Beams Effective width will be minimum of the following: 1. L/4 2. 16hf + bw 3. bw + ½ x (clear spacing of beams (Si) on both sides) = c/c spacing for beams at regular interval 4
  5. 5. Plain & Reinforced Concrete-1 Effective With of T & L Beams L-Beams Effective width will be minimum of the following: 1. L/12 2. 6hf + bw 3. bw + Si/2 on one side Note: Only above discussion is different for isolated (pre- cast) T or L beam. Other discussion is same (analysis and design formula). 5
  6. 6. Plain & Reinforced Concrete-1 Flexural Behavior Case-I: Flange is in Tension +ve Moment -ve Moment In both of the above cases beam can be designed as rectangular beam T C C T 6
  7. 7. Plain & Reinforced Concrete-1 Flexural Behavior (contd…) Case-II: Flange is in Compression and N.A. lies with in Flange beam can be designed as a rectangular beam of total width “b” and effective depth “d”. c N.A. hf fhc  b T Td C 7
  8. 8. Plain & Reinforced Concrete-1 Flexural Behavior (contd…) Case-III: Flange is in Compression and N.A. lies out of the Flange Beam has to be designed as a T-Beam. Separate expressions are to be developed for analysis and design. c N.A. hf fhc  b d C or a > β1 hf 8
  9. 9. Plain & Reinforced Concrete-1 Flexural Behavior (contd…) Cw T = Asfs N.A. εcu= 0.003 Strain Diagram Internal Force Diagram εs c 0.85fc a Whitney’s Stress Diagram (d-a/2) fs Cf d – β1hf/2 hf Cw Cf / 2 β1hf/2Cf / 2 Cw = Compression developed in the web = 0.85fc’bwa Cf = Compression developed in the overhanging flange = 0.85fc’(b-bw) β1hf C = Total Compression = Cw + Cf T = Total Tension = Tw + Tf Tw = Tension to balance Cw Tf =Tension to balance Cf 9
  10. 10. Plain & Reinforced Concrete-1 Flexural Behavior (contd…) • It is convenient to divide total tensile steel into two parts. The first part, Asf represents the steel area which, when stressed to fy, is required to balance the longitudinal compressive force in the overhanging portions of the flange that are stressed uniformly at 0.85fc’. • The remaining steel area As – Asf, at a stress fy, is balanced by the compression in the rectangular portion web above the N.A. ssff fAT    ssfsssww fAAfAT  10
  11. 11. Plain & Reinforced Concrete-1 Flexural Behavior (contd…) Majority of T and L beams are under-reinforced (tension controlled). Because of the large compressive concrete area provided by the flange. In addition, an upper limit can be established for the reinforcement ratio to ensure the yielding of steel. 0F  For longitudinal equilibrium ff CT  ww CT & 11
  12. 12. Plain & Reinforced Concrete-1 Flexural Behavior (contd…) ff CT    f1wcysf hβbb'f85.0fA   w y c f1sf bb f 'f hβ85.0A  Only for case-III ww CT    ab'f85.0fAA wcysfs    wc ysfs b'f85.0 fAA a   1β a c and If N.A. is outside the flangefhc  12
  13. 13. Plain & Reinforced Concrete-1 Flexural Behavior (contd…) Flexural Capacity From Compression Side nwnfn MMM               2 a dC 2 hβ dCM w f1 fn                2 a dab'f85.0 2 hβ dhβbb'f85.0M wc f1 f1wcn 13
  14. 14. Plain & Reinforced Concrete-1 Flexural Behavior (contd…) Flexural Capacity From Tension Side nwnfn MMM               2 a dT 2 hβ dTM w f1 fn                2 a dfAA 2 hβ dfAM ysfs f1 ysfn 14
  15. 15. Plain & Reinforced Concrete-1 Tension Controlled Failure of T-Beam db A ρ w s w  = Total tension steel area (all steel will be in web) db A ρ w sf f  = Steel ratio to balance the flange compressive force bρ = Balanced steel ratio for the singly reinforced rectangular section  maxwρ = Maximum steel ratio for T-Beam maxρ = Maximum steel ratio for the singly reinforced rectangular section 15
  16. 16. Plain & Reinforced Concrete-1 Tension Controlled Failure of T-Beam (contd…)   db A f 'f 8 3 β85.0ρ w sf y c 1maxw    fmaxmaxw ρρρ   maxww ρρIf  Tension controlled section  maxww ρρIf  Transition or Compression controlled section Or If a < β1d (3/8) then Tension controlled section 16
  17. 17. Concluded 17

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