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By Dr. Attaullah Shah Swedish College of Engineering and Technology Wah Cantt.

By Dr. Attaullah Shah Swedish College of Engineering and Technology Wah Cantt. Reinforced Concrete Design-4 Design of doubly reinforced beams. Due to size limitations compression reinforcement may be required in addition to anchor bars to support stirrups.

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By Dr. Attaullah Shah Swedish College of Engineering and Technology Wah Cantt.

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  1. ByDr. Attaullah ShahSwedish College of Engineering and Technology Wah Cantt. Reinforced Concrete Design-4 Design of doubly reinforced beams

  2. Due to size limitations compression reinforcement may be required in addition to anchor bars to support stirrups. If the applied ultimate moment is more than the factored nominal capacity allowed by maximum steel ratio, the additional steel may be required in compression and tension to support the excess moment.

  3. Analysis of Doubly Reinforced Sections Effect of Compression Reinforcement on the Strength and Behavior Less concrete is needed to resist the T and thereby moving the neutral axis (NA) up.

  4. Analysis of Doubly Reinforced Sections Effect of Compression Reinforcement on the Strength and Behavior

  5. Reasons for Providing Compression Reinforcement • Reduced sustained load deflections. • Creep of concrete in compression zone • transfer load to compression steel • reduced stress in concrete • less creep • less sustained load deflection

  6. Doubly Reinforced Beams Four Possible Modes of Failure • Under reinforced Failure • ( Case 1 ) Compression and tension steel yields • ( Case 2 ) Only tension steel yields • Over reinforced Failure • ( Case 3 ) Only compression steel yields • ( Case 4 ) No yielding Concrete crushes

  7. Analysis of Doubly Reinforced Rectangular Sections Strain Compatibility Check Assume es’ using similar triangles

  8. Analysis of Doubly Reinforced Rectangular Sections Strain Compatibility Using equilibrium and find a

  9. Analysis of Doubly Reinforced Rectangular Sections Strain Compatibility The strain in the compression steel is

  10. Analysis of Doubly Reinforced Rectangular Sections Strain Compatibility Confirm

  11. Analysis of Doubly Reinforced Rectangular Sections Strain Compatibility Confirm

  12. Analysis of Doubly Reinforced Rectangular Sections Find c confirm that the tension steel has yielded

  13. Analysis of Doubly Reinforced Rectangular Sections If the statement is true than else the strain in the compression steel

  14. Analysis of Doubly Reinforced Rectangular Sections Return to the original equilibrium equation

  15. Analysis of Doubly Reinforced Rectangular Sections Rearrange the equation and find a quadratic equation Solve the quadratic and find c.

  16. Analysis of Doubly Reinforced Rectangular Sections Find the fs’ Check the tension steel.

  17. Analysis of Doubly Reinforced Rectangular Sections Another option is to compute the stress in the compression steel using an iterative method.

  18. Analysis of Doubly Reinforced Rectangular Sections Go back and calculate the equilibrium with fs’ Iterate until the c value is adjusted for the fs’ until the stress converges.

  19. Analysis of Doubly Reinforced Rectangular Sections Compute the moment capacity of the beam

  20. Limitations on Reinforcement Ratio for Doubly Reinforced beams Lower limit on r same as for single reinforce beams. (ACI 10.5)

  21. Example: Doubly Reinforced Section Given: f’c= 4000 psi fy = 60 ksi A’s = 2 #5 As = 4 #7 d’= 2.5 in. d = 15.5 in h=18 in. b =12 in. Calculate Mn for the section for the given compression steel.

  22. Example: Doubly Reinforced Section Compute the reinforcement coefficients, the area of the bars #7 (0.6 in2) and #5 (0.31 in2)

  23. Example: Doubly Reinforced Section Compute the effective reinforcement ratio and minimum r

  24. Example: Doubly Reinforced Section Compute the effective reinforcement ratio and minimum r Compression steel has not yielded.

  25. Example: Doubly Reinforced Section Instead of iterating the equation use the quadratic method

  26. Example: Doubly Reinforced Section Solve using the quadratic formula

  27. Example: Doubly Reinforced Section Find the fs’ Check the tension steel.

  28. Example: Doubly Reinforced Section Check to see if c works The problem worked

  29. Example: Doubly Reinforced Section Compute the moment capacity of the beam

  30. Example: Doubly Reinforced Section If you want to find the Mu for the problem From ACI (figure R9.3.2)or figure (pg 100 in your text) The resulting ultimate moment is

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