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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

ByDr. Attaullah ShahSwedish College of Engineering and Technology Wah Cantt.

Reinforced Concrete Design-4

Design of doubly reinforced beams


By dr attaullah shah swedish college of engineering and technology wah cantt

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.


Analysis of doubly reinforced sections

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.


Analysis of doubly reinforced sections1

Analysis of Doubly Reinforced Sections

Effect of Compression Reinforcement on the Strength and Behavior


Reasons for providing compression reinforcement

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


Doubly reinforced beams

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


Analysis of doubly reinforced rectangular sections

Analysis of Doubly Reinforced Rectangular Sections

Strain Compatibility Check Assume es’ using similar triangles


Analysis of doubly reinforced rectangular sections1

Analysis of Doubly Reinforced Rectangular Sections

Strain Compatibility

Using equilibrium and find a


Analysis of doubly reinforced rectangular sections2

Analysis of Doubly Reinforced Rectangular Sections

Strain Compatibility The strain in the compression steel is


Analysis of doubly reinforced rectangular sections3

Analysis of Doubly Reinforced Rectangular Sections

Strain Compatibility Confirm


Analysis of doubly reinforced rectangular sections4

Analysis of Doubly Reinforced Rectangular Sections

Strain Compatibility Confirm


Analysis of doubly reinforced rectangular sections5

Analysis of Doubly Reinforced Rectangular Sections

Find c

confirm that the tension steel has yielded


Analysis of doubly reinforced rectangular sections6

Analysis of Doubly Reinforced Rectangular Sections

If the statement is true than

else the strain in the compression steel


Analysis of doubly reinforced rectangular sections7

Analysis of Doubly Reinforced Rectangular Sections

Return to the original equilibrium equation


Analysis of doubly reinforced rectangular sections8

Analysis of Doubly Reinforced Rectangular Sections

Rearrange the equation and find a quadratic equation

Solve the quadratic and find c.


Analysis of doubly reinforced rectangular sections9

Analysis of Doubly Reinforced Rectangular Sections

Find the fs’

Check the tension steel.


Analysis of doubly reinforced rectangular sections10

Analysis of Doubly Reinforced Rectangular Sections

Another option is to compute the stress in the compression steel using an iterative method.


Analysis of doubly reinforced rectangular sections11

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.


Analysis of doubly reinforced rectangular sections12

Analysis of Doubly Reinforced Rectangular Sections

Compute the moment capacity of the beam


Limitations on reinforcement ratio for doubly reinforced beams

Limitations on Reinforcement Ratio for Doubly Reinforced beams

Lower limit on r

same as for single reinforce beams.

(ACI 10.5)


Example doubly reinforced section

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.


Example doubly reinforced section1

Example: Doubly Reinforced Section

Compute the reinforcement coefficients, the area of the bars #7 (0.6 in2) and #5 (0.31 in2)


Example doubly reinforced section2

Example: Doubly Reinforced Section

Compute the effective reinforcement ratio and minimum r


Example doubly reinforced section3

Example: Doubly Reinforced Section

Compute the effective reinforcement ratio and minimum r

Compression steel has not yielded.


Example doubly reinforced section4

Example: Doubly Reinforced Section

Instead of iterating the equation use the quadratic method


Example doubly reinforced section5

Example: Doubly Reinforced Section

Solve using the quadratic formula


Example doubly reinforced section6

Example: Doubly Reinforced Section

Find the fs’

Check the tension steel.


Example doubly reinforced section7

Example: Doubly Reinforced Section

Check to see if c works

The problem worked


Example doubly reinforced section8

Example: Doubly Reinforced Section

Compute the moment capacity of the beam


Example doubly reinforced section9

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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