Design of R.C

8/18/2019 Design of R.C

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SUST

Collage of Engineering

School of Civil Engineering

3rd

Class –

6th

Semester –

2014

Design of Reinforced Concrete I According to American Standards (ACI 318M-11)

Tutorial No. (1)

Analysis and Design of the Section for F

lexure

Eng. Nyazi Tawfeeg


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Structural Design of Reinforced Concrete (ACI 318M-11) Analysis and Design for Flexure

E n g . N y a z i T a w f e e g

2

Example 1

(Reinforcement for given Moment & Section)

Determine the reinforcing bars for a rectangular section of beam subjected to ultimate moment usingthe following design data:

Solution:

1) Assume the strength reduction factor & the corresponding minimum tensile strain :

2)

Maximum reinforcement ratio for singly reinforced section : 3) Required reinforcement ratio :

4) The reinforcement:

(

√ )

5) Check the ductility of the section at the failure:

* +* +

Either of the following pairs may be chosen


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Example 2


Design the flexural reinforcement for a beam with cross-section of to carry animposed load of and dead load of .The beam is simply supported over

span, and the materials grades

are ( ), and the reinforcement cover to center of bars .Solution:

The ultimate moment :

The effective depth : The design:

1) Assume the strength reduction factor & corresponding minimum tensile strain : 2)

Maximum reinforcement ratio for singly reinforced section : 3)

Required reinforcement ratio :

4)

The reinforcement: ( √ )


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Example 3 (Reinforcement for given Moment & Section)

Calculate the flexural reinforcement of a rectangular section of beam with width of andoverall depth of to resist an ultimate moment of using concrete grade and reinforcement grade , and cover to the center of reinforcement .Solution:

The effective depth : The design:

1) Assume the strength reduction factor & corresponding minimum tensile strain : 2) Maximum reinforcement ratio for singly reinforced section

:

3) Required reinforcement ratio :

4) Compression reinforcement :

* + * +


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( )

()

5)

Tension reinforcement : * +

6)

Check the ductility of the section at the failure:

( ) ( ) 7)

Recheck the flexural capacity : * + * +

The effective depth of the section (d=630 mm) is the distancefrom the extreme compression fiber to the centroid of the

longitudinal tension reinforcement, so that the overall depth

of the section (700 mm) should be increased to allow for

placing two layers of the tensile reinforcement of (6 T 32).

Is the net tensile strain at the centroid of tension steel(at depth ).

Is the net tensile strain at the extreme layer of tensionsteel (at depth ).

The value of the flexural strength reduction factor ()depends on the not , but it has been calculatedconservatively in this example, and it is more safety

because .


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Example 4


The figure below shows a reinforced concrete floor slab thick supported monolithically onbeams with cross-section of to resist an ultimate positive moment of .Using

,

( ) and cover to the center of reinforcement

, design the

flexural reinforcement if the beam span is .

Solution:

The effective depth :

The effective breadth of the flange ():

The design:

1) Assume the strength reduction factor & corresponding minimum tensile strain : 2) Check that how the section should be designed (rectangular or T-section):

*

+

* + Like this

3) Moment of resistance provided by the Slab (overhanging flange) & the required steel ( ): *( ) +

*

+

( )


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4) Moment of resistance required of the beam alone (web) & the required steel :4.1

Moment of resistance required of the beam alone (web) : 4.2

Maximum reinforcement ratio for singly reinforced section : 4.3 Required reinforcement ratio :

4.4

The required steel : 5) The total tension reinforcement for the T-section :

( √ ) 6) Check the ductility of the section at the failure:

()

* ( ) + * +


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Example 5


A reinforced concrete floor slab thick supported monolithically on beams with effectivecross-section of to resist an ultimate positive moment of . If the materialsgrades are

,

( ) design the flexural reinforcement of the beam to span

.

Solution:


The design: 1) Assume the strength reduction factor & corresponding minimum tensile strain : 2)

Check that how the section should be designed (rectangular or T-section):

* +

*

+

Like this 3)

Maximum reinforcement ratio for singly reinforced section : 4)


5)

The reinforcement: ( √ )


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New type of problems

Example 6

(Flexural strength for given Section & Reinforcement)

Determine the ultimate flexural strength of the singly reinforced rectangular

section of beam shown, considering the following design data:

Solution:

The effective depth :

The Ultimate flexural strength:

1)

flexural strength reduction factor

:

2)

Ultimate flexural strength : * + * + Check the ACI-code requirements for minimum reinforcement :

( √ )


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Example 7


Calculate the ultimate flexural strength of the doubly reinforced rectangularsection of beam shown, using:

Solution:


1)

Stress in the compression steel

:

( ) ( )

2) flexural strength reduction factor

:

3) Ultimate flexural strength : * +

*

+

Example 8


Calculate the ultimate flexural strength of the beam shown,using:


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Solution:


Check that how the section should be treated rectangular or T-section):

( ) Like this


1) Nominal flexural strength of the Slab (overhanging flange) (): ( )

* +

2) Nominal flexural strength of the beam alone (web) :

( ) * +

3) flexural strength reduction factor :

4)

Ultimate flexural strength : [ ]


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Check the ACI-code requirements for minimum reinforcement :

Example 9


Calculate the ultimate flexural strength of the beam

shown, using:

Solution:


Check that how the section should be treated rectangular or T-section): ( )

Like this


1) flexural strength reduction factor :


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2) Ultimate flexural strength : * +

* + Check the ACI-code requirements for minimum reinforcement :

New type of problems

Example 1 (Section & Reinforcement for given Moment)

Determine the rectangular cross-section of beam and the required steel to resist an ultimate design

moment of using the following data:

Solution:


Maximum reinforcement ratio for singly reinforced section :

3)

The effective cross-sectional dimensions :


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√ 5) Check the ductility of the section at the failure:

6)

Structural detailing (sketch):

* +* +


Determine the rectangular cross-section of beam and the required steel to carry an ultimate momentof considering the following design data: Solution:

1)

Assume the strength reduction factor & corresponding minimum tensile strain : 2)

Maximum reinforcement ratio for singly reinforced section

:


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3) The effective cross-sectional dimensions :


5)

Check the ductility of the section at the failure: 6) Structural detailing (sketch):


Using concrete grade and reinforcing bars grade design a suitable rectangularsection to resist an ultimate moment of Solution:

1) Assume the strength reduction factor & corresponding minimum tensile strain : 2) Maximum reinforcement ratio for singly reinforced section

:


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4)

The reinforcement:


6) Structural detailing (sketch):

* +* +


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Example 13

(Section & Reinforcement for given Moment)

Design a rectangular reinforced concrete section using the following design data:

Solution:

1)

Assume the strength reduction factor & corresponding minimum tensile strain : 2) Maximum reinforcement ratio for singly reinforced section :

3)

The effective cross-sectional dimensions :

4) Required reinforcement ratio :


√

6) Check the ductility of the section at the failure: 7) Structural detailing (sketch):


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Example 14

(Section & Reinforcement for given Moment)

Design a rectangular reinforced concrete section using the following design data:

Solution:


Maximum reinforcement ratio for singly reinforced section :

3) The effective cross-sectional dimensions : 4)


5) Compression reinforcement :

* + * + ( )

()


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6) Tension reinforcement : * +


( ) ( ) 8) Recheck the flexural capacity

:

* + * + * +

9)

Structural detailing (sketch):


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Example 15

(Design of a beam for Flexure and Shear)

The figure shows a concrete beam supported directly on masonry walls. The beam is required to carry

uniformly distributed characteristic load comprises an imposed load of and estimated deadload of (including the beam self-weight). Using concrete with characteristic compressivestrength (for cylindrical sample) of , flexural reinforcement with yield strength of shear reinforcement with yield strength of and cover to the center ofreinforcement , design the beam.Solution: The ultimate moment

:

The design:

1)

Assume the strength reduction factor & corresponding minimum tensile strain : 2) Maximum reinforcement ratio for singly reinforced section :



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5)

Check the ductility of the section at the failure: 6) Structural detailing (sketch):

The ultimate shear force

:

The design:

1)

Ultimate shear strength provided by concrete :

[ ] [ √ ] 2) Check that the shear reinforcement is required or not: .3)

Choose the shear reinforcement (diameter & shape):


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4) Spacing of stirrups : 4.1 Through the near the support:

( ) (√ ) or .

√

4.2 After from support:

.

5) Structural detailing (sketch):

This shear reinforcement is conservative, but it is practical and convenient. More accurate shear reinforcement can be provided by considering more intervals for distribution of Stirrups spacing.


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Table-2 ( )

Design of R.C

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