DESIGN OF DESIGN OF SINGLY REINFORCED SINGLY REINFORCED

BEAMBEAM

Er. RANDEEP SINGH Er. RANDEEP SINGH

(B-Tech. CIVIL)(B-Tech. CIVIL)

GNDEC,LUDHIANA.GNDEC,LUDHIANA.

BEAMBEAM:-:-

A Beam is any structural member which resists A Beam is any structural member which resists load mainly by bending. Therefore it is also load mainly by bending. Therefore it is also called flexural member. Beam may be singly called flexural member. Beam may be singly reinforced or doubly reinforced. When steel is reinforced or doubly reinforced. When steel is provided only in tensile zone (i.e. below neutral provided only in tensile zone (i.e. below neutral axis) is called axis) is called singly reinforced beam,singly reinforced beam, but when but when steel is provided in tension zone as well as steel is provided in tension zone as well as compression zone is called doubly reinforced compression zone is called doubly reinforced beam. beam.

The aim of design is:The aim of design is:

To decide the size (dimensions) of the member To decide the size (dimensions) of the member and the amount of reinforcement required.and the amount of reinforcement required.

To check whether the adopted section will To check whether the adopted section will perform safely and satisfactorily during the life perform safely and satisfactorily during the life time of the structure.time of the structure.

FEW DEFINITIONSFEW DEFINITIONS

OVER ALL DEPTHOVER ALL DEPTH :- :-

THE NORMAL DISTANCE FROM THE TOP EDGE THE NORMAL DISTANCE FROM THE TOP EDGE OF THE BEAM TO THE BOTTOM EDGE OF THE OF THE BEAM TO THE BOTTOM EDGE OF THE BEAM IS CALLED OVER ALL DEPTH. IT IS BEAM IS CALLED OVER ALL DEPTH. IT IS DENOTED BY DENOTED BY ‘D’.‘D’.

EFFECTIVE DEPTHEFFECTIVE DEPTH:- :-

THE NORMAL DISTANCE FROM THE TOP EDGE THE NORMAL DISTANCE FROM THE TOP EDGE OF BEAM TO THE CENTRE OF TENSILE OF BEAM TO THE CENTRE OF TENSILE REINFORCEMENT IS CALLED EFFECTIVE REINFORCEMENT IS CALLED EFFECTIVE DEPTH. IT IS DENOTED BY DEPTH. IT IS DENOTED BY ‘d’.‘d’.

CLEAR COVERCLEAR COVER:- :-

THE DISTANCE BETWEEN THE BOTTOM OF THE DISTANCE BETWEEN THE BOTTOM OF THE BARS AND BOTTOM MOST THE EDGE OF THE BARS AND BOTTOM MOST THE EDGE OF THE BEAM IS CALLED CLEAR COVER.THE BEAM IS CALLED CLEAR COVER.

CLEAR COVER = 25mm OR DIA OF MAIN BAR, CLEAR COVER = 25mm OR DIA OF MAIN BAR, (WHICH EVER IS GREATER).(WHICH EVER IS GREATER).

EFFECTIVE COVEREFFECTIVE COVER:- :-

THE DISTANCE BETWEEN CENTRE OF TENSILE THE DISTANCE BETWEEN CENTRE OF TENSILE REINFORCEMENT AND THE BOTTOM EDGE OF REINFORCEMENT AND THE BOTTOM EDGE OF THE BEAM IS CALLED EFFECTIVE COVER. THE BEAM IS CALLED EFFECTIVE COVER. EFFECTIVE COVER = CLEAR COVER + ½ DIA EFFECTIVE COVER = CLEAR COVER + ½ DIA OF BAR.OF BAR.

END COVEREND COVER:- :-

END COVER = 2XDIA OF BAR OR 25mm (WHICH END COVER = 2XDIA OF BAR OR 25mm (WHICH EVER IS GREATER)EVER IS GREATER)

NEUTRAL AXISNEUTRAL AXIS:- THE LAYER / LAMINA WHERE :- THE LAYER / LAMINA WHERE NO STRESS EXIST IS KNOWN AS NEUTRAL AXIS. NO STRESS EXIST IS KNOWN AS NEUTRAL AXIS. IT DIVIDES THE BEAM SECTION INTO TWO IT DIVIDES THE BEAM SECTION INTO TWO ZONES, COMPRESION ZONE ABOVE THE ZONES, COMPRESION ZONE ABOVE THE NETURAL AXIS & TENSION ZONE BELOW THE NETURAL AXIS & TENSION ZONE BELOW THE NEUTRAL AXIS.NEUTRAL AXIS.

DEPTH OF NETURAL AXISDEPTH OF NETURAL AXIS:- THE NORMAL :- THE NORMAL DISTANCE BETWEEN THE TOP EDGE OF THE DISTANCE BETWEEN THE TOP EDGE OF THE BEAM & NEUTRAL AXIS IS CALLED DEPTH OF BEAM & NEUTRAL AXIS IS CALLED DEPTH OF NETURAL AXIS. IT IS DENOTED BY NETURAL AXIS. IT IS DENOTED BY ‘n’‘n’..

LEVER ARMLEVER ARM:- THE DISTANCE BETWEEN THE :- THE DISTANCE BETWEEN THE RESULTANT COMPRESSIVE FORCE (C) AND RESULTANT COMPRESSIVE FORCE (C) AND TENSILE FORCE (T) IS KNOWN AS LEVER ARM. IT TENSILE FORCE (T) IS KNOWN AS LEVER ARM. IT IS DENOTED BY IS DENOTED BY ‘z’. ‘z’. THE TOTAL COMPRESSIVE THE TOTAL COMPRESSIVE FORCE (C) IN CONCRETE ACT AT THE C.G. OF FORCE (C) IN CONCRETE ACT AT THE C.G. OF COMPRESSIVE STRESS DIAGRAM i.e. n/3 FROM COMPRESSIVE STRESS DIAGRAM i.e. n/3 FROM THE COMPRESSION EDGE. THE TOTAL TENSILE THE COMPRESSION EDGE. THE TOTAL TENSILE FORCE (T) ACTS AT C.G. OF THE FORCE (T) ACTS AT C.G. OF THE REINFORCEMENT.REINFORCEMENT.

LEVER ARM = d-n/3 LEVER ARM = d-n/3

TENSILE REINFORCEMENTTENSILE REINFORCEMENT:- :-

THE REINFORCEMENT PROVIDED TENSILE THE REINFORCEMENT PROVIDED TENSILE ZONE IS CALLED TENSILE REINFORCEMENT. ZONE IS CALLED TENSILE REINFORCEMENT. IT IS DENOTED BY IT IS DENOTED BY AAstst..

  

COMPRESSION REINFORCEMENTCOMPRESSION REINFORCEMENT :- :-

THE REINFORCEMENT PROVIDED THE REINFORCEMENT PROVIDED COMPRESSION ZONEIS CALLED COMPRESSION ZONEIS CALLED COMPRESSION REINFORCEMENT. IT IS COMPRESSION REINFORCEMENT. IT IS DENOTED BY DENOTED BY AAscsc

TYPES OF BEAM SECTIONTYPES OF BEAM SECTION:- THE BEAM :- THE BEAM SECTION CAN BE OF THE FOLLOWING TYPES:SECTION CAN BE OF THE FOLLOWING TYPES:

1.1.BALANCED SECTIONBALANCED SECTION

2.2.UNBALNCED SECTIONUNBALNCED SECTION

(a) (a) UNDER- REINFORCED SECTIONUNDER- REINFORCED SECTION

(b) (b) OVER-REINFORCED SECTIONOVER-REINFORCED SECTION

1.BALANCED SECTION1.BALANCED SECTION:- A SECTION IS :- A SECTION IS KNOWN AS BALANCED SECTION IN WHICH KNOWN AS BALANCED SECTION IN WHICH THE COMPRESSIVE STREE IN CONCRETE (IN THE COMPRESSIVE STREE IN CONCRETE (IN COMPRESSIVE ZONES) AND TENSILE STRESS IN COMPRESSIVE ZONES) AND TENSILE STRESS IN STEEL WILL BOTH REACH THE MAXIMUM STEEL WILL BOTH REACH THE MAXIMUM PERMISSIBLE VALUES SIMULTANEOUSLY. PERMISSIBLE VALUES SIMULTANEOUSLY.

THE NEUTRAL AXIS OF BALANCED (OR THE NEUTRAL AXIS OF BALANCED (OR CRITICAL) SECTION IS KNOWN AS CRITICAL CRITICAL) SECTION IS KNOWN AS CRITICAL NEUTRAL AXIS NEUTRAL AXIS (n(ncc)). THE AREA OF STEEL . THE AREA OF STEEL

PROVIDED AS ECONOMICAL AREA OF STEEL. PROVIDED AS ECONOMICAL AREA OF STEEL. REINFORCED CONCRETE SECTIONS ARE REINFORCED CONCRETE SECTIONS ARE DESIGNED AS BALANCED SECTIONS.DESIGNED AS BALANCED SECTIONS.

2. UNBALNCED SECTION2. UNBALNCED SECTION:-THIS IS A SECTION IN :-THIS IS A SECTION IN WHICH THE QUANTITY OF STEEL PROVIDED IS WHICH THE QUANTITY OF STEEL PROVIDED IS DIFFERENT FROM WHAT IS REQUIRED FOR THE DIFFERENT FROM WHAT IS REQUIRED FOR THE BALANCED SECTION. BALANCED SECTION.

UNBALANCED SECTIONS MAY BE OF THE UNBALANCED SECTIONS MAY BE OF THE FOLLOWING TWO TYPES:FOLLOWING TWO TYPES:

(a)(a) UNDER-REINFORCED SECTIONUNDER-REINFORCED SECTION

(b)(b) OVER-REINFORCED SECTIONOVER-REINFORCED SECTION

(a)(a)UNDER-REINFORCED SECTION:-UNDER-REINFORCED SECTION:- IF THE AREA IF THE AREA OF STEEL PROVIDED IS LESS THAN THAT REQUIRED OF STEEL PROVIDED IS LESS THAN THAT REQUIRED FOR BALANCED SECTION, IT IS KNOWN AS UNDER-FOR BALANCED SECTION, IT IS KNOWN AS UNDER-REINFORCED SECTION. DUE TO LESS REINFORCED SECTION. DUE TO LESS REINFORCEMENT THE POSITION OF ACTUAL REINFORCEMENT THE POSITION OF ACTUAL NEUTRAL AXIS NEUTRAL AXIS (n) (n) WILL SHIFT ABOVE THE CRITICAL WILL SHIFT ABOVE THE CRITICAL NEUTRAL AXIS NEUTRAL AXIS (n(ncc))i.e. i.e. n< nn< ncc. IN UNDER-REINFORCED . IN UNDER-REINFORCED

SECTION STEEL IS FULLY STRESSED AND CONCRETE SECTION STEEL IS FULLY STRESSED AND CONCRETE IS UNDER STRESSED (i.e. SOME CONCRETE REMAINS IS UNDER STRESSED (i.e. SOME CONCRETE REMAINS UN-UTILISED). STEEL BEING DUCTILE, TAKES SOME UN-UTILISED). STEEL BEING DUCTILE, TAKES SOME TIME TO BREAK. THIS GIVES SUFFICIENT WARNING TIME TO BREAK. THIS GIVES SUFFICIENT WARNING BEFORE THE FINAL COLLAPSE OF THE STRUCTURE. BEFORE THE FINAL COLLAPSE OF THE STRUCTURE. FOR THIS REASON AND FROM ECONOMY POINT OF FOR THIS REASON AND FROM ECONOMY POINT OF VIEW THE UNDER-REINFORCED SECTIONS ARE VIEW THE UNDER-REINFORCED SECTIONS ARE DESIGNED.DESIGNED.

(b)(b) OVER-REINFORCED SECTION:- OVER-REINFORCED SECTION:- IF THE AREA IF THE AREA OF STEEL PROVIDED IS MORE THAN THAT OF STEEL PROVIDED IS MORE THAN THAT REQUIRED FOR A BALANCED SECTION, IT IS REQUIRED FOR A BALANCED SECTION, IT IS KNOWN AS OVER-REINFORCED SECTION. AS THE KNOWN AS OVER-REINFORCED SECTION. AS THE AREA OF STEEL PROVIDED IS MORE, THE AREA OF STEEL PROVIDED IS MORE, THE POSITION OF N.A. WILL SHIFT TOWARDS STEEL, POSITION OF N.A. WILL SHIFT TOWARDS STEEL, THEREFORE ACTUAL AXIS THEREFORE ACTUAL AXIS (n) (n) IS BELOW THE IS BELOW THE CRITICAL NEUTRAL AXIS CRITICAL NEUTRAL AXIS (n(ncc))i.e. i.e. n > nn > ncc. IN THIS . IN THIS

SECTION CONCRETE IS FULLY STRESSED AND SECTION CONCRETE IS FULLY STRESSED AND STEEL IS UNDER STRESSED. UNDER SUCH STEEL IS UNDER STRESSED. UNDER SUCH CONDITIONS, THE BEAM WILL FAIL INITIALLY DUE CONDITIONS, THE BEAM WILL FAIL INITIALLY DUE TO OVER STRESS IN THE CONCRETE. CONCRETE TO OVER STRESS IN THE CONCRETE. CONCRETE BEING BRITTLE, THIS HAPPENS SUDDENLY AND BEING BRITTLE, THIS HAPPENS SUDDENLY AND EXPLOSIVELY WITHOUT ANY WARNING.EXPLOSIVELY WITHOUT ANY WARNING.

Basic rules for design of beamBasic rules for design of beam:- :-

1. Effective span1. Effective span:- In the case of simply supported :- In the case of simply supported beam the effective length, beam the effective length,

l = l = ii. Distance between the centre of support. Distance between the centre of support

iiii. Clear span + eff. Depth . Clear span + eff. Depth

eff. Span = least of eff. Span = least of i.i. & & ii. ii. 2. 2. Effective depthEffective depth:- The normal distance from the :- The normal distance from the top edge of beam to the centre of tensile top edge of beam to the centre of tensile reinforcement is called effective depth. It is denoted reinforcement is called effective depth. It is denoted by by ‘d’.‘d’.

d= D- effect. Coverd= D- effect. Cover

where D= over all depthwhere D= over all depth

3. Bearing :-3. Bearing :- Bearings of beams on brick walls may Bearings of beams on brick walls may be taken as follow:be taken as follow:

Up to 3.5 m span, bearing = 200mmUp to 3.5 m span, bearing = 200mm Up to 5.5 m span, bearing =300mmUp to 5.5 m span, bearing =300mm Up to 7.0 m span, bearing =400mmUp to 7.0 m span, bearing =400mm

4. Deflection control:-4. Deflection control:- The vertical deflection limits The vertical deflection limits assumed to be satisfied if assumed to be satisfied if (a) (a) For span up to 10mFor span up to 10m

Span / eff. Depth = 20Span / eff. Depth = 20

(For simply supported beam)(For simply supported beam)

Span / eff. Depth = 7Span / eff. Depth = 7

(For cantilever beam)(For cantilever beam)

(b) (b) For span above 10m, the value in (a) should For span above 10m, the value in (a) should be multiplied by 10/span (m), except for be multiplied by 10/span (m), except for cantilever for which the deflection calculations cantilever for which the deflection calculations should be made.should be made.

(c) (c) Depending upon the area and type of steel the Depending upon the area and type of steel the value of (a&b) modified as per modification value of (a&b) modified as per modification factor.factor.

5. Reinforcement 5. Reinforcement :-:-

(a) (a) Minimum reinforcement:- The minimum area Minimum reinforcement:- The minimum area of tensile reinforcement shall not be less than that of tensile reinforcement shall not be less than that given by the following: given by the following:

AAstst = 0.85 bd / f = 0.85 bd / fyy

(b)(b)Maximum reinforcement:- The maximum area of Maximum reinforcement:- The maximum area of tensile reinforcement shall not be more than tensile reinforcement shall not be more than 0.4bD0.4bD

(c)(c)Spacing of reinforcement bars:-Spacing of reinforcement bars:-

i. i. The horizontal distance between to parallel main bars The horizontal distance between to parallel main bars shall not be less than the greatest of the following:shall not be less than the greatest of the following: Diameter of the bar if the bars are of same diameter.Diameter of the bar if the bars are of same diameter. Diameter of the larger bar if the diameter are unequal.Diameter of the larger bar if the diameter are unequal. 5mm more than the nominal maximum size of coarse 5mm more than the nominal maximum size of coarse aggregate. aggregate.

ii. ii. When the bars are in vertical lines and the minimum When the bars are in vertical lines and the minimum vertical distance between the bars shall be greater of the vertical distance between the bars shall be greater of the following:following: 15mm.15mm. 2/32/3rdrd of nominal maximum size of aggregate. of nominal maximum size of aggregate. Maximum diameter of the bar.Maximum diameter of the bar.6. Nominal cover to reinforcement6. Nominal cover to reinforcement :-:- The Nominal The Nominal cover is provided in R.C.C. design:cover is provided in R.C.C. design: To protect the reinforcement against corrosion.To protect the reinforcement against corrosion. To provide cover against fire.To provide cover against fire. To develop the sufficient bond strength along the To develop the sufficient bond strength along the surface area of the steel bar.surface area of the steel bar.

As per IS 456-2000, the value of nominal cover As per IS 456-2000, the value of nominal cover to meet durability requirements as follow:-to meet durability requirements as follow:-

Exposure conditions

Nominal cover(mm)Not less than

MildModerateSevereVery severeExtreme

2030455075

Procedure for Design of Singly Reinforced Procedure for Design of Singly Reinforced Beam by Working Stress MethodBeam by Working Stress Method

Given :Given :

(i) Span of the beam ((i) Span of the beam (ll))

(ii) Loads on the beam(ii) Loads on the beam

(iii)Materials-Grade of Concrete and type of steel.(iii)Materials-Grade of Concrete and type of steel.

1. 1. Calculate design constants for the given materials Calculate design constants for the given materials (k, j and R)(k, j and R)

k = m k = m σσcbccbc / m / m σσcbccbc + + σσstst

where k is coefficient of depth of Neutral Axiswhere k is coefficient of depth of Neutral Axis

j = 1- k/3j = 1- k/3

where j is coefficient of lever arm.where j is coefficient of lever arm.

R= 1/2 R= 1/2 σσcbccbc kj kj

where R is the resisting moment factor.where R is the resisting moment factor.

2. 2. Assume dimension of beam:Assume dimension of beam:

d = Span/10 to Span/8d = Span/10 to Span/8

Effective cover = 40mm to 50mmEffective cover = 40mm to 50mm

b = D/2 to 2/3Db = D/2 to 2/3D

3. 3. Calculate the effective span (l) of the beam.Calculate the effective span (l) of the beam.

4. 4. Calculate the self weight (dead load) of the beam. Calculate the self weight (dead load) of the beam.

Self weight = D x b x 25000 N/mSelf weight = D x b x 25000 N/m

5.5. Calculate the total Load & maximum bending Calculate the total Load & maximum bending moment for the beam. moment for the beam.

Total load (w) = live load + dead loadTotal load (w) = live load + dead load

Maximum bending moment, M = wlMaximum bending moment, M = wl2 2 / 8 at the centre / 8 at the centre of beam for simply supported beam.of beam for simply supported beam.

M = wlM = wl2 2 / 2 at the support / 2 at the support of beam for cantilever beam. of beam for cantilever beam.

6. 6. Find the minimum effective depthFind the minimum effective depth

M = MM = Mrr

= Rbd= Rbd22

ddreqd.reqd. = √ M / R.b = √ M / R.b

7. 7. Compare dCompare dreqd.reqd. With assumed depth value. With assumed depth value.

(i) (i) If it is less than the assumed d, then assumption is If it is less than the assumed d, then assumption is correct.correct.

(ii) (ii) IfIf ddreqd.reqd. is more than assumed d, then revise the is more than assumed d, then revise the

depth value and repeat steps 4, 5 & 6.depth value and repeat steps 4, 5 & 6.

8. 8. Calculate the area of steel required (ACalculate the area of steel required (Astst). ).

AAstst = M / = M / σσstst jd jd

Selecting the suitable diameter of bar calculate the Selecting the suitable diameter of bar calculate the number of bars requirednumber of bars required

Area of one bar = Area of one bar = ππ/4 x /4 x φφ22 = A = Aφφ

No. of bars required = ANo. of bars required = Astst /A /Aφφ

9. 9. Calculate minimum area of steel (ACalculate minimum area of steel (ASS) required ) required

by the relation: by the relation:

AASS = 0.85 bd / f = 0.85 bd / fyy

Calculate maximum area of steel by the area Calculate maximum area of steel by the area relation:relation:

Maximum area of steel = 0.04bDMaximum area of steel = 0.04bD

Check that the actual ACheck that the actual AStSt provided is more than provided is more than

minimum and less than maximum requirements.minimum and less than maximum requirements.

10. 10. Check for shear and design shear reinforcement.Check for shear and design shear reinforcement.

11.11. Check for development length. Check for development length.

12. 12. Check for depth of beam from deflection.Check for depth of beam from deflection.

13. 13. Write summary of design and draw a neat sketch. Write summary of design and draw a neat sketch.