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Design of singly reinforced.

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Deep Lachhar

This document provides information on the design of singly reinforced concrete beams. It defines key terms like overall depth, effective depth, cover, and neutral axis. It explains that a singly reinforced beam only has steel reinforcement in the tension zone. The document also describes balanced and unbalanced beam sections, including under-reinforced and over-reinforced beams. It lists design rules for beams and explains the procedure for designing a singly reinforced beam using the working stress method.

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Design of singly reinforced.
DESIGN OFDESIGN OF SINGLY REINFORCEDSINGLY REINFORCED BEAMBEAM Er. RANDEEP SINGHEr. RANDEEP SINGH (B-Tech. CIVIL)(B-Tech. CIVIL) GNDEC,LUDHIANA.GNDEC,LUDHIANA.
BEAMBEAM:-:- A Beam is any structural member which resistsA Beam is any structural member which resists load mainly by bending. Therefore it is alsoload mainly by bending. Therefore it is also called flexural member. Beam may be singlycalled flexural member. Beam may be singly reinforced or doubly reinforced. When steel isreinforced or doubly reinforced. When steel is provided only in tensile zone (i.e. below neutralprovided only in tensile zone (i.e. below neutral axis) is calledaxis) is called singly reinforced beam,singly reinforced beam, but whenbut when steel is provided in tension zone as well assteel is provided in tension zone as well as compression zone is called doubly reinforcedcompression zone is called doubly reinforced beam.beam.
The aim of design is:The aim of design is: To decide the size (dimensions) of the memberTo 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 willTo check whether the adopted section will perform safely and satisfactorily during the lifeperform 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 EDGETHE NORMAL DISTANCE FROM THE TOP EDGE OF THE BEAM TO THE BOTTOM EDGE OF THEOF THE BEAM TO THE BOTTOM EDGE OF THE BEAM IS CALLED OVER ALL DEPTH. IT ISBEAM IS CALLED OVER ALL DEPTH. IT IS DENOTED BYDENOTED BY ‘D’.‘D’. EFFECTIVE DEPTHEFFECTIVE DEPTH:-:- THE NORMAL DISTANCE FROM THE TOP EDGETHE NORMAL DISTANCE FROM THE TOP EDGE OF BEAM TO THE CENTRE OF TENSILEOF BEAM TO THE CENTRE OF TENSILE REINFORCEMENT IS CALLED EFFECTIVEREINFORCEMENT IS CALLED EFFECTIVE DEPTH. IT IS DENOTED BYDEPTH. IT IS DENOTED BY ‘d’.‘d’.
CLEAR COVERCLEAR COVER:-:- THE DISTANCE BETWEEN THE BOTTOM OFTHE DISTANCE BETWEEN THE BOTTOM OF THE BARS AND BOTTOM MOST THE EDGE OFTHE 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 TENSILETHE DISTANCE BETWEEN CENTRE OF TENSILE REINFORCEMENT AND THE BOTTOM EDGE OFREINFORCEMENT AND THE BOTTOM EDGE OF THE BEAM IS CALLED EFFECTIVE COVER.THE BEAM IS CALLED EFFECTIVE COVER. EFFECTIVE COVER = CLEAR COVER + ½ DIAEFFECTIVE COVER = CLEAR COVER + ½ DIA OF BAR.OF BAR.
END COVEREND COVER:-:- END COVER = 2XDIA OF BAR OR 25mm (WHICHEND 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 TWOIT DIVIDES THE BEAM SECTION INTO TWO ZONES, COMPRESION ZONE ABOVE THEZONES, COMPRESION ZONE ABOVE THE NETURAL AXIS & TENSION ZONE BELOW THENETURAL 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 THEDISTANCE BETWEEN THE TOP EDGE OF THE BEAM & NEUTRAL AXIS IS CALLED DEPTH OFBEAM & NEUTRAL AXIS IS CALLED DEPTH OF NETURAL AXIS. IT IS DENOTED BYNETURAL AXIS. IT IS DENOTED BY ‘n’‘n’.. LEVER ARMLEVER ARM:- THE DISTANCE BETWEEN THE:- THE DISTANCE BETWEEN THE RESULTANT COMPRESSIVE FORCE (C) ANDRESULTANT COMPRESSIVE FORCE (C) AND TENSILE FORCE (T) IS KNOWN AS LEVER ARM. ITTENSILE FORCE (T) IS KNOWN AS LEVER ARM. IT IS DENOTED BYIS DENOTED BY ‘z’.‘z’. THE TOTAL COMPRESSIVETHE TOTAL COMPRESSIVE FORCE (C) IN CONCRETE ACT AT THE C.G. OFFORCE (C) IN CONCRETE ACT AT THE C.G. OF COMPRESSIVE STRESS DIAGRAM i.e. n/3 FROMCOMPRESSIVE STRESS DIAGRAM i.e. n/3 FROM THE COMPRESSION EDGE. THE TOTAL TENSILETHE COMPRESSION EDGE. THE TOTAL TENSILE FORCE (T) ACTS AT C.G. OF THEFORCE (T) ACTS AT C.G. OF THE REINFORCEMENT.REINFORCEMENT. LEVER ARM = d-n/3LEVER ARM = d-n/3
TENSILE REINFORCEMENTTENSILE REINFORCEMENT:-:- THE REINFORCEMENT PROVIDED TENSILETHE REINFORCEMENT PROVIDED TENSILE ZONE IS CALLED TENSILE REINFORCEMENT.ZONE IS CALLED TENSILE REINFORCEMENT. IT IS DENOTED BYIT IS DENOTED BY AAstst.. COMPRESSION REINFORCEMENTCOMPRESSION REINFORCEMENT :-:- THE REINFORCEMENT PROVIDEDTHE REINFORCEMENT PROVIDED COMPRESSION ZONEIS CALLEDCOMPRESSION ZONEIS CALLED COMPRESSION REINFORCEMENT. IT ISCOMPRESSION REINFORCEMENT. IT IS DENOTED BYDENOTED 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 WHICHKNOWN AS BALANCED SECTION IN WHICH THE COMPRESSIVE STREE IN CONCRETE (INTHE COMPRESSIVE STREE IN CONCRETE (IN COMPRESSIVE ZONES) AND TENSILE STRESS INCOMPRESSIVE ZONES) AND TENSILE STRESS IN STEEL WILL BOTH REACH THE MAXIMUMSTEEL WILL BOTH REACH THE MAXIMUM PERMISSIBLE VALUES SIMULTANEOUSLY.PERMISSIBLE VALUES SIMULTANEOUSLY.
THE NEUTRAL AXIS OF BALANCED (ORTHE NEUTRAL AXIS OF BALANCED (OR CRITICAL) SECTION IS KNOWN AS CRITICALCRITICAL) SECTION IS KNOWN AS CRITICAL NEUTRAL AXISNEUTRAL 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 AREREINFORCED 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 ISWHICH THE QUANTITY OF STEEL PROVIDED IS DIFFERENT FROM WHAT IS REQUIRED FOR THEDIFFERENT FROM WHAT IS REQUIRED FOR THE BALANCED SECTION.BALANCED SECTION. UNBALANCED SECTIONS MAY BE OF THEUNBALANCED 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 AREAIF THE AREA OF STEEL PROVIDED IS LESS THAN THAT REQUIREDOF 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 LESSREINFORCED SECTION. DUE TO LESS REINFORCEMENT THE POSITION OF ACTUALREINFORCEMENT THE POSITION OF ACTUAL NEUTRAL AXISNEUTRAL AXIS (n)(n) WILL SHIFT ABOVE THE CRITICALWILL SHIFT ABOVE THE CRITICAL NEUTRAL AXISNEUTRAL AXIS (n(ncc))i.e.i.e. n< nn< ncc. IN UNDER-REINFORCED. IN UNDER-REINFORCED SECTION STEEL IS FULLY STRESSED AND CONCRETESECTION STEEL IS FULLY STRESSED AND CONCRETE IS UNDER STRESSED (i.e. SOME CONCRETE REMAINSIS UNDER STRESSED (i.e. SOME CONCRETE REMAINS UN-UTILISED). STEEL BEING DUCTILE, TAKES SOMEUN-UTILISED). STEEL BEING DUCTILE, TAKES SOME TIME TO BREAK. THIS GIVES SUFFICIENT WARNINGTIME 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 OFFOR THIS REASON AND FROM ECONOMY POINT OF VIEW THE UNDER-REINFORCED SECTIONS AREVIEW THE UNDER-REINFORCED SECTIONS ARE DESIGNED.DESIGNED.
(b)(b) OVER-REINFORCED SECTION:-OVER-REINFORCED SECTION:- IF THE AREAIF THE AREA OF STEEL PROVIDED IS MORE THAN THATOF STEEL PROVIDED IS MORE THAN THAT REQUIRED FOR A BALANCED SECTION, IT ISREQUIRED FOR A BALANCED SECTION, IT IS KNOWN AS OVER-REINFORCED SECTION. AS THEKNOWN AS OVER-REINFORCED SECTION. AS THE AREA OF STEEL PROVIDED IS MORE, THEAREA OF STEEL PROVIDED IS MORE, THE POSITION OF N.A. WILL SHIFT TOWARDS STEEL,POSITION OF N.A. WILL SHIFT TOWARDS STEEL, THEREFORE ACTUAL AXISTHEREFORE ACTUAL AXIS (n)(n) IS BELOW THEIS BELOW THE CRITICAL NEUTRAL AXISCRITICAL NEUTRAL AXIS (n(ncc))i.e.i.e. n > nn > ncc. IN THIS. IN THIS SECTION CONCRETE IS FULLY STRESSED ANDSECTION CONCRETE IS FULLY STRESSED AND STEEL IS UNDER STRESSED. UNDER SUCHSTEEL IS UNDER STRESSED. UNDER SUCH CONDITIONS, THE BEAM WILL FAIL INITIALLY DUECONDITIONS, THE BEAM WILL FAIL INITIALLY DUE TO OVER STRESS IN THE CONCRETE. CONCRETETO OVER STRESS IN THE CONCRETE. CONCRETE BEING BRITTLE, THIS HAPPENS SUDDENLY ANDBEING 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 ofeff. 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 tensiletop edge of beam to the centre of tensile reinforcement is called effective depth. It is denotedreinforcement is called effective depth. It is denoted byby ‘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 mayBearings 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 limitsThe vertical deflection limits assumed to be satisfied ifassumed 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) shouldFor span above 10m, the value in (a) should be multiplied by 10/span (m), except forbe multiplied by 10/span (m), except for cantilever for which the deflection calculationscantilever for which the deflection calculations should be made.should be made. (c)(c) Depending upon the area and type of steel theDepending upon the area and type of steel the value of (a&b) modified as per modificationvalue of (a&b) modified as per modification factor.factor. 5. Reinforcement5. Reinforcement :-:- (a)(a) Minimum reinforcement:- The minimum areaMinimum reinforcement:- The minimum area of tensile reinforcement shall not be less than thatof 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 ofMaximum reinforcement:- The maximum area of tensile reinforcement shall not be more thantensile 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 barsThe 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 coarse5mm more than the nominal maximum size of coarse aggregate.aggregate.
ii.ii. When the bars are in vertical lines and the minimumWhen the bars are in vertical lines and the minimum vertical distance between the bars shall be greater of thevertical 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 NominalThe 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 theTo 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 coverAs 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 Mild Moderate Severe Very severe Extreme 20 30 45 50 75
Procedure for Design of Singly ReinforcedProcedure 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 materialsCalculate design constants for the given materials (k, j and R)(k, j and R) k = mk = 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= 1/2R= 1/2 σσcbccbc kjkj 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 bendingCalculate 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 = wl22 / 8 at the centre/ 8 at the centre of beam for simply supported beam.of beam for simply supported beam. M = wlM = wl22 / 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 isIf it is less than the assumed d, then assumption is correct.correct. (ii)(ii) IfIf ddreqd.reqd. is more than assumed d, then revise theis 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 jdjd Selecting the suitable diameter of bar calculate theSelecting 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 areaCalculate 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 thanprovided 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.
Design of singly reinforced.

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Design of singly reinforced.

  • 2. DESIGN OFDESIGN OF SINGLY REINFORCEDSINGLY REINFORCED BEAMBEAM Er. RANDEEP SINGHEr. RANDEEP SINGH (B-Tech. CIVIL)(B-Tech. CIVIL) GNDEC,LUDHIANA.GNDEC,LUDHIANA.
  • 3. BEAMBEAM:-:- A Beam is any structural member which resistsA Beam is any structural member which resists load mainly by bending. Therefore it is alsoload mainly by bending. Therefore it is also called flexural member. Beam may be singlycalled flexural member. Beam may be singly reinforced or doubly reinforced. When steel isreinforced or doubly reinforced. When steel is provided only in tensile zone (i.e. below neutralprovided only in tensile zone (i.e. below neutral axis) is calledaxis) is called singly reinforced beam,singly reinforced beam, but whenbut when steel is provided in tension zone as well assteel is provided in tension zone as well as compression zone is called doubly reinforcedcompression zone is called doubly reinforced beam.beam.
  • 4. The aim of design is:The aim of design is: To decide the size (dimensions) of the memberTo 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 willTo check whether the adopted section will perform safely and satisfactorily during the lifeperform safely and satisfactorily during the life time of the structure.time of the structure.
  • 6. OVER ALL DEPTHOVER ALL DEPTH :-:- THE NORMAL DISTANCE FROM THE TOP EDGETHE NORMAL DISTANCE FROM THE TOP EDGE OF THE BEAM TO THE BOTTOM EDGE OF THEOF THE BEAM TO THE BOTTOM EDGE OF THE BEAM IS CALLED OVER ALL DEPTH. IT ISBEAM IS CALLED OVER ALL DEPTH. IT IS DENOTED BYDENOTED BY ‘D’.‘D’. EFFECTIVE DEPTHEFFECTIVE DEPTH:-:- THE NORMAL DISTANCE FROM THE TOP EDGETHE NORMAL DISTANCE FROM THE TOP EDGE OF BEAM TO THE CENTRE OF TENSILEOF BEAM TO THE CENTRE OF TENSILE REINFORCEMENT IS CALLED EFFECTIVEREINFORCEMENT IS CALLED EFFECTIVE DEPTH. IT IS DENOTED BYDEPTH. IT IS DENOTED BY ‘d’.‘d’.
  • 7. CLEAR COVERCLEAR COVER:-:- THE DISTANCE BETWEEN THE BOTTOM OFTHE DISTANCE BETWEEN THE BOTTOM OF THE BARS AND BOTTOM MOST THE EDGE OFTHE 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 TENSILETHE DISTANCE BETWEEN CENTRE OF TENSILE REINFORCEMENT AND THE BOTTOM EDGE OFREINFORCEMENT AND THE BOTTOM EDGE OF THE BEAM IS CALLED EFFECTIVE COVER.THE BEAM IS CALLED EFFECTIVE COVER. EFFECTIVE COVER = CLEAR COVER + ½ DIAEFFECTIVE COVER = CLEAR COVER + ½ DIA OF BAR.OF BAR.
  • 8. END COVEREND COVER:-:- END COVER = 2XDIA OF BAR OR 25mm (WHICHEND 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 TWOIT DIVIDES THE BEAM SECTION INTO TWO ZONES, COMPRESION ZONE ABOVE THEZONES, COMPRESION ZONE ABOVE THE NETURAL AXIS & TENSION ZONE BELOW THENETURAL AXIS & TENSION ZONE BELOW THE NEUTRAL AXIS.NEUTRAL AXIS.
  • 9. DEPTH OF NETURAL AXISDEPTH OF NETURAL AXIS:- THE NORMAL:- THE NORMAL DISTANCE BETWEEN THE TOP EDGE OF THEDISTANCE BETWEEN THE TOP EDGE OF THE BEAM & NEUTRAL AXIS IS CALLED DEPTH OFBEAM & NEUTRAL AXIS IS CALLED DEPTH OF NETURAL AXIS. IT IS DENOTED BYNETURAL AXIS. IT IS DENOTED BY ‘n’‘n’.. LEVER ARMLEVER ARM:- THE DISTANCE BETWEEN THE:- THE DISTANCE BETWEEN THE RESULTANT COMPRESSIVE FORCE (C) ANDRESULTANT COMPRESSIVE FORCE (C) AND TENSILE FORCE (T) IS KNOWN AS LEVER ARM. ITTENSILE FORCE (T) IS KNOWN AS LEVER ARM. IT IS DENOTED BYIS DENOTED BY ‘z’.‘z’. THE TOTAL COMPRESSIVETHE TOTAL COMPRESSIVE FORCE (C) IN CONCRETE ACT AT THE C.G. OFFORCE (C) IN CONCRETE ACT AT THE C.G. OF COMPRESSIVE STRESS DIAGRAM i.e. n/3 FROMCOMPRESSIVE STRESS DIAGRAM i.e. n/3 FROM THE COMPRESSION EDGE. THE TOTAL TENSILETHE COMPRESSION EDGE. THE TOTAL TENSILE FORCE (T) ACTS AT C.G. OF THEFORCE (T) ACTS AT C.G. OF THE REINFORCEMENT.REINFORCEMENT. LEVER ARM = d-n/3LEVER ARM = d-n/3
  • 10. TENSILE REINFORCEMENTTENSILE REINFORCEMENT:-:- THE REINFORCEMENT PROVIDED TENSILETHE REINFORCEMENT PROVIDED TENSILE ZONE IS CALLED TENSILE REINFORCEMENT.ZONE IS CALLED TENSILE REINFORCEMENT. IT IS DENOTED BYIT IS DENOTED BY AAstst.. COMPRESSION REINFORCEMENTCOMPRESSION REINFORCEMENT :-:- THE REINFORCEMENT PROVIDEDTHE REINFORCEMENT PROVIDED COMPRESSION ZONEIS CALLEDCOMPRESSION ZONEIS CALLED COMPRESSION REINFORCEMENT. IT ISCOMPRESSION REINFORCEMENT. IT IS DENOTED BYDENOTED BY AAscsc
  • 11. 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 WHICHKNOWN AS BALANCED SECTION IN WHICH THE COMPRESSIVE STREE IN CONCRETE (INTHE COMPRESSIVE STREE IN CONCRETE (IN COMPRESSIVE ZONES) AND TENSILE STRESS INCOMPRESSIVE ZONES) AND TENSILE STRESS IN STEEL WILL BOTH REACH THE MAXIMUMSTEEL WILL BOTH REACH THE MAXIMUM PERMISSIBLE VALUES SIMULTANEOUSLY.PERMISSIBLE VALUES SIMULTANEOUSLY.
  • 12. THE NEUTRAL AXIS OF BALANCED (ORTHE NEUTRAL AXIS OF BALANCED (OR CRITICAL) SECTION IS KNOWN AS CRITICALCRITICAL) SECTION IS KNOWN AS CRITICAL NEUTRAL AXISNEUTRAL 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 AREREINFORCED 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 ISWHICH THE QUANTITY OF STEEL PROVIDED IS DIFFERENT FROM WHAT IS REQUIRED FOR THEDIFFERENT FROM WHAT IS REQUIRED FOR THE BALANCED SECTION.BALANCED SECTION. UNBALANCED SECTIONS MAY BE OF THEUNBALANCED 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
  • 13. (a)(a)UNDER-REINFORCED SECTION:-UNDER-REINFORCED SECTION:- IF THE AREAIF THE AREA OF STEEL PROVIDED IS LESS THAN THAT REQUIREDOF 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 LESSREINFORCED SECTION. DUE TO LESS REINFORCEMENT THE POSITION OF ACTUALREINFORCEMENT THE POSITION OF ACTUAL NEUTRAL AXISNEUTRAL AXIS (n)(n) WILL SHIFT ABOVE THE CRITICALWILL SHIFT ABOVE THE CRITICAL NEUTRAL AXISNEUTRAL AXIS (n(ncc))i.e.i.e. n< nn< ncc. IN UNDER-REINFORCED. IN UNDER-REINFORCED SECTION STEEL IS FULLY STRESSED AND CONCRETESECTION STEEL IS FULLY STRESSED AND CONCRETE IS UNDER STRESSED (i.e. SOME CONCRETE REMAINSIS UNDER STRESSED (i.e. SOME CONCRETE REMAINS UN-UTILISED). STEEL BEING DUCTILE, TAKES SOMEUN-UTILISED). STEEL BEING DUCTILE, TAKES SOME TIME TO BREAK. THIS GIVES SUFFICIENT WARNINGTIME 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 OFFOR THIS REASON AND FROM ECONOMY POINT OF VIEW THE UNDER-REINFORCED SECTIONS AREVIEW THE UNDER-REINFORCED SECTIONS ARE DESIGNED.DESIGNED.
  • 14. (b)(b) OVER-REINFORCED SECTION:-OVER-REINFORCED SECTION:- IF THE AREAIF THE AREA OF STEEL PROVIDED IS MORE THAN THATOF STEEL PROVIDED IS MORE THAN THAT REQUIRED FOR A BALANCED SECTION, IT ISREQUIRED FOR A BALANCED SECTION, IT IS KNOWN AS OVER-REINFORCED SECTION. AS THEKNOWN AS OVER-REINFORCED SECTION. AS THE AREA OF STEEL PROVIDED IS MORE, THEAREA OF STEEL PROVIDED IS MORE, THE POSITION OF N.A. WILL SHIFT TOWARDS STEEL,POSITION OF N.A. WILL SHIFT TOWARDS STEEL, THEREFORE ACTUAL AXISTHEREFORE ACTUAL AXIS (n)(n) IS BELOW THEIS BELOW THE CRITICAL NEUTRAL AXISCRITICAL NEUTRAL AXIS (n(ncc))i.e.i.e. n > nn > ncc. IN THIS. IN THIS SECTION CONCRETE IS FULLY STRESSED ANDSECTION CONCRETE IS FULLY STRESSED AND STEEL IS UNDER STRESSED. UNDER SUCHSTEEL IS UNDER STRESSED. UNDER SUCH CONDITIONS, THE BEAM WILL FAIL INITIALLY DUECONDITIONS, THE BEAM WILL FAIL INITIALLY DUE TO OVER STRESS IN THE CONCRETE. CONCRETETO OVER STRESS IN THE CONCRETE. CONCRETE BEING BRITTLE, THIS HAPPENS SUDDENLY ANDBEING BRITTLE, THIS HAPPENS SUDDENLY AND EXPLOSIVELY WITHOUT ANY WARNING.EXPLOSIVELY WITHOUT ANY WARNING.
  • 15. 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 ofeff. 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 tensiletop edge of beam to the centre of tensile reinforcement is called effective depth. It is denotedreinforcement is called effective depth. It is denoted byby ‘d’.‘d’. d= D- effect. Coverd= D- effect. Cover where D= over all depthwhere D= over all depth
  • 16. 3. Bearing :-3. Bearing :- Bearings of beams on brick walls mayBearings 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 limitsThe vertical deflection limits assumed to be satisfied ifassumed 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)
  • 17. (b)(b) For span above 10m, the value in (a) shouldFor span above 10m, the value in (a) should be multiplied by 10/span (m), except forbe multiplied by 10/span (m), except for cantilever for which the deflection calculationscantilever for which the deflection calculations should be made.should be made. (c)(c) Depending upon the area and type of steel theDepending upon the area and type of steel the value of (a&b) modified as per modificationvalue of (a&b) modified as per modification factor.factor. 5. Reinforcement5. Reinforcement :-:- (a)(a) Minimum reinforcement:- The minimum areaMinimum reinforcement:- The minimum area of tensile reinforcement shall not be less than thatof 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
  • 18. (b)(b)Maximum reinforcement:- The maximum area ofMaximum reinforcement:- The maximum area of tensile reinforcement shall not be more thantensile 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 barsThe 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 coarse5mm more than the nominal maximum size of coarse aggregate.aggregate.
  • 19. ii.ii. When the bars are in vertical lines and the minimumWhen the bars are in vertical lines and the minimum vertical distance between the bars shall be greater of thevertical 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 NominalThe 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 theTo develop the sufficient bond strength along the surface area of the steel bar.surface area of the steel bar.
  • 20. As per IS 456-2000, the value of nominal coverAs 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 Mild Moderate Severe Very severe Extreme 20 30 45 50 75
  • 21. Procedure for Design of Singly ReinforcedProcedure 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 materialsCalculate design constants for the given materials (k, j and R)(k, j and R) k = mk = m σσcbccbc / m/ m σσcbccbc ++ σσstst where k is coefficient of depth of Neutral Axiswhere k is coefficient of depth of Neutral Axis
  • 22. j = 1- k/3j = 1- k/3 where j is coefficient of lever arm.where j is coefficient of lever arm. R= 1/2R= 1/2 σσcbccbc kjkj 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
  • 23. 5.5. Calculate the total Load & maximum bendingCalculate 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 = wl22 / 8 at the centre/ 8 at the centre of beam for simply supported beam.of beam for simply supported beam. M = wlM = wl22 / 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
  • 24. 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 isIf it is less than the assumed d, then assumption is correct.correct. (ii)(ii) IfIf ddreqd.reqd. is more than assumed d, then revise theis 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 jdjd Selecting the suitable diameter of bar calculate theSelecting 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
  • 25. 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 areaCalculate 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 thanprovided is more than minimum and less than maximum requirements.minimum and less than maximum requirements.
  • 26. 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.