Elementary Structural Design in Concrete to CP aao

l RI llli B l1 Ill Ill sII A. W. Astill and L. H. Martin Un~versltv ot Aston 117 Bqrrnlngham

F; dn~ard Arnol d i l di~i;isinn of I-Tor-lrlrr k: Stol~gl~tnn TAOYDOS MELHOLMNE dLI(;KL,tl'D

r Contents

MATERIALS & LOADS The Object of S t r u c t u r a l D e s i ~ ( c l . 2 . 1 (CP110)) The Object o f L i m i t S t a t e Design (c1.2.1(CP110)) Variation of Mater ia l Proper t ies (c1.2.3.2(CP110)) charac te r i s t i c Strength (cl. 2 . 3 . 2 (CPllO)) Design Strength - P a r t i a l Safety Factor f o r S t r e n g t h

( c l s . 2 . 3 . 2 , 2 . 3 . 3 . 2 (CP110) 1 Stress-Strain r e l a t ionsh ip f o r concrete I d e a l i s e d S t ress-St ra in r e l a t i o n s h i p f o r concrete

(Fig.1 (CP110)) H S t r e s s -S t ra in r e l a t i o n s h i p f o r steel (Fig. 2 (CP110) ) I Characteristic Loads ( c l . 2 .3 .1 (CP110)) J Design Load (c1.2.3.3.1(CP110)) K S t ruc tu ra l Safety

FRAME ANALYSIS FOR VERTICAL LOADS Method of Analysis S t i f f n e s s o f a member (c1.3.2.1(CP11C)) Sub Framing (c1.3.2.2.1(CP110)) Continuous Beam (Beam 6 CO lurnn S t ~ u c t u r e )

Accurate Method ( c l . 5.3.3 (CP110) 1 Approximate Method (c1.3.3.4(CP110))

h e Free Joint Subframe (Beam 6 Colurn S t ruc tu re ) (c1.3.5.2(CPl10))

Two Free Joint Subframe ( c l . 3.2.2.1 (CP110)) One Floor Level Subframe (c1.3.2.2.1[~~110])

3 FRAME ANALYSIS FOR HORIZONTAL AND VERTICAL LOADS A In t roduct ion B Lateral S t a b i l i t y

Frame Shape and Overall S t a b i l i t y Braced and Unbraced Frames

C Overturning (c1,2.3.J.I(CP110)) D Unbraced Frames (cl . 5 . 2 . 2 (CP110) ) E Tying Forces (c1.3.1.2.2 (CPIIO))

4 REDISTRIBUTION OF MOMENTS A Theory of Collapse of Beams B Redis t r ibu t ion C Points of Contraflexure [c1.3.2.2.3[CP110)) D Redis t r ibu t ion f o r Multi-Span Beams E R Quicker Method o f R e d i s t r i b u t i o n F The Design of Sec t i ons af ter Redistribution

5 S E R V I C E A B I L I T Y L I M I T STATES & REINFORCEMENT DETAILS A Serv iceab i l i t y L i m i t States

(a) I n t r o d u c t i o n (b) Deflection (c) Cracking ( d ] Durability (e) Fire Resistance

B Section Dimension (a) Overall Dimensions (h] Reinforcement (c) Fi re Resistance

C Arrangement of Reinfoxcement (a) Minimum d i s t ance between ba r s (b) Concrete cover t o t h e r eh fo r semen t (c l . 3.11.2 (CP110) ) (c) Maximum cover and maximum distance between bars

(c1.3.11.8.2(CP110)) (d) Effective depth 66 {e] Use of Bar Area Tables ' 67 ( f ) Minimum Area of Main Tensile Reinforcement 69

(c1.3.11.4.1(CPllO)) (g) Minimum Area of Secondary Reinforcement 70

(c1.3.11.4.2(CPllO]) (h) Minimum Area of Links (c1.3.11.4.3(CP110)) 71 (i) Maximum Area of Reinforcement (cl.J.11.5(CPL10)) 72

D Deflection [cl.J.3.8(CP110)] 72 F S lender B e a m s (C1.3.3.1.3(CP110)) 76

S I N G L Y R E I N F O R C E D CONCRETE BEAMS Concrete Beams Reinforced Concrete Beams (c1.3.3.5.l(CPllQ)) Depth of Compression Zone Lever Arm (c1.3.3.5.3(CPl10]) The Moment of R e s i s t a n c e at t h e Ultimate Limit State Maximum Depth of the Compression Zone (cl.3.3.5.I(CP110)) Maximm Moment of Resistance (c1.3.5.5.3(CP110)) Design Graphs (c1.3.3.5.2(CP110))

FLANGED BEAMS I n t r o d u c t i o n Effective Width of Flange (c l . 3.5.1.2(CP110)) Moment of Resistance a t t h e Ultimate Limit S t a t e Depth o f t h e compression zone Maximmn Moment of Res is t ance Al terna t ive Simple Method o f Design of Flanged Beams Transverse Reinforcement i n Flanges {cl. 3 . 1 1 . 4 . 2 (CP110)) Deflection o f Flanged Beams (cl. 3.3.8. ~(CPILQ])

8 DOUBLY R E I N F O R C E D BEAMS 94 A Introduction 94 B Maximum Moment of Resistance of a Singly Reinforced Sect ion 94 C Maximum Area o f S tee l for a Singly Reinforced Section 9 S

D Area of Compression Steel (cl.3.3.5.8(CPllO)) E Addit ional Area of Tens i le Steel F Moment of Resistance of Doubly Reinforced Beams

~c1.3.3.5.5(CP110)) G Design Graphs H Depth of t h e Compression Zone

CURTAILMENT OF REINFORCEMENT introduction Anchorage of a straight bar (c1.3.11.6.2(CP110)) Bundled Bars (c1 .3.11.6.3 (CP110) 1 Joints in Bars (c1.3.11.6.5 and c1.3.11.6.6(CP110)) Anchorage by Hooks and Bends (c 1.3.11.6.7 (CP110) ) Bearing Stresses Inside Bends ( c l . 3.11.6.8 (CPll0)) Anchorage a t Ends of Members (c1.3.11.7.1(CP110)) Theoretical Cut off i n Bending (cl.3.11.J(CP110]) Extension Beyond Theoretical Cut Off (cl.3.11.7.1(CP110)) Extension i n t h e Tension Zone Ic1.3.11.7.1(CPllO)) Simplified Rules for Curtailment (c l . 3.11 .?. 2 (CP110))

SHEAR IN REINFORCED CONCRETE 11 9 Shear Fa i lu re 119 Shear Resistance o f a Member with Longitudinal Steel ORly 120

( c l . 3.3.6.1 (CP110)) Shear Stress (c1.3.3.6.1(CP110)) 12 1 Shear Reinforcement ( c l . 3.3.6.1 (CP110)) 1 2 2

[a] General 12 2 (b) Vert ical Links 12 3 (c) Bens Up (Inclined) Bars 126

Minimum Shear Reinforcement (c1.3.11.4.3(CP110)) 150 Shear Resis tance of Flanged Beams and Doubly Reinforced Beams 131 Shear Resistance f o r Concentrated Loads Near Supports 132 Local Bond Stresses Produced by Shear Forces (cl. 3.11.6.1 (CP110)) 133

2 1 TORS ION I N RE INFORCED CONCRETE 135 A Introduction 135 B S t i f f n e s s o f a Member i n Torsion (cl . 3.3.7 (CP110) 3 135 C Torsional Shear Stress (c1.3.3.7(CIJ110)) 136 D Torsional Resistance (cl. 3.3.7(CP110)) 137 E Tors ion Reinforcement (c 1 . 3 . 3 . 7 (CP 110) 1 138 F Extra Longitudinal Steel (c1.3.3.7(CP110)) l39

REINFORCED CONCRETE COLUMNS 141 Strength of Colurns 141 Slenderness Ratio 141 Effective Height (c1.3.S.1.4(CP110)) 142 Size of Column 4 Reinforcement ( c l . 3.5.3(CP110)) 145

(a) Method of Design 145 (b) Axially loaded columns 145 (c) Eccentrically Loaded Columns 146

Biaxial Bending ( c l . 3.5.6(CP110)) 148 Forces i n Slender Columns (c1.3.5.7(CP110)) 150 Limi t a t i onsonRe in fo rcemen t (c1.3.11.5and3.11.4.3(CP110)) 152

SLABS AND STAIRS 154 Def in i t ion 154 Slabs spanning i n one d i r e c t i o n 154 Cons t ruc t ion of Slabs 154 Def lec t ion and Effective Depth (cl. 3.4.6 (CP110)) 156 Moment of r e s i s t a n c e of s labs (c1.3.4.4, c1.3.11.8.2, 15 7

c1.3.11.8.1(CF110)) Sheas Resis tance of Slabs 157 Minimum Area o f Secondary Reinforcement (c l . 3.11.4.2 (CP110)) 158 Example o f Design of Hollow Block Slab 158 Concentrated Loads 161 Sta i rcases 162

SLABS & FLAT SLABS Two Way Spanning Slabs ( c l . 3.4 (CP110)) Simply Supported Slabs (c1.3.4.3.l(CP110)) Restrained Slabs ( c l . 3.4.3.2(CP110)) F l a t S l a b s (c1.3.6(CP110)) Forces and Moments i n F l a t Slabs (c1.3.6.5.l(CPLlO)) Design o f Slabs f o r Bending (c1.3.6.5.2 (CP110)) Design o f Slabs f o r Shear (c1.3.6.2(CPlIO)) F0 l u m s

15 FOUNDAT IONS 182 A In t roduc t ion 182

I Independent Foundations 182 2 Combined Foundations 184

B S t r e s s on S o i l Beneath Independent Bases (cl. 3.10.3 (CP110) 3 185 C S t r e s s on t h e S o i l Beneath Combined Foundations 190 D Design o f Independent Colurrm Bases 190 E Design of Combined Foundat ions 198 F P i l e Caps 199

1 6 E L A S T I C ANALYSIS OF PRESTRESSED CONCRETE A Prestressed Concrete B Bending Moment Due t o Prestress C S t r e s s due t o t h e p r e s t r e s s i n g force D S t r e s s e s i n Non-rectangular Sect ion E Loss o f p r e s t r e s s i n g force F Bending S t r e s s e s due t o loads

DESIGN OF PRESTRESSED CONCRETE FOR B E N D I N G Introduct ion S t r e s s Limitat ions Under Service Conditions U l t i m a t e s t r e n g t h of p re s t r e s sed concrete beams

(a) Bonded Tendons (b] Unbonded Tendons

Minimum P rac t i ca l Cross Section E l a s t i c Analysis f o r Se rv iceab i l i t y Stresses Cable Shape Check f o r S t r e s s e s a t Other Conditions Adjustments t o Sec t ion and Cable Position Serviceability Limit State a 5 Deflect ion (c1.4.3.7(CP110))

(a) Deflection Limits (b) E l a s t i c Deflection (c) Long Term Deflection

J E l a s t i c Analysis f o r Beams with Straight Cables

LOSS OF PRESTRESS ~ntroductian ~elaxation of the S t e e l (cl. 4 . 8 . 2 . 2 (CPZ10) 1 ~ L a s t i c Deformation (c1.4.8.2.3 (CP110)] Shrinkage of the Concrete (cl. 4 . 8 . 2 . 4 (CP110)) Creep of Concrete (c l . 4 . 8 . 2 . 5 (CP110) ) S l i p a t Anchorage tc1.4.8.2.6 (CP110)) Fr ic t ion in the Duct

(a) Due t o Unintentional Error i n t h e Profile (c1.4.8.3.3(CPllO)]

(b) Due to Curvature of t h e Tendon [cl - 4 . 8 . 3 . 4 (CP110) )

19 SHEAR I N PRESTRESSED CONCRETE A Introduction B Web Shear Cracks a t the U l t i m a t e Limit S t a t e

( c 1 . 4 . 3 . 5 . 1 ( C P l l O ) ) C Flexural Shear Cracks (cl. 4.3. S . Z(CP110)) D Minimum Shear Reinforcement lc1.4.3.5.2 (CPI10)) E Shear Reinforcement (c1.4.3.5,3(CP110)) F Maximum Shear Farce [ c 1 . 4 . 3 . 5 . 4 ( C P 1 1 0 ) )

20 E N D BLOCKS 249 A Anchorage Zones f o r Post-tensioned C a b l e s 249 B Burs t ing Tensile Forces f o r Post-tensioned Members

(cl.l.4.8.5, l{CPllO)) 249

C Transmission Length f o r Pre-tensioned Beams ( c l . 4 . 8 . 4 (CP110) ) 251 D Anchorage Zone Stresses f o r Pre-tensioned Members 251

APPEND I CE S

ANALYSIS OF C0LU.W SECTIONS Introduction Derivat ion of t h e forumulae for the column design graphs Determination of Nbal

ANALYSIS OF REINFORCED CONCRETE BEAMS Introduction Derivation of formulae

ANALYSIS OF PRESTRESSED CONCRETE BEAMS Introduction Derivation of formulae

I N D E X

Index

Aggregate i n t e r lock Analysis - continuous beam

frame o f s t r u c t u r e

Anchorage at ends of members bear ing stress by hooks and bends i n groups in p re tens ioned members o f bars o f l i n k s

Bar a r e a tables Beam - ana lys i s o f re inforced

- formulae for r e i n f o r c e d - analysis o f prestressed - formulae for pres t ressed

Beam and column structures cont inuous - accurate method

approximate method Bearing stress in bends Bending in base s labs

moment enve l ap e moment r e d i s t r i b u t i o n s t r e s s in p r e s t r e s s e d concre te t ransverse

Bends Bent up bars Bond

anchorage local

Bonded tendons Bracing Brick i n f i l l i n g Buckling o f bars Bundled bars Burs t ing f o r c e s

Cable Cable band C h a r a c t e r i s t i c load C h a r a c t e r i s t i c s t r eng th

s teel f o r prestressing concre te f o r prestressed concrete

Col lapse Column - analysis

- a x i a l l y loaded - bending moment - b i a x i a l bending

268 Index

Column - e c c e n t r i c a l l y loaded - effective height - formulae - graphs - method of design - m i n i m u m bending moment - s i z e - slender - strength - s t r i p - supporting f l a t slabs - reinforcement

Column bases - combined - independent

Compression zone depth maximum depth

Concentrated load Concrete beams

reinforced Concrete s t r eng th Contraflexure - points of Cover Cracks Creep o f concrete Curt ailment C u t - o f f - tension zone

practical t heo re t i ca l

Deflect ion of prestressed beams of slabs

Density o f concre te Design graph - singly r e i n f o r c e d beams

columns doubly re inforced beams p re s t r e s sed beams

Distribution reinforcement Doubly reinforced beams Dowel force Ducts Durab i l i t y

Eccen t r i c i t y - minimum in columns - o f cable

Effective dep th depth of slabs h e i g h t width o f f l a n g e

Elastic analys is of prestressed sections for beams w i t h s t r a i g h t cables

deformation (shortening)

I46 142 254 254 145 146 145 150 14 1 174 181 145

190,198 185,190

78,90,102 8 1 L62

77 77

78,212 48

61,64 2,56,64,214

4,240 see Cut off

115 115 11 2

Index 269

End b locks p l a t e

Envelope - bending moment - shear force

Fire resistance Flange - e f f e c t i v e width o f Flanges o f prestressed beams F l a t slabs Foundat ions Frames - braced

unbraced Fr i c t i on i n duct

Graph - design

Handling stresses Hooks

Inc l ined bars I n f i l l i n g panels

Jacking force Joints in bars

L beams Lap joint Lateral buckling ef beams Lever arm

minimum value maximum value

L i m i t s t a t e s Links

- buckling o f compression bars - in ca1umns - min imum area - maximum spacing - vert ica l

Load - c h a r a c t e r i s t i c - concentrated - design

Loading arrangement Loss af prestress

Material prope r t i e s Middle strip Minimum cross-sec t ion fo r prestressed beams Modulus of elasticity o f concrete

s t e e l Moment -Curvatus e Moment o f resistance

doubly re inforced beam f langed beam maximum

57,58 88

211,218 174

see Column bases 33

33 ,35 242

see Design graph

a1

Neutral axis Normal d i s t r ibu t ion

Opt imum cross-sect ion

Pile cap foundation

Plastic analys is Post-tensionkng Pre-compression Prestress ing force Prestressed concrete

- c l a s s i f i c a t i o n Pre-tensioning Punching shear

Redis t r ibut ion Reinforcement

- addi t ional tension - arrangement - bar area t ab les - column - compression - minimum area - maximum area - secondary - strength - tension - t o r s ion

Relaxation of s t e e l Ribbed s lab - design

Safety - structural Safety f a c t o r - p a r t i a l Sect ion - concrete

dimens ions gross transformed

Self weight Serviceability - cracking

def lec t ion l i m i t state v ib ra t i on

Service stress i n prestressed concrete Shear

- bond - due t o concentrated loads - fa i lu re - force envelope - in base slabs - i n doubly reinforced beams - in flanged beams

Shear - i n f l a t slabs - i n p r e s t r e s sed beams - re i n f orc ement - reinforcement i n prestressed beams - stress - strength, maximum, of p r e s t r e s s e d beams

of cracked sections of vncracked sections

- t o r s iona l Shrinkage of concre te Slabs

concentrated loads on de f l ec t i on flat moment of r e s i s t ance r e s t r a i n e d r i b spacing secondary reinforcement shear resistance simply supported, two way two way spanning types

S l i p at anchorage S l ender bearns

columns Slenderness ratio Spacing of ba r s Spacing of cables o r ba r s Span Jdepth r a t i o S t a b i l i t y S t a i r s Standard devia t ion Steel S t i f f n e s s - bending

flexural torsional

Stirrups Strain - compatibi l i ty

- d i s t r i b u t i o n - in prestressing s t e e l - i n reinforcement

s t r e n g t h - des ign St ress - block S t r e s s - d i s t r i b u t i o n i n concrete

- in s t e e l reinforcement - in p r e s t r e s s i n g s t e e l

Stress-stmin r e l a t i onsh ip , concrete steel

Structural design, objec t Sub frame - continuous beam

- one f l o o r l eve l - one free joint - two free j o i n t

Sub framing

Index 271

137 244 122 247 1 2 1 24 8 24 6 24 5 135 239 154 261 156 174

157,159 167 156 158

157,160 L66 166 154 241

76 150 141

73 32 163

2 see Reinforcement

15 15

135 see Links

&3,254 255 265 258

4 79

255 258 2 65

4,s 6 ,8 I

18 ,23 30 24 26 16

272 Index

T beams Tendon

curved s t r a i g h t

Tors ion re in forcement

Tors iona l constant Transfer - stress a t Transmission length Tying forces and t i e s

Ultimate limit s t a t e s t r e n g t h o f prestressed beams s t r e n g t h of reinforced beams

Unbonded Tendons Untens koned steel in prestressed beams

Web of prestressed beam Weight of s t r u c t u r e

Yield lines Youngs modulus - steel

concrete