AASHTO LRFD Bridge Design With Culvert

(1)

The Use of AASHTO LRFD

Bridge Design Specifications with

Culverts

Josh Beakley Josh Beakley November, 2010 November, 2010

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2

LRFD is Required

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AASHTO

Design

Specifications

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AASHTO Standard Specifications

for Highway Bridges



 Section 3 Section 3 –– LoadsLoads 

 Section 6Section 6 –– CulvertsCulverts 

 Section 6 Section 6 CulvertsCulverts 

 Section 8 Section 8 –– Reinforced ConcreteReinforced Concrete

S ti 12

S ti 12 S ilS il CC t d M t lt d M t l



 Section 12 Section 12 –– SoilSoil--Corrugated Metal Corrugated Metal

Structure Interaction Systems Structure Interaction Systems



 Section 16 Section 16 –– SoilSoil--Reinforced Concrete Reinforced Concrete

Structure Interaction Systems Structure Interaction Systems



 Section 17 Section 17 –– SoilSoil--Thermoplastic Pipe Thermoplastic Pipe

Interaction Systems Interaction Systems

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AASHTO LRFD Bridge Design

Specifications



 Section 3 Section 3 –– Loads and Load FactorsLoads and Load Factors 

 Section 4Section 4 –– Structural Analysis andStructural Analysis and 

 Section 4 Section 4 Structural Analysis and Structural Analysis and

Evaluation Evaluation



 Section 5Section 5 Concrete StructuresConcrete Structures 

 Section 5 Section 5 –– Concrete StructuresConcrete Structures 

 Section 12 Section 12 –– Buried Structures and Tunnel Buried Structures and Tunnel

Li Li

Liners Liners

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Structures Designed Per Section 12



 Section 12.7 Section 12.7 -- Metal Pipe, Pipe Arch, and Metal Pipe, Pipe Arch, and

Arch Structures Arch Structures



 Section 12.8 Section 12.8 -- LongLong--Span Structural Plate Span Structural Plate

Structures Structures Structures Structures



 Section 12.9 Section 12.9 -- Structural Plate Box Structural Plate Box

Structures Structures Structures Structures



 Section 12.12 Section 12.12 –– Thermoplastic PipesThermoplastic Pipes 

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Concrete Structures Designed Per

Section 12



 Section 12.10 Section 12.10 –– Reinforced Concrete PipeReinforced Concrete Pipe 

 Section 12.11Section 12.11 -- Precast Box Culverts, CastPrecast Box Culverts, Cast--

 Section 12.11 Section 12.11 Precast Box Culverts, CastPrecast Box Culverts, Cast

in

in--place Box Culverts, Castplace Box Culverts, Cast--inin--place Archesplace Arches



 Section 12 14Section 12 14 Precast ThreePrecast Three SidedSided 

 Section 12.14 Section 12.14 -- Precast ThreePrecast Three--Sided Sided

Structures Structures

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What We Will Discuss



 LoadsLoads 

 Load FactorsLoad Factors 

 Load ModifiersLoad Modifiers

C it C l l ti



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Live Load

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Live Load



 3.6.1.2 Design Vehicular Live Load3.6.1.2 Design Vehicular Live Load



 3.6.1.2.1 General3.6.1.2.1 General 

 “Vehicular live loading on the roadways “Vehicular live loading on the roadways

of bridges or incidental structures of bridges or incidental structures of bridges or incidental structures, of bridges or incidental structures, designated HL

designated HL--93, shall consist of a 93, shall consist of a combination of:

combination of: combination of: combination of:



Design truck or design tandem, andDesign truck or design tandem, and 

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Live Load Spacing – HL-93

4000 lb. 14 f 6 f 12,500 lb. 12,500 lb. 14 ft. 6 ft. 12,500 lb. 12,500 lb. 16000 lb. 16000 lb. AASHTO AASHTO (12,00 lb per STD)

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Applied Live loads – No Lane

Load



 3 6 1 3 3 Design Loads for Decks Deck3 6 1 3 3 Design Loads for Decks Deck 

 3.6.1.3.3 Design Loads for Decks, Deck 3.6.1.3.3 Design Loads for Decks, Deck

Systems, and the Top Slabs of Box Culverts Systems, and the Top Slabs of Box Culverts



 Where the slab spans primarily in the Where the slab spans primarily in the

longitudinal direction: longitudinal direction: longitudinal direction: longitudinal direction:



 For top slabs of box culverts of all spans and For top slabs of box culverts of all spans and

for all other cases, including slab

for all other cases, including slab--type type

bridges where the span does not exceed 15 0 bridges where the span does not exceed 15 0 bridges where the span does not exceed 15.0 bridges where the span does not exceed 15.0 ft, only the axle loads of the design truck or ft, only the axle loads of the design truck or design tandem of Articles 3.6.1.2.2 and

design tandem of Articles 3.6.1.2.2 and 3 6 1 2 3 respectively shall be applied 3 6 1 2 3 respectively shall be applied 3.6.1.2.3, respectively, shall be applied. 3.6.1.2.3, respectively, shall be applied.

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Applied Live loads – No Lane

Load

3 6 1 3 3 D i L d f D k D k



 3.6.1.3.3 Design Loads for Decks, Deck 3.6.1.3.3 Design Loads for Decks, Deck

Systems, and the Top Slabs of Box Systems, and the Top Slabs of Box Culverts

Culverts Culverts Culverts



 Where the slab spans primarily in the Where the slab spans primarily in the

transverse direction, only the axles of transverse direction, only the axles of the design truck of Article 3.6.1.2.2 or the design truck of Article 3.6.1.2.2 or design tandem of Article 3.6.1.2.3

design tandem of Article 3.6.1.2.3

shall be applied to the deck slab or the shall be applied to the deck slab or the shall be applied to the deck slab or the shall be applied to the deck slab or the top of box culverts.

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Lane Load – 3.6.1.3



 LRFDLRFD –– 20042004 –– Truck and Lane LoadTruck and Lane Load 

 LRFD LRFD 2004 2004 Truck and Lane LoadTruck and Lane Load



 64 lbs across a 10 ft width64 lbs across a 10 ft width 

 DLA not appliedDLA not applied 

 DLA not appliedDLA not applied



 LRFD LRFD –– 2005 2005 –– Truck onlyTruck only

St d d S ifi ti

St d d S ifi ti 3 7 1 13 7 1 1



 Standard Specification Standard Specification –– 3.7.1.13.7.1.1



 Either truck or Lane LoadEither truck or Lane Load 

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Pipe Culverts



 Lane Loads not applied to pipeLane Loads not applied to pipe



 For top slabs of box culverts of all spans and For top slabs of box culverts of all spans and for all for all

other cases, including slab

other cases, including slab--type bridges where the span type bridges where the span does not exceed 15.0 ft,

does not exceed 15.0 ft, only the axle loads of the only the axle loads of the

design truck or design tandem of Articles 3.6.1.2.2 and design truck or design tandem of Articles 3.6.1.2.2 and design truck or design tandem of Articles 3.6.1.2.2 and design truck or design tandem of Articles 3.6.1.2.2 and 3.6.1.2.3, respectively, shall be applied.

3.6.1.2.3, respectively, shall be applied. 

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Tire Footprint

  LRFD LRFD –– 3.6.1.2.63.6.1.2.6   w = 20 in.w = 20 in.   w 20 in.w 20 in.   l = 10 in.l = 10 in. St d d S ifi ti St d d S ifi ti 6 4 16 4 1 

 Standard Specification Standard Specification –– 6.4.16.4.1



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Box Under Shallow Fill

Distribution Width

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Distribution Width



 LRFD (4.6.2.10)LRFD (4.6.2.10)



 E = 96 + 1.44S (for axle)E = 96 + 1.44S (for axle) 

 E 96 + 1.44S (for axle)E 96 + 1.44S (for axle) 

 E in inches and S in feetE in inches and S in feet

St d d (3 24 3 2) St d d (3 24 3 2)



 Standard (3.24.3.2)Standard (3.24.3.2)



 E = 4 + 0.06S (for wheel)E = 4 + 0.06S (for wheel) 

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Live Load Distribution Parallel to

Box Culvert Span under Shallow

Fill

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Live Load Distribution

STD Spread a = a + 1 75*H STD Spread b = b + 1 75*H STD – Spread a = a + 1.75*H LRFD – Spread a = a + 1.15*H STD – Spread b = b + 1.75*H LRFD – Spread b = b +1.15*H

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Live Load Area for Depths ≥ 2 ft.

  LRFD (3.6.1.2.6) LRFD (3.6.1.2.6)   AA_L_L = (20/12 + 1.15D= (20/12 + 1.15D_E_E)(10/12 + 1.15D)(10/12 + 1.15D_E_E))   AA_L_L (20/12 + 1.15D (20/12 + 1.15D_E_E)(10/12 + 1.15D)(10/12 + 1.15D_E_E)) 

1.15 above should be replaced with 1.0 1.15 above should be replaced with 1.0 if select granular backfill is not used

if select granular backfill is not used if select granular backfill is not used if select granular backfill is not used



 Standard (6.4.1)Standard (6.4.1)



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Dynamic Load Allowance



 LRFD LRFD –– Dynamic Load Allowance (3.6.2.2)Dynamic Load Allowance (3.6.2.2)



 DLA = 0.33(1.0DLA = 0.33(1.0 -- 0.125D0.125D_E_E)) 

 DLA 0.33(1.0 DLA 0.33(1.0 0.125D0.125D_E_E))



 Standard Standard –– Impact Factor (3.8.2.3)Impact Factor (3.8.2.3)

IM 0 3 IM 0 3 0’0’ 0” t 1’0” t 1’ 0” INCL0” INCL   IM = 0.3 IM = 0.3 –– 0’0’--0” to 1’0” to 1’--0” INCL.0” INCL.   IM = 0.2 IM = 0.2 –– 1’1’--1” to 2’1” to 2’--0” INCL.0” INCL.   IM = 0.1 IM = 0.1 –– 2’2’--1” to 2’1” to 2’--11” INCL.11” INCL.

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Live Load Distribution through

Pipe and Soil

(29)

Multiple Presence Factor

Design Code Design Code

Lanes AASHTO AASHTO CHBDC

STD LRFD 1 1.0 1.2 1.0 2 1.0 1.0 0.90 3 0.90 0.85 0.80 4 0 75 0 65 0 70 4 0.75 0.65 0.70

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Box Culverts – Shallow Fill

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Soil Load

Frictional Soil P i Frictional Soil P i Forces Prism Forces Prism N t l G d N t l G d

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Soil Load



 WW_E_E = = FF_ee_ssBB_ccHH



 Boxes Boxes –– Section 12.11.2.2.1Section 12.11.2.2.1 

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Soil-Structure Interaction Factor

Soil Structure Interaction Factor

Boxes

  WW_E_E = = FF_ee_ssBB_ccHH  FF_ee_ee = 1 + 0.20(H/= 1 + 0.20(H/B(( B_cc_cc)))) 

FF_ee shall not exceed 1.15 for installations shall not exceed 1.15 for installations with compacted fill along the sides of with compacted fill along the sides of pp gg

the box section, or 1.40 for installations the box section, or 1.40 for installations with

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Soil-Structure Interaction Factor

Soil Structure Interaction Factor

Pipe



 “Standard installations for both “Standard installations for both

embankments and trenches shall be embankments and trenches shall be designed for positive projection,

designed for positive projection,

embankment loading conditions where F embankment loading conditions where Fgg _ee_ee shall be taken as the vertical arching factor, shall be taken as the vertical arching factor, VAF, specified in Table 12.10.2.1

VAF, specified in Table 12.10.2.1--3 for pp 3 for each type of standard installation.”

each type of standard installation.”

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AASHTO LRFD 12 10 2 1

AASHTO LRFD 12.10.2.1

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Vertical Soil Load

0.8 1.2 1.6 2 VAFi 1 2 3 4 5 6 7 8 0 0.4 li

“Bedding and Fill Heights for Concrete Roadway Pipe And Box Culverts” – C. Yoo, F. Parker, and J. Kang, Auburn University, June 2005

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Bottom Reaction to Vertical

Loads

(39)

LRFD (C12.11.2.3)



 “While typical designs assume a uniform “While typical designs assume a uniform

pressure distribution across the bottom slab, pressure distribution across the bottom slab,

p ,

a refined analysis that considers the actual a refined analysis that considers the actual soil stiffness under box sections will result soil stiffness under box sections will result in pressure distributions that reduce bottom in pressure distributions that reduce bottom slab shear and moment forces (McGrath et slab shear and moment forces (McGrath et (( al. 2004.”

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LRFD C12.11.2.3



 “Such an analysis requires knowledge of in“Such an analysis requires knowledge of

in--situ soil properties to select the appropriate situ soil properties to select the appropriate p pp p pp ppp p stiffness for the supporting soil. A refined stiffness for the supporting soil. A refined analysis taking this into account may be analysis taking this into account may be yy gg yy beneficial when analyzing existing

beneficial when analyzing existing culverts.”

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(42)

Lateral Live Load



 LRFD (3.11.6.2)LRFD (3.11.6.2)



 “The horizontal pressure“The horizontal pressure  _hh in ksf, on ain ksf, on a 

 The horizontal pressure The horizontal pressure _ph_ph in ksf, on a in ksf, on a

wall resulting from a point load may be wall resulting from a point load may be taken as:” taken as:” taken as: taken as: P 3ZX2 R (1 2)

[

]

_ph = P R2 3ZX2 R3 R (1 - 2) R + Z

[

]

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B i Di t ib ti Boussinesq Distribution

(44)

Live Load Lateral Uniform Pressure

  LRFD LRFD –– 3.11.6.4 3.11.6.4   ΔΔ_pp_pp = K = K γγγγ_ss_ss hh_eq_eq_eq_eq   H H << 5 ft 5 ft –– hh_eq_eq = 4 ft= 4 ft   HH << 10 ft10 ft –– hh = 3 ft= 3 ft   H H 10 ft 10 ft hh_eq_eq 3 ft 3 ft   H H << 20 ft 20 ft –– hh_eq_eq = 2 ft= 2 ft

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(46)

“In general, LRFD produces greater live load surcharge

pressures than Standard for depths of fill of 5 ft or less and less pressure for greater depths In addition live load

less pressure for greater depths. In addition, live load

surcharge pressures from AASHTO M 259 and M 273 are much greater than those from LRFD for depths of fill from

0 1 f d l h LRFD f fill h i h I

0 to 1 ft and less than LRFD for greater fill heights. In spite of the significant differences in live load surcharge pressures, their impact on reinforcement areas is relatively

p p y

minor”

“Comparison of AASHTO Standard and LRFD Code Provisions for Buried Concrete Box

C l t ” R R d & T M G th STP 1368 Culverts” – R. Rund & T. McGrath, STP 1368, 2000, Concrete Pipe for the New Millenium

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Lateral Earth Load - LRFD



 3.11.5.5 3.11.5.5 –– Equivalent Fluid MethodEquivalent Fluid Method



 Loose Sand or Gravel = 55 pcfLoose Sand or Gravel = 55 pcf 

 Loose Sand or Gravel 55 pcfLoose Sand or Gravel 55 pcf 

 Dense Sand or Gravel = 45 pcfDense Sand or Gravel = 45 pcf

3 11 5 2

3 11 5 2 At R t PAt R t P



 3.11.5.2 3.11.5.2 –– At Rest PressureAt Rest Pressure



 kk_oo = 1= 1--sinsin



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Other Loads



 Always ConsideredAlways Considered



 Self WeightSelf Weight 

 Internal Fluid LoadInternal Fluid Load

S ti C id d



 Sometimes ConsideredSometimes Considered



 Construction LoadsConstruction Loads 

 External Hydrostatic LoadsExternal Hydrostatic Loads 

 Internal Fluid PressureInternal Fluid Pressure 

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Load Factors

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Load Factors

Load Load Factor

Standard LRFD Minimum Maximum Minimum Maximum Dead 1.3 0.90 1.25 Water 1.3 1.0 1.0 E h V i l 1 3 0 90 1 30 Earth – Vertical 1.3 0.90 1.30 Earth - Horizontal 1.3 0.90* 1.35 Live 1.3 x 1.67 = 2.17 0.0 1.75**

*Per 3.11.7, a 50% reduction in load may be used in lieu of the minimum load factor

the minimum load factor.

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(53)

Phi Factors



 Strength Reduction FactorsStrength Reduction Factors

  _ff = 1.0= 1.0   _ff 1.0 1.0   _vv = 0.9= 0.9 LRFD LRFD 12 5 512 5 5 11   LRFD LRFD –– 12.5.512.5.5--11   Standard Standard –– 16.7.4.616.7.4.6

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“Basis of LRFD Methodology”



 ηη_ii_iiQQ_ii << RR_nn

 _i = a statistically based load factor

  = a statistically based resistance factor  Q_i = force effect

 R_n_n = nominal resistance

 η_i = load modifier relating to ductility,

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Load Modifier - Culverts



 LRFD 12.5.4LRFD 12.5.4



 “Load modifiers shall be applied to“Load modifiers shall be applied to 

 Load modifiers shall be applied to Load modifiers shall be applied to

buried structures and tunnel liners as buried structures and tunnel liners as specified in Article 1.3, except that the specified in Article 1.3, except that the specified in Article 1.3, except that the specified in Article 1.3, except that the load modifiers for construction loads load modifiers for construction loads shall be taken as 1.0”

shall be taken as 1.0” shall be taken as 1.0 shall be taken as 1.0

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Load Modifiers



 LRFD C 1.3.2.1LRFD C 1.3.2.1



 “Ductility, redundancy, and operational“Ductility, redundancy, and operational 

 Ductility, redundancy, and operational Ductility, redundancy, and operational

importance are significant aspects importance are significant aspects

affecting the margin of safety of bridges.” affecting the margin of safety of bridges.” affecting the margin of safety of bridges. affecting the margin of safety of bridges.

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Load Modifiers (LRFD)

For Culverts



 Standard = N/AStandard = N/A   LRFD (1.3.2)LRFD (1.3.2)   LRFD (1.3.2)LRFD (1.3.2)   Ductility = Ductility = ηη_D_D = 1.0= 1.0 R d d R d d 1 051 05 1 01 0   Redundancy = Redundancy = ηη_R_R = 1.05 or 1.0= 1.05 or 1.0   Importance = Importance = ηη_II = 1.0 or 1.05= 1.0 or 1.05

(59)

Load Modifier Culverts



 LRFD 1.3.3 LRFD 1.3.3 –– DuctilityDuctility



 “The structural system of a bridge shall“The structural system of a bridge shall 

 The structural system of a bridge shall The structural system of a bridge shall

be proportioned and detailed to ensure the be proportioned and detailed to ensure the development of significant and visible

development of significant and visible development of significant and visible development of significant and visible

inelastic deformations at the strength and inelastic deformations at the strength and extreme event limit states before failure.” extreme event limit states before failure.” extreme event limit states before failure. extreme event limit states before failure.

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Load Modifier - Culverts



 LRFD 12.5.4 LRFD 12.5.4 -- RedundancyRedundancy



 “For strength limit states, buried“For strength limit states, buried 

 For strength limit states, buried For strength limit states, buried

structures shall be considered structures shall be considered nonredundant

nonredundant (1.05)(1.05) under earth fill andunder earth fill and nonredundant

nonredundant (1.05) (1.05) under earth fill and under earth fill and redundant

redundant (1.0) (1.0) under live load and under live load and dynamic load allowance.”

dynamic load allowance.” dynamic load allowance. dynamic load allowance.

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Load Modifier - Culverts



 LRFD 12.5.4 LRFD 12.5.4 -- ImportanceImportance



 “Operational importance shall be“Operational importance shall be 

 Operational importance shall be Operational importance shall be

determined on the basis of continued determined on the basis of continued function and/or safety of the roadway.” function and/or safety of the roadway.” function and/or safety of the roadway. function and/or safety of the roadway.

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Design Capacity

(63)

Design for:



 FlexureFlexure



 Steel ReinforcementSteel Reinforcement 

 Concrete CompressionConcrete Compression



 Crack ControlCrack Control 

 ShearShear 

 Radial Tension (for pipe only)Radial Tension (for pipe only) 

 Fatigue (not required for box culverts or Fatigue (not required for box culverts or

pipe per LRFD) pipe per LRFD)

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Box Culverts and Pipe



 Section 12.10 Section 12.10 –– Reinforced Concrete PipeReinforced Concrete Pipe



 Section 12.10.4.2 Section 12.10.4.2 –– Direct Design Direct Design –– Agg A_ss_ss = ?= ? 

 Section 12.10.4.3 Section 12.10.4.3 –– Indirect Design Indirect Design –– Class = ?Class = ?



 Section 12 11Section 12 11 -- Precast Box CulvertsPrecast Box Culverts 

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Flexure

Asi g df  Nu g g

 

fd 2   Nu 2



 d_f  t



 2 Mu      f  fy E ti 12 10 4 2 4 1 F Di t D i f Pi Equation 12.10.4.2.4a-1 – For Direct Design of Pipe

Section 5.7.2 – Assumptions for Strength and Extreme Event Limit States takes a broader view of flexural design

(66)

Flexure (Minimum Steel)

LRFD - 12.11.4.3.2: STD - 16.7.4.8



 AsAs_min_min = 0.002 b h= 0.002 b h



 b = 12 inch unit widthb = 12 inch unit width 

 b 12 inch unit widthb 12 inch unit width 

 h = thickness of member in inchesh = thickness of member in inches

LRFD (12 11 4 3 2) LRFD (12 11 4 3 2)   LRFD (12.11.4.3.2)LRFD (12.11.4.3.2)   Standard (16.7.4.8)Standard (16.7.4.8)

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ACI 318-08

ACI 318 08

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(69)

Flexure (maximum steel)



 Box culvert walls and slabs are designed as Box culvert walls and slabs are designed as

tension controlled members, with a tension controlled members, with a ,,

maximum steel area of 75% of the balanced maximum steel area of 75% of the balanced condition (steel will always yield before

condition (steel will always yield before (( y yy y concrete crushes)

concrete crushes)



 Compression controlled design is allowedCompression controlled design is allowed 

 Compression controlled design is allowed Compression controlled design is allowed

with other concrete structures as long as a with other concrete structures as long as a modified phi factor is applied.

modified phi factor is applied. modified phi factor is applied. modified phi factor is applied.

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(71)

Crack Control (LRFD – 5.7.3.4)

s

700 



e

 f



2 d



c





_s



f

_s 

 LRFD Concerns itself with steel spacingLRFD Concerns itself with steel spacing 

 Standard Specification concerns itself withStandard Specification concerns itself with 

 Standard Specification concerns itself with Standard Specification concerns itself with

stress in the steel (maximum of 0.6 fy?) stress in the steel (maximum of 0.6 fy?)

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Service Load Stress

M

N



d

h



fs

Ms Ns d







_



₂



_



s

As j i d



Equation C12 11 3 1 Equation C12.11.3-1

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(74)

(75)

SHEAR

(76)

Shear

LRFD – 5.14.5.3: STD – 8.16.6.7 LRFD 5.14.5.3: STD 8.16.6.7 Slabs under 2 feet or more of fill

V   0 0676 f'c  4 6 As  Vude  db

Slabs under 2 feet or more of fill

V_c 0.0676 f c 4.6 b d _e M_u     b de 

Need not be taken less than Need not be taken less than

V

_c



0.0948



f'c

 d

b



_e

(77)

Shear

LRFD 5 8 3 3 STD 8 16 6 2 1 LRFD – 5.8.3.3: STD – 8.16.6.2.1

Slabs with less than two feet of cover, and sidewalls

V



0 0316

 f'c b d

and sidewalls

V

_c



0.0316







f c



b

_v



d

_v

 is based on the dimensions of the element and the strain in the steel

(78)

Shear

LRFD 5 8 3 3 STD 8 16 6 2 1 LRFD – 5.8.3.3: STD – 8.16.6.2.1

Slabs with less than two feet of cover, and sidewalls

F ti ith ll d th l th 16 i h

For sections with an overall depth less than 16 inches, and no tension,  can be assumed equal to 2

(79)

Top Slab

12X12 @20’ 12X12 @20’

(80)

Side Wall

(81)

(82)

Distribution Steel



 In bottom of top slab (LRFD 9.7.3.2)In bottom of top slab (LRFD 9.7.3.2)



 Percentage of main positive momentPercentage of main positive moment 

 Percentage of main positive moment Percentage of main positive moment

reinforcement = 100/S reinforcement = 100/S1/21/2



 S = span in feetS = span in feet 

 Need not be more than 50 percentNeed not be more than 50 percent



 In top of top slabIn top of top slab



(83)

CONCRETE PIPE DESIGN

(84)

Concrete Pipe Indirect Design – 12.10.4.3 D-Load Equation

(85)

(86)

E th L d B ddi F t Earth Load Bedding Factor

(87)

Extra Safety Factor for Type 1 Installations

Installations

(88)

(89)

Pipe Indirect Design D-Load Equation

(90)

(91)

Concrete Pipe

Special Design/Direct Design

Special Design/Direct Design –

12.10.4.2



 Flexure Flexure –– 12.10.4.2.4.a & b12.10.4.2.4.a & b 

 Radial TensionRadial Tension –– 12.10.4.2.4c12.10.4.2.4c 

 Radial Tension Radial Tension 12.10.4.2.4c12.10.4.2.4c 

 Crack Control Crack Control –– 12.10.4.2.4d12.10.4.2.4d

Sh

Sh 12 10 4 2 512 10 4 2 5



(92)

FLEXURE

CRACK CONTROL

(93)

The End

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