The Use of AASHTO LRFD Bridge Design Specifications with Culverts

The Use of AASHTO LRFD 

Bridge Design Specifications with 

Culverts 

Josh Beakley 

November, 2010

LRFD is Required 

June 28 th , 2000 FHWA Memo 

2

AASHTO 

Design 

Specifications

AASHTO Standard Specifications 

for Highway Bridges 

�� Section 3 – Loads 

�� Section 6 6 – Culverts 

�� Section 8 – Reinforced Concrete 

�� S Section ti 12 12 – Soil-Corrugated S SSoil il C CCorrugated t d Metal M t l 

Structure Interaction Systems 

�� Section 16 – Soil Soil-Reinforced Reinforced Concrete 

Structure Interaction Systems 

�� Section 17 – Soil Soil-Thermoplastic Thermoplastic Pipe 

Interaction Systems

AASHTO LRFD Bridge Design 

Specifications 

�� Section 3 – Loads and Load Factors 

�� Section 4 4 – Structural Analysis Analysis and 

and 

Evaluation 

�� Section 5 5 – Concrete Concrete Structures 

�� Section 12 – Buried Structures and Tunnel 

Li Liners

Structures Designed Per Section 12 

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

Arch Structures 

�� Section 12.8 - Long Long-Span Span Structural Plate 

Structures 

�� Section 12.9 - Structural Plate Box 

Structures 

�� Section 12.12 – Thermoplastic Pipes 

�� Section 12.13 – Steel Tunnel Liner Plate

Concrete Structures Designed Per 

Section 12 

�� Section 12.10 – Reinforced Concrete Pipe 

�� Section 12.11 12.11 - Precast Precast Box Box Culverts, Culverts, Cast 

Castin 

in-place place Box Culverts, Cast Cast-in in-place place Arches 

�� Section 12.14 12 14 - Precast Precast Three Three-Sided Three Sided 

Structures

What We Will Discuss 

�� Loads 

�� Load Factors 

�� Load Modifiers 

�� C Capacity it Calculations 

C l l ti

Live Load

Live Load 

�� 3.6.1.2 Design Vehicular Live Load 

��3.6.1.2.1 ��3.6.1.2.1 3.6.1.2.1 General 

General 

��“Vehicular “Vehicular live loading on the roadways 

of bridges or incidental structures structures, 

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

combination of: 

��Design Design truck or design tandem, and 

��Design Design lane load

Live Load Spacing – HL-93 

4000 lb. 

6f 6 ft. 

16000 lb. 16000 lb. 

14 fft. 

12,500 lb. 12,500 lb. 

12,500 lb. 12,500 lb. 

(12,00 lb per STD) 

AASHTO AASHTO 

HS 20 LOAD ALTERNATE LOAD

Applied Live loads – No Lane 

Load 

�� 36133DesignLoadsforDecks 3.6.1.3.3 Design Loads for Decks, Deck 

Systems, and the Top Slabs of Box Culverts 

�� Where the slab spans primarily in the 

longitudinal longitudinal direction: 

direction: 

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

for all other cases, including slab slab-type type 

bridges where the span does not exceed 15.0 15 0 

ft, only the axle loads of the design truck or 

design tandem of Articles 3.6.1.2.2 and 

36123 3.6.1.2.3, respectively, respectively shall shallbeapplied be applied.

Applied Live loads – No Lane 

Load 

�� 36133D 3.6.1.3.3 Design i Loads L d for f Decks, D k Deck D k 

Systems, and the Top Slabs of Box 

Culverts 

��Where Where the slab spans primarily in the 

transverse direction, only the axles of 

the design truck of Article 3.6.1.2.2 or 

design tandem of Article 3.6.1.2.3 

shall be be applied applied to to the the deck deck slab slab or or the 

the 

top of box culverts.

Lane Load – 3.6.1.3 

�� LRFD – 2004 – Truck Truck and and Lane Lane Load 

Load 

��64 64 lbs across a 10 ft width 

��DLA ��DLA DLA not not applied 

�� LRFD – 2005 – Truck only 

�� St Standard d d Specification S ifi ti – 3711 3.7.1.1 

��Either Either truck or Lane Load 

��Truck Truck governs for shorter spans

Pipe Culverts 

�� Lane Loads not applied to pipe 

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

other cases, including slab slab-type type bridges where the span 

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

design truck or or design design tandem of Articles 3.6.1.2.2 and 

and 

3.6.1.2.3, respectively, shall be applied. 

��History History

Tire Footprint 

�� LRFD – 3.6.1.2.6 

��w ��w w = 20 in. 

��l l = 10 in. 

�� St Standard d d Specification S ifi ti – 641 6.4.1 

��“Concentrated “Concentrated Load”

Box Under Shallow Fill 

Distribution Width

Distribution Width 

�� LRFD (4.6.2.10) 

��E ��E E = 96 + 1.44S (for axle) 

axle) 

��E E in inches and S in feet 

�� St Standard d d(32432) (3.24.3.2) 

��E E = 4 + 0.06S (for wheel) 

��E E in feet and S in feet

Distribution Steel

Live Load Distribution Parallel to 

Box Culvert Span under Shallow 

Fill

Live Load Distribution 

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

LRFD – Spread a = a + 1.15*H LRFD – Spread b = b +1.15*H

Pipe Under Shallow Fill

Live Load Area for Depths ≥ 2 ft. 

�� LRFD (3.6.1.2.6) 

= (20/12 + 1.15D E)(10/12 E)(10/12 )(10/12 + + 1.15D 1.15DE) E) 

��A ��A L = (20/12 + 1.15D 

��1.15 1.15 above should be replaced with 1.0 

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

used 

�� Standard (6.4.1) 

��A L = (1.75D (1.75DE) 2

Live Load Spread

Dynamic Load Allowance 

�� LRFD – Dynamic Load Allowance (3.6.2.2) 

��DLA ��DLA DLA = 0.33(1.0 - 0.125D 0.125DE) E) 

�� Standard – Impact Factor (3.8.2.3) 

��IM IM = 0 0.3 3 – 0’ 0’-0” 0” 0” to t 1’ 1’-0” 1’ 0” INCL INCL. 

��IM IM = 0.2 – 1’ 1’-1” 1” to 2’-0” 2’ 0” INCL. 

��IM IM = 0.1 – 2’ 2’-1” 1” to 2’-11” 2’ 11” INCL.

Two Trucks Passing

Live Load Distribution through 

Pipe and Soil

Multiple Presence Factor 

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 

4 075 0.75 065 0.65 070 0.70

Box Culverts – Shallow Fill 

Design Using Single Lane

Soil Load 

Soil 

Pi Prism 

Frictional 

Forces 

Soil 

Pi Prism 

Nt Natural lG Groundd Nt Natural lG Groundd 

Frictional 

Forces

Soil Load 

= Fe�� sBcH ��Boxes Boxes – Section 12.11.2.2.1 

��Pipe Pipe – Section 12.10.2.1 

�� W E =

Soil-Structure Soil Structure Interaction Factor 

Boxes 

�� WE = Fe�� sBcH ��F e = 1 + 0.20(H/B 0.20(H/ ( c) c) 

��F e shall not exceed 1.15 for installations 

with compacted p fill along g the sides of 

the box section, or 1.40 for installations 

with uncompacted fill

Soil-Structure Soil Structure Interaction Factor 

Pipe 

�� “Standard installations for both 

embankments and trenches shall be 

designed for positive projection, 

embankment loading g conditions where F e 

shall be taken as the vertical arching factor, 

VAF, specified specified p in Table 12.10.2.1 12.10.2.1-3 3 for 

each type of standard installation.” 

www.concrete-pipe.org

AASHTO LRFD 12 12.10.2.1 

10 2 1

Vertical Pressures and Reactions

Vertical Soil Load 

2 

1.6 

1.2 

VAFi 0.8 

0.4 

0 

1 2 3 4 5 6 7 8 

“Bedding and Fill Heights for Concrete Roadway Pipe 

And Box Culverts” – C. Yoo, F. Parker, and J. Kang, 

Auburn University, June 2005 

l i

Bottom Reaction to Vertical 

Loads

LRFD (C12.11.2.3) 

�� “While typical designs assume a uniform 

pressure p distribution across the bottom slab, , 

a refined analysis that considers the actual 

soil stiffness under box sections will result 

in pressure distributions that reduce bottom 

slab shear and moment forces (McGrath ( et 

al. 2004.”

LRFD C12.11.2.3 

�� “Such an analysis requires knowledge of in- 

situ soil properties p p to select the appropriate pp p 

stiffness for the supporting soil. A refined 

analysis y taking g this into account may y be 

beneficial when analyzing existing 

culverts.”

Pipe Pressure Distribution

Lateral Live Load 

�� LRFD (3.11.6.2) 

��“The �� “The The horizontal pressure �� ph h in ksf, ksf, on on a 

a 

wall resulting from a point load may be 

taken taken as:” as: 

[ ] 

P 3ZX2 R(1 2�) 

�ph = P 

�R2 3ZX2 R3 R (1 - 2�) 

R + Z

BBoussinesq i Distribution 

Di t ib ti

Live Load Lateral Uniform Pressure 

�� LRFD – 3.11.6.4 

�� Δ p = K γ s h eq 

��H H < 5 ft – h eq = 4 ft 

��H ��H H < 10 ft – h eq = 3ft 3 ft 

��H H < 20 ft – h eq = 2 ft

Lateral Uniform Live Load

“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 depths. In addition 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 to 1 fft and d lless than h LRFD ffor greater fill heights. h i h In I 

spite of the significant differences in live load surcharge 

pressures, p their impact p on reinforcement areas is relatively y 

minor” 

“Comparison of AASHTO Standard and LRFD 

Code Provisions for Buried Concrete Box 

CCulverts” l t ” – RR. Rund R d & T. T McGrath, M G th STP 1368, 1368 

2000, Concrete Pipe for the New Millenium

Lateral Earth Pressure

Lateral Earth Load - LRFD 

�� 3.11.5.5 – Equivalent Fluid Method 

��Loose ��Loose Loose Sand Sand or Gravel = 55 pcf 

��Dense Dense Sand or Gravel = 45 pcf 

�� 31152 3.11.5.2 – At Rest R t Pressure P 

��k o = 11-sin 

sin�� 

�� = 30°, 30 , k o = 0.5, press = 60 pcf

Other Loads 

�� Always Considered 

��Self ��Self Self Weight 

Weight 

��Internal Internal Fluid Load 

�� S Sometimes ti Considered C id d 

��Construction Construction Loads 

��External External Hydrostatic Loads 

��Internal ��Internal Internal Fluid Pressure

Load Factors

Load Factors 

Load Load Factor 

Standard LRFD 

Minimum Maximum 

Dead 1.3 0.90 1.25 

Water 1.3 1.0 1.0 

EEarth h– VVertical i l 13 1.3 090 0.90 130 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. factor 

**A multiple presence factor is included in the total load.

LRFD Design

Phi Factors 

�� Strength Reduction Factors 

�� f = 1.0 

�� v = 0.9 

��LRFD LRFD – 12.5.5-1 1255 12551 12.5.5 

��Standard Standard – 16.7.4.6

“Basis of LRFD Methodology” 

�� η i�� iQ i < ��R n 

�� i = a statistically based load factor 

�� = a statistically based resistance factor 

�Q i = force effect 

�R n = nominal resistance 

n 

�ηi = load modifier relating to ductility, 

redundancy, y, and operational p importance p

Load Modifier - Culverts 

�� LRFD 12.5.4 

��“Load �� “Load Load modifiers shall shall be be applied applied to 

to 

buried structures and tunnel liners as 

specified in in Article Article 1.3, 1.3, except except that that the 

the 

load modifiers for construction loads 

shall be be taken taken as as 1.0 

1.0”

Load Modifiers 

�� LRFD C 1.3.2.1 

��“Ductility, �� “Ductility, Ductility, redundancy, redundancy, and and operational 

importance are significant aspects 

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

bridges.”

Load Modifiers (LRFD) 

For Culverts 

�� Standard = N/A 

�� LRFD LRFD (1.3.2) 

��Ductility Ductility = ηD = 1.0 

��Redundancy Rd Redundancy d = ηR = 105 1.05 or 10 1.0 

��Importance Importance = ηI = 1.0 or 1.05

Load Modifier Culverts 

�� LRFD 1.3.3 – Ductility 

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

shall 

be proportioned and detailed to ensure the 

development of significant and and visible 

visible 

inelastic deformations at the strength and 

extreme event limit states before failure.” failure.


�� LRFD 12.5.4 - Redundancy 

��“For �� “For For strength limit states, states, buried 

buried 

structures shall be considered 

nonredundant (1.05) under earth fill and 

and 

redundant (1.0) under live load and 

dynamic dynamic load load allowance.” allowance.


�� LRFD 12.5.4 - Importance 

��“Operational �� “Operational Operational importance importance shall shall be 

be 

determined on the basis of continued 

function and/or and/or safety of of the roadway.” roadway. 

roadway.”

Design Capacity

Design for: 

�� Flexure 

��Steel Steel Reinforcement 

��Concrete Concrete Compression 

�� Crack Crack Control 

�� Shear 

�� Radial Tension (for pipe only) 

�� Fatigue (not required for box culverts or 

pipe per LRFD)

Box Culverts and Pipe 

�� Section 12.10 – Reinforced Concrete Pipe 

�� Section 12.10.4.2 – Direct Design – As = ? 

g s 

�� Section 12.10.4.3 – Indirect Design – Class = ? 

�� Section 12.11 12 11 - Precast Box Box Culverts 

Culverts

Flexure 

Asi 

� 

� 

� 

� � 2 

� � 

g��f� d � Nu � g�g��f�d � Nu� 2��f� d � t � 2Mu � 

EEquation ti 12.10.4.2.4a-1 1210424 1 – FFor Di Direct tDDesign i of fPi Pipe 

Section 5.7.2 – Assumptions for Strength and Extreme Event 

Limit States takes a broader view of flexural design 

ffy 

� 

�

Flexure (Minimum Steel) 

LRFD - 12.11.4.3.2: STD - 16.7.4.8 

�� As min = 0.002 b h 

��b ��b b = 12 inch unit width 

width 

��h h = thickness of member in inches 

�� LRFD(1211432) 

LRFD (12.11.4.3.2) 

�� Standard (16.7.4.8)

ACI 318 318-08 08

Flexure (maximum steel) 

�� Box culvert walls and slabs are designed as 

tension controlled members, , with a 

maximum steel area of 75% of the balanced 

condition (steel ( will always y y yield before 

concrete crushes) 

�� Compression controlled controlled design design is is allowed 

allowed 

with other concrete structures as long as a 

modified modified phi phi factor factor is is applied. 

applied.

Tension Controlled - Ductile

Crack Control (LRFD – 5.7.3.4) 

s 

700�� e 

� 

��s � f fs � 

2d � c 

�� LRFD Concerns itself with steel spacing 

�� Standard Specification Specification concerns concerns itself with 

with 

stress in the steel (maximum of 0.6 fy?)

Service Load Stress 

f s 

� 

Equation C12.11.3-1 

C12 11 3 1 

� 

� 

� 

M Ms � N Ns� d 

As� j�i� 

d 

h 

� � 

� 

2 

� 

� 

�

Factors affecting crack control

Exposure Conditions

SHEAR

Shear 

LRFD – 5.14.5.3: STD – 8.16.6.7 

Slabs under 2 feet or more of fill 

� 

V 0 0676� f'c 46 A s Vu� de Vc �� 

�� 

0.0676 fc �� 

4.6� � �� b b� d de bde � M u 

� 

Need not be taken less than 

Vc � 0.0948 � f'c� 

b� 

d e 

Equivalent to � = 3 

� 

� 

�

Shear 

LRFD – 5833 5.8.3.3: STD – 816621 8.16.6.2.1 

Slabs with less than two feet of cover, 

and sidewalls 

V Vc �� 

00.0316 0316�� f'c fc� 

b bv� d dv � is based on the dimensions of the element and the strain 

in the steel

Shear 

LRFD – 5833 5.8.3.3: STD – 816621 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

Top Slab 

12X12 @20’

Side Wall 

12X12 @ 

20’

Distribution Steel

Distribution Steel 

�� In bottom of top slab (LRFD 9.7.3.2) 

��Percentage ��Percentage Percentage of of main main positive positive moment 

moment 

reinforcement = 100/S 1/2 

��S ��S S = span in feet 

feet 

��Need Need not be more than 50 percent 

�� In top of top slab 

��As As6 = 0.002 x Ag Agg 

6

CONCRETE PIPE DESIGN

Concrete Pipe Indirect Design – 12.10.4.3 

D-Load Equation 



EEarth th LLoad d BBedding ddi FFactor t

Extra Safety Factor for Type 1 

Installations 


Live Load Bedding Factor

www.concrete-pipe.org 

Pipe Indirect Design 

D-Load Equation

Class V Pipe (C76/M 170)

Concrete Pipe 

Special Design/Direct Design – 

12.10.4.2 

�� Flexure – 12.10.4.2.4.a & b 

�� Radial Tension Tension – 12.10.4.2.4c 

�� Crack Control – 12.10.4.2.4d 

�� Sh Shear – 12.10.4.2.5 

1210425 12.10.4.2.5

FLEXURE 

RADIAL TENSION 

CRACK CONTROL 

SHEAR

The End 

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