1. Designing for Live Load on Buried Precast Structures According to AASHTO
Josh Beakley
It is common for us to discuss live load at Pipe School. However, we usually treat it in generic terms. Because the live load design in AASHTO has become so unique in recent years, and does not always follow the basic practices of live load evaluation, it was decided to focus just on AASHTO Live Load Design this year.

2. Rigid Rugged Resilient
What is live load?
What types of live load do we commonly encounter?
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3. Live Loads AASHTO AREMA FAA Rigid Rugged Resilient
We will be discussing AASHTO Live Load Design.
What other forms of transportation are their?
Are their design concepts similar? Not really. Hence the need for a class on AASHTO Live Loads only.
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4. Rigid Rugged Resilient
We will be following the 8th Edition of the AASHTO LRFD Bridge Design Specifications.
This edition just came into print in November, 2017, and does have some changes in the live load design method over the previous editions.
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5. OR? Surface Loading Rigid Rugged Resilient
Which of these do you think is a more accurate evaluation of the live load pressure through the soil. Higher pressure immediately under the load, or a uniform pressure all the way across?
Which of these design methods would you imagine is easier for the engineer to utilize?
While the Boussinesq method (on left) is more accurate, it is also more difficult to use. Hence, AASHTO uses the simplified method of uniform pressure through the soil (right).
The Canadians use the uniform method as well. The Europeans use the Boussinesq Method.
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6. Wheel on Structure
In addition to the distribution of live load through the soil, we will discuss live load spread through the structure itself.

7. Load Distribution Through Structure
This figure has existed in ACPA Literature for years.
Why doesn’t it show any spread through the top of the pipe like we use for box culverts?
Do you think live load spreads through a structure differently when it has to pass through the soil first?
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8. Outline HL-93 Load Box Culverts – Less than 2 feet
Concrete Pipe – Less than 2 feet
Culverts – Equal to or Greater than 2 feet
We will follow a very basic outline.
We will discuss the basic AASHTO Live Load Parameters.
We will discuss the similarities and differences in how AASHTO treats box culverts and concrete pipe under less than 2 feet.
We will discuss installations equal to or greater than 2 feet where the live load must go through the soil first.
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9. HL-93 Live Load Properties
Length of tire patch
lt = 10 inches
Width of tire patch
wt = 20 inches
Spacing of wheels on a single axle
sw = 6 ft.
Spacing of tandem axles
sta = 4 ft
Spacing of single axles
ssa = 14 ft
Basics of live load.
You will need to know this when performing an AASHTO design.
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10. AASHTO HL-93
Designing for the AASHTO HL-93 Live Load means designing for the worst case of either the design tandem axles, or design single axle.

11. Applied Live loads
Design Loads for Decks, Deck Systems, and the Top Slabs of Box Culverts
Where the slab spans primarily in the transverse direction, only the axles of the design truck of Article or design tandem of Article shall be applied to the deck slab of the top of box culverts.
If you noticed, the previous slide said that the live load design had to take the worst case of the axles when combined with the lane load. However, AASHTO exempts culverts from the lane load.
This section exempts box culverts from the lane load when the traffic is perpendicular to the span of the box.

12. Applied Live loads
Design Loads for Decks, Deck Systems, and the Top Slabs of Box Culverts
Where the slab spans primarily in the longitudinal direction:
For top slabs of box culverts of all spans and for all other cases, including slab-type bridges where the span does not exceed ft, only the axle loads of the design truck or design tandem of Articles and , respectively, shall be applied.
This second article exempts box culverts from being evaluated for the lane load when the traffic is parallel to the span.
Notice that it is for box culverts of “all spans” and box culverts are not limited to the 15 foot span limit used for other slab-type bridges.

13. No Lane Load
“Only the axle loads of the design truck or design tandem of Articles and , respectively shall be applied as live load on culverts, regardless of traffic orientation.”
This information was just incorporated into the 8th Edition of the AASHTO LRFD Bridge Design Specifications.
The previous articles specifically mentioned box culverts. However, it was never intended that lane load be included for pipe either. AASHTO has always intended that pipe be exempted from the lane load, but did not make it specific until 2017.
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14. Rigid Rugged Resilient
If you are going to design buried structures for AASHTO Live Loads, you need to start here.
As shown in the previous slides, this section has a few new twists since it came out in November.
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15. 3.6.1.2.6 Distribution Width for Box Culverts
“Live load shall be distributed to the top slabs of flat top three-sided, or long- span concrete arch culverts with less than 2.0 ft of fill as specified in Article ”
When you have less than 2 feet of fill over the structure, than you are allowed to assume more distribution through the structure itself.
For box culverts, when you have less than 2 feet of fill, AASHTO sends you to another chapter that contains equations for bridge structures.

16. Distribution Width for Box Culverts
LRFD ( ) – Traffic Travels Parallel to Span
E = S (for axle)
E in inches and S in feet
LRFD ( ) – Traffic Travels Perpendicular to Span
E = S (for axle) +M
E = S (for axle) -M
For box culverts, the spread through the structure under 2feet or less is different depending upon the traffic orientation.
AASHTO really pushes for the use of axial loads versus wheel loads.
Lucky for us, most designs are for spans parallel to traffic.
The designs for traffic perpendicular to the span are extremely restrictive, and really don’t make sense for box culverts. They were never intended for box culverts in the first place, but AASHTO goes to them by default.
The shorter the span, the worse off you are when you use Your span has to be at least 10 feet for the axle distribution from the first equation to even equal the width of the axle. Thus, you know this equation would not be reasonable for concrete pipe. Yet, until the November printing of the 8th Edition, this method is what was referenced for pipe as well as box culverts.

17. Distribution Width
Do you think the box culvert really cares which direction the load is coming from?
AASHTO does not provide for any spread through the structure beyond the spread across the top slab.

18. Distribution Width for Concrete Pipe
– “Live load shall be distributed to concrete pipe culverts with less than 2.0 ft of cover in accordance with Eq , regardless of the direction of travel. Round concrete culverts with 1.0 ft or more but less than 2.0 ft of cover shall be designed for a depth of 1.0 ft.”
This is the change incorporated into the 8th Edition.
For pipe, you use only the one equation for pipe under less than 2 feet of cover, regardless of the direction of traffic.
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19. Distribution Width for Box Concrete Pipe Culverts
LRFD ( ) – Traffic Travels Parallel or Perpendicular to Span
E = S (for axle) Eq
E in inches and S in feet
LRFD ( ) – Traffic Travels Perpendicular to Span
E = S (for axle) +M
E = S (for axle) -M
So, pipe is similar to box culverts, but we get to use only the first equation for both directions.

20. Live Load Spread for Less Than 2 feet of Cover (single axle)
(Parallel)
Direction of Traffic E
So, when traffic is parallel to the pipe span, you spread the load as an axle width plus some. S
Espan

21. For Trucks Traveling Perpendicular to the Span of the Pipe
E = Distribution width perpendicular to span in inches
S = Clear Span in feet
Note: Equation is for an axle load.
With pipe, having much smaller spans than boxes
a distribution for wheel loads is more appropriate.
Ewheel = S
For traffic perpendicular to the span of the pipe, you follow the same equation you would for traffic parallel to the span of the pipe. However, you will not have an entire axle over the length of the pipe when the traffic is perpendicular to the pipe. So how do you apply equation ?
AASHTO does not give any guidance on this. The best method is to apply the method for each wheel individually. So you divide the equation by 2 : ( S). However, wheel footprint is oriented differently, and you are starting the spread from the 10 inch length of the wheel as opposed to the 20 inch width of the wheel. Thus, subtract 10 inches from the spread : ( S).

22. Live Load Spread for Less Than 2 feet of Cover (Perpendicular)
The width of the live load through the pipe is starting from the 10 inch dimension of the footprint, so you use 38 inches plus 0.72S. WE
Direction of Traffic

23. ALL = lw ww (3.6.1.2.6a-1) ALL = Espan * E ALL = rectangular area
Live Load Spread for Less
Than 2 feet of Cover (single axle)
(Parallel)
ALL = lw ww ( a-1)
ALL = Espan * E
ALL = rectangular area
at depth H (ft2)
Espan = LT + LLDF(H)
LT = length of tire footprint (ft) (10/12) E
So the E dimension we calculate for the axle is spread along the pipeline.
The live load spread in the direction of the span is taken as the tire footprint length plus the distribution through the soil, if any. In the case of 0 feet, the value is just the footprint length.
In the earlier codes, you were never allowed to spread the load in the direction of the span for anything less than 2 feet of cover. Now they allow you that slight benefit.
Espan

24. Concrete Pipe under Depths > 2 Feet
– “Where the depth of fill over round, nonconcrete culverts is greater than 1.0 ft, or when the depth of fill over flat top three- sided, or long-span concrete arch culverts, or concrete pipe is 2.0 feet or greater the live load shall be distributed to the structure as wheel loads uniformly distributed over a rectangular area with sides equal to the dimension of the tire contact area specified in Article increased by the live load distribution factors (LLDF) specified in Table a-1 and the provisions of Articles b and c.”
When we get to fills equal to or greater than 2 feet, we start working with individual wheel loads.
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25. Live Load Distribution Through Soil
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Live Load Distribution Through Soil
Have you seen this figure before? It has existed in our Design Manual for decades. The figure never changes. However the live load distribution value governing how the load distributes through the soil has changed many times over the last decade.

26. Live Load Distribution Factors
The latest live load distribution through the soil is as shown here. It is not a constant number. The LLDF is dependent on the pipe size.

27. Boussinesq Distribution - Footprint
Surface loading Z1 Z3 Z2
Remember, we are using a linear distribution to model something that is not linear, so the LLDF has to change to account for this.
Variation of vertical stress at different depths Z.

28. Interaction Depth for Wheels (Parallel)
Direction of Traffic
We use the linear spread for individual wheels and determine when the influence from individual wheels overlap each other.
Wheel Pressures do not overlap
Wheel Pressures overlap
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29. How Many Lanes?
– “For traffic parallel to the span, culverts shall be analyzed for a single loaded lane with the single lane multiple presence factor. For traffic perpendicular to the culvert span, analysis shall include consideration of multiple lane loadings with appropriate multiple presence factors.”
How many wheels do we have to check for overlapping?
For the majority of installations, we only have to worry about one lane, since in most cases the traffic is traveling parallel to the span of the pipe.
However, for traffic running perpendicular to the culvert span we must check multiple lanes.
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30. Multiple Presence Factor
Design Code
Lanes
AASHTO
STD
LRFD 1
1.0
1.2 2 3
0.90
0.85 4
0.75
0.65
Depending upon how many lanes we evaluate, we must apply a multiple presence factor. The multiple presence factor accounts for the likelihood that multiple lanes will be overloaded. The more lanes you are evaluating, the less likely you are to have all of them overloaded at the same time. Thus, the multiple presence factor reduces with an increase in the amount of lanes.
This has always existed, but as you can see, we previously didn’t think about it much because it was 1.0 for either one or two lanes before, so the issue was never brought forward.

31. 2 Feet or More Article 3.6.1.2.5 Direction of Traffic Tire Patch
lt = 10 in.
So we start at the surface with the wheel footprint. A 10 inch by 20 inch footprint represents two wheels on the end of an axle.
wt = 20 in.

32. Interaction Depth for Wheels (Parallel)
Wws for a single wheel sw
Wws for two wheels
Plan View
Direction of Traffic sw
We spread the load through the soil and concern ourselves with when the live load distribution prisms overlap.
AASHTO has equations for the calculation of the height of interaction. Depending upon whether the height you are evaluating is greater or less than the height of interaction, you will determine the live load area you use to analyze the pipe.
Hintw
Wws if H< Hintw
Wws if H> Hintw
Elevation View

33. Interaction Depth for Wheels (Parallel)
Wws for a single wheel sw
Wws for two wheels
Plan View
We can first consider the example where the traffic is traveling parallel to the span of the pipe.
Remember that for this case, we only have to evaluate one lane.
In evaluating the spread width, we must consider the spread through the pipe as well as the spread though the soil.
The spread through the pipe is 0.06 x Di. This is much less than the 1.75 x 0.75 x Do that our industry has used in the past.
DTP/2
DTP/2
W + LLDF*H
Elevation View

34. Width Spread for One Wheel
Spread = wt/12 + LLDF x H + (0.06 x Di)/12
Spread = sw
sw = wt/12 + LLDF x H + (0.06 x Di)/12
LLDF x H = sw – wt/12 – (0.06 x Di)/12
Let’s think about when the spread width from two footprints on the same axle will overlap.
The spread from each wheel footprint is the width of the wheel footprint plus the spread through the soil, plus the spread through the pipe. When this value equals the center-to-center spacing of the wheels on the axle, we will have to concern ourselves with both wheels.
½ Width
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35. Interaction Depth sw = wheel spacing, 6.0 ft
wt = tire patch width, 20 in.
Di = inside diameter or clear span of the culvert (in)
The previous slide took you most of the way through the derivation of this equation that exists in AASHTO for the height of interaction between wheels of the same axle when the traffic is parallel to the span of the pipe.

36. Interaction Depth – Distribution Transverse to Culvert Span
Where H < Hint-t
Ww = wt/12 + LLDF(H) (Di/12) ( b-2)
Where H > Hint-t
If your height of cover is less than the height of interaction, than the live load intensity from only one wheel needs to be considered.
If your height of cover is equal to or greater than the height of interaction, than you must consider the effects from both wheels. Since the spacing of wheels on an axle is 6 feet, the width when the wheels interact is simply 6 feet wider than when they do not.
These equations are taken straight from AASHTO.
Ww = wt/12 + sw + LLDF(H) (Di/12) ( b-3)

37. Pressure Area at the Top of the Pipelw ww lw
So we calculate the width of the live load on the top of the pipe as being the width of influence from one wheel or two wheels.
We also need to determine the length of the live load spread. ww
Plan View
ALL = lw ww ( a-1)

38. Interaction Depth for Tandem Axles (Parallel)
Direction of Traffic sa sa
Hintd
lws when H<Hintd
For the live load spread length when traffic is parallel to the span, we must consider when loads from separate axles overlap.
The possibility of tandem axles overlapping is the most obvious concern, but we must also remember that the single axles are spaced 14 feet apart, and their live load distributions through the soil may overlap at higher depths.
lws
lws when H>Hintd
lwt when H>Hintd
lwt
Elevation View
Plan View

39. Length Spread for One Wheel
Spread = lt/12 + LLDF x H
Spread = sa
sa = lt/12 + LLDF x H
LLDF x H = sa – lt/12
Once again, like we did for wheel loads, we must consider when the live load influence from the various axles will overlap. However, in this case we do not need to consider live load distributing through the pipe in the length direction. Thus, we only concern ourselves with when the length of the wheel footprint plus the distribution through the soil equals the spacing of the axles.
½ Length sa
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40. Interaction Depth Parallel
“For live load distribution parallel to culvert span, the wheel/axle load
Interaction depth Hint-p shall be determined as:” lt
sa - 12
Hint-p =
( b-4)
LLDF
The previous slide took us through the basic derivation of how AASHTO came up with its equation for the height of interaction between axles.
sa = axle spacing (ft)
lt = tire patch length, 10 (in)
LLDF = live load distribution factor

41. Interaction Depth – Distribution Parallel to Culvert Span
Where H < Hint-p
lw = lt/12 + LLDF(H) ( b-5)
Where H > Hint-p
If your height of cover is less than the height of interaction than you only concern yourself with one axle. If your height of cover is equal to or greater than the height of interaction, than you must concern yourself with two axles.
lw = lt/12 + sa + LLDF(H) ( b-6)

42. Interaction Depth for Tandem Axles (Parallel)
Direction of Traffic sa sa
Hintd
lws when H<Hintd
So, in summary, your live load spread width is dependent upon the wheel interaction depth, and your live load spread length is dependent upon the axle interaction depth.
lws
lws when H>Hintd
lwt when H>Hintd
lwt
Elevation View
ALL = lw x ww
Plan View

43. Pressure at the Top of the Pipe( ) IM P
1 +
(m)
100
PL =
( b-7)
ALL
PL = live load vertical crown pressure (ksf)
P = live load applied at surface on all interacting wheels (kips)
IM = dynamic load allowance as specified in Article
m = multiple presence factor specified in Article
So if you know the load, and you know the area, you can calculate the live load pressure on the pipe.
We have already talked about the multiple presence factor (m) based on how many lanes we are dealing with.
We use a single lane when analyzing for traffic parallel to the span of the pipe, and we must consider multiple lanes for traffic perpendicular to the span of the pipe.

44. Dynamic Load Allowance
LRFD – Dynamic Load Allowance ( )
DLA = 33( DE)
DE = Depth of cover (ft)
The impact factor, or what is sometimes referred to as the Dynamic Load Allowance in the LRFD Code, starts at 33% at the surface, reducing to 0 at 8 feet in depth.

45. For Concrete Pipe, Load must be in
Terms of lbs/ft Do lw
1 ft.
After we calculate the live load pressure we must convert it to load in terms of pounds per foot of pipe length.
If we multiple the pressure (lbs/ft2) by the appropriate length of the load on top of the pipe (ft), we will get our value in terms of lbs/ft.
Sometimes the length of the load is less than the outside pipe diameter, in which case we need to multiply the pressure by the length of the load. Other times, the length of the load extends beyond the outer diameter of the pipe (as shown in this slide). In these cases, we only multiple by the outside diameter of the pipe, since it is only the load on top of the pipe that concerns us.
WL = PL * L = live load (lbs/ft)
L = Smaller of lw or Do

46. For Concrete Pipe, Load must be in
Terms of lbs/ft sw Do lw
If the length of the live load is less than the outside diameter of the pipe, than there is no sense multiplying the pressure by the OD, since the pressure does not extend that far out.
WL = PL * L = live load (lbs/ft)
L = Smaller of lw or Do

47. Concrete Pipe Indirect Design – 12.10.4.3 D-Load Equation
Once you have the live load in lbs/ft, you can include the earth load and fluid load in lbs/ft and apply the standard D-load equation.

48. Embankment Earth Load Bedding Factor
The earth load and fluid load bedding factor is per the Standard Installations.

49. TYPE 1
1.5
1.0
0.5
0.0
1.5
1.0
0.5
0.0
0.0
0.5
1.0
1.5
0.0
0.5
1.0
For the earth load, we know the governing location for stress is at the invert due to nonuniform pressure at the bottom.
1.5
2.0
2.5
3.0
3.5
4.0
4.5

50. Live Load Bedding FactorP
For live load at shallow fills, a concentrated load can result in the critical stress being at the crown of the pipe. When the resulting live load bedding factor is lower than the earth load bedding factor, than the live load bedding factor is what you use for live load.

51. Previous Live Load Bedding Factors
These are the previous live load bedding factors that were used for RCP in AASHTO. They no longer exist in the AASHTO LRFD Bridge Design Specifications.
These bedding factors made logical sense. You had lower values for lower fill heights, and you had lower values for larger diameter pipe (ex: a load with a spread of 1 foot would be a more concentrated load on a 144 inch pipe than it would be for a 12 inch pipe).

52. Live Load Bedding Factors
Table c-1
Pipe
Diameter, in
Fill Height, ft
< 2 ft
> 2 ft 12
3.2
2.4 18 24
30 and larger
2.2
This is what the current values for live load bedding factors are in AASHTO.
When you look at them, they do not seem rational since deeper fills have lower bedding factors.
AASHTO is trying to make up for the error in the live load distribution through the pipe by inducing an error in the bedding factor to compensate for it. Using two wrongs in an attempt to make a right.

53. AASHTO Explanation for Live Load Bedding Factors
C c
The relatively large bending stiffness in the longitudinal direction of concrete pipe results in the distribution of the live load force along the length of the pipe. This ratio of distribution length to pipe diameter is higher in small diameter pipes designed by the Indirect Design Method. The bedding factor has been adjusted in Table c-1 to account for this higher distribution length.
This is how AASHTO describes the live load bedding factors in its commentary.
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54. Traffic Running Perpendicular to Span
– Traffic Perpendicular to the Culvert Span
The provisions of Article b shall apply with the terms wt and sw in
Eqs b-1 through b-3 replaced by lt and sa respectively, and
the terms lt and sa in Eqs b-4 through b-6 replaced by wt
and sw respectively.
We went through the basic steps required to come up with a D-load when traffic is traveling parallel to the span of the pipe, which is a vast majority of the cases.
We know we must consider more than one lane when evaluating traffic perpendicular to the span of the pipe. This is the guidance that AASHTO gives you on how to distribute the wheel loads through the soil.
You follow the same concept that you did for traffic parallel to the span. However, now, you use the length of the wheel footprint to determine the spread width of the live load, and you use the width of the wheel footprint to determine the spread length of the live loa.
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55. Example: Perpendicular
60 inch RCP
B-Wall Pipe
Direction of Traffic is Perpendicular to the Span
HL-93 Loads
H = 4 ft
The process for evaluating live loads that are perpendicular to the span can be confusing at times, so we will perform an actual example calculation for instructional purposes, and to verify our understanding of the concepts we learned for traffic parallel to the span.
These are the parameters for the design example.
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56. Pipe Information Pipe ID = 60 in. Pipe Wall Thickness = 6 in.
Pipe OD = (60 + 2(6))/12 = 6 ft.
Basic Pipe Information.
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57. Live Load Parameters Wheel = 16,000 lbs.
Single Axle Load = 32,000 lbs.
Individual Tandem Axle = 25,000 lbs.
lt = 10 in. – length along pipe line
wt = 20 in. – width along pipe span
Direction of Traffic lt wt
The live load parameters do not change. However, we use the length of the tire to determine the width of the live load spread over the pipe, and we used the width of the tire to determine the length of the live load spread over the pipe.
The live load distribution factor is the same regardless of the direction of traffic.
(60-24)
LLDF =
(1.75 – 1.15)
(96-24)
LLDF = 1.45
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58. Dynamic Load Allowance
LRFD – Dynamic Load Allowance ( )
DLA = 33( DE)
DLA = 33[1.0 – 0.125(4 ft.)]
DLA = 16.5
The dynamic load allowance (impact factor) is the same regardless of the direction of traffic as well.
In this case, we have an impact factor of 16.5%. This is half of the 33 percent maximum value, since we are at 4 feet (halfway between zero and 8 feet).

59. Height of Interaction for Wheelswt
sw - 12
Hintw =
sw = 6 ft. – spacing of axle wheels
sp = 4 ft. – spacing of passing wheels
LLDF
20 in.
6 ft. - 12
Hintw =
1.45
This is how we would be evaluating the height of interaction for wheel loads.
The wheel loads will be interacting in the direction of the span for traffic perpendicular to the pipe. Thus, we do not need the spread along the pipe length this time.
Since we now have to consider more than one lane, we must consider the overlap from wheels of different axles passing each other at a distance of 4 feet apart.
In this example I only calculated the height of interaction for wheels on the same axle spaced 6 feet apart. The height of interaction is less than our design cover of 4 feet. If the influence from wheels spaced 6 feet apart overlap, than we know that the influence from wheels spaced 4 feet apart will overlap. Thus, there is no need to calculate the height of interaction for passing wheels. We know we need to consider both cases. Since we know we need to consider the case where wheels overlap, we know we need to evaluate multiple lanes. If wheels from separate lanes were not overlapping, it would have been sufficient to simply analyze a single lane.
If our height of cover was less than the height of interaction for the 6 foot wheel spacing, than we would have had to calculate the height of interaction for the 4 foot wheel spacing to determine if multiple lanes needed to be considered.
Hintw = 2.99 ft. – Check Overlapping
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60. Interaction Depth for Wheels (Perpendicular)sw sw
Direction of Traffic
Hintw
Wws if H< Hintw
Our height of interaction is less than the design height, so we know we must consider both wheels of an axle, and since we must consider both wheels of an axle with 6 foot wheel spacing, we know we must consider multiple lanes.
Wws if H> Hintw
Elevation View
Plan View

61. Passing Vehicles – Check Effects as Well
As a visual. If the influence from wheels of the same axle need to be considered, than since passing wheels are even closer, we know their influences need to be considered together as well.
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62. Height of Interaction for Axles
12500 lb.
12500 lb.
Now we must consider the live load spread width for traffic perpendicular to the span. In this case, we need to consider if the influence from axles overlap each other. Once again, the 4 foot spacing of the tandem axles is an obvious consideration, but we cannot forget the influence from single axles spaced 14 feet apart for deeper fills.
12500 lb.
12500 lb.
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63. Height of Interaction for Axleslt
0.06Di lt
0.06Di
ssa - -
sta - - 12 12 12 12
Hint-sa =
Hint-ta =
LLDF
LLDF
10 in.
0.06(60 in.)
10 in.
0.06(60 in.)
14 ft. - -
4 ft. - - 12 12 12 12
Hint-sa =
Hint-ta =
1.45
1.45
Since we are considering the spread width along the pipe axis, we must include the distribution of the live load through the pipe itself.
The calculation on the left is for the height of interaction of single axles, and the calculation on the right is for the height of interaction of tandem axles.
The single axles do not overlap at a depth of 4 feet (8.87 > 4). Thus, we do not have to worry about more than one single axle being included in the calculation of the spread width.
The height of interaction for the tandem axles is less than our design earth cover, thus we must consider two cases for the spread width through the pipe. One case will involve a spread from one axle, along with the spread lengths of the various multiple lane applications The other case will involve the spread width from tandem axles with the same spread lengths of the various multiple lane applications.
Note that we could pretty much tell by common sense that the single axles spaced at 14 feet apart were not going to overlap at a depth of 4 feet. However, I wanted to show their interaction depth. For smaller diameter pipe, the overlapping of single axles is not an issue since live load need not be considered below 8 feet. However, for larger pipe sizes, the live load needs to be considered down to a depth equal to the outside diameter of the pipe. Thus, the overlapping of single axles can come into play with pipes that have outside diameters greater than 8.87 feet.
Hint-sa = 8.87 ft.
Hint-ta = 1.98 ft. – Check Overlapping
Tandem Axles
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64. Interaction Depth for Tandem Axles (Perpendicular)sa sa
Hintd
lws when H<Hintd
For our example, we have determined that we must consider the overlapping of live load spread from the tandem axles.
lwt when H>Hintd
Direction of Traffic
Elevation View
Plan View

65. Determine the Width of Spread in the Pipe
For a Single Axle Ws = lt/12 + LLDF x H Di/12 Ws = 10 in./ x 4 ft. + [0.06(60 in.)]/12 Ws = 6.93 ft. For Tandem Axles Wt = Ws + sta Wt = 6.93 ft. + 4 ft. Wt = ft. lt
Direction of Traffic wt
We have determined for our example that we need to check the width based on a single axle and the width based on tandem axles.
Our width includes the spread of the live load through the pipe.
Note that the width of the tire patch (wt – using lower case w) is not the same as the width along the pipe axis (Wt –using upper case W). They are perpendicular to each other when evaluating for traffic perpendicular to the span.
For tandem axles the axles are spaced 4 feet apart, so we simply need to add 4 feet to our single axle width.
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66. Determine the Length of Spread Over the Pipe for the Various Lane Combinations
For a Single Lane Ls = wt/12 + sw + LLDF x H Ls = 20 in./ ft x 4 ft. Ls = ft. For Passing Wheels Lp = wt/12 + spw = LLDF x H Lp = 20 in./ ft x 4 ft. Lp = ft. lt wt
Direction of Traffic
For the length of spread, we will start out by calculating the length of spread for a single axle and for wheels of passing axles. Since passing wheels are 4 feet apart instead of 6 ft, the length for passing wheels is 2 feet less than it is for a single axle.
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67. Length of Spread for Multiple Lanes
In reality, we have to account for up to four lanes of vehicles. However, anything beyond two lanes is probably not going to govern structures as small as our pipes.
For every additional lane you include, you add 10 feet to account for it. 10 feet is comprised of the 6 foot spacing of the wheels on the axle plus the 4 foot passing distance.
4 ft.
1 Lane = 6 ft. Ls = ft
2 Lanes = 16 ft. L2 = ft = ft.
3 Lanes = 26 ft. L3 = ft = ft.
4 Lanes = 36 ft. L4 = ft = ft.
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68. Four Lanes Ws Passing Wheels Single Lane Two Lanes Lp
Direction of Traffic Ls
Single Lane
So for a single axle, we are evaluating the various live load distribution area scenarios. L2
Two Lanes
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69. Calculate the Load Areas for a Single Axle
ALLp = Ws x Lp = 6.93 ft x ft = ft2
ALLs = Ws x Ls = 6.93 ft x ft = ft2
ALL2 = Ws x L2 = 6.93 ft x ft = ft2
ALL3 = Ws x L3 = 6.93 ft x ft = ft2
ALL4 = Ws x L4 = 6.93 ft x ft = ft2
This would be the areas for the different cases we are considering for the single axle load calculation. The width from the single axle multiplied by the length from the various lengths resulting from wheels overlapping.
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70. ( ) ( ) ( ) ( ) Live Load Pressures at Top of Pipe Single Lane
Passing Wheels ( ) ( ) IM IM P
1 +
(m) P
1 +
(m)
100
100
PLp =
PLs =
ALLp
ALLs ( )
16.5 ( )
32000
1 +
(1.0)
16.5
32000
100
1 +
(1.2)
We will start with the two smaller footprints of a single lane, and two wheels passing (2 lanes).
The single lane results in the higher live load pressure. In both cases we are applying two wheels, so the load is a single axle load of 32 kips.
In reality, the passing wheels have the higher pressure intensity since they have the same total load as the single lane load, and a smaller footprint. However, because the multiple presence factor for a single lane is 1.2 versus 1.0 for two lanes, the design load for the single lane ends up being higher.
100
PLp =
PLs =
79.49
93.35
PLs = 479 psf
PLP = 469 psf
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71. ( ) ( ) ( ) ( ) Live Load Pressures at Top of Pipe Two Lanes
Three Lanes ( ) ( ) IM IM P
1 +
(m) P
1 +
(m)
100
100
PL3 =
PL2 =
ALL3
ALL2 ( ) ( )
16.5
16.5
3 x 32000
1 +
(0.85)
2 x 32000
1 +
(1.0)
100
We can check the two and three lane conditions as well. However, they are even less than the single lane and passing wheel applications.
Once again, if all things were equal, the pressure from two lanes would be higher than it is for one lane by virtue of the load being doubled while the distribution area is not increased proportionately. However, the lower multiple presence factor used for the design load for two lanes results in the single lane pressure being higher.
100
PL3 =
PL2 =
231.95
162.65
PL2 = 458 psf
PL3 = 410 psf
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72. For Concrete Pipe, Load must be in
Terms of lbs/ft
WLs = PLx * L
L = Smaller of Lx or Do
Lp < Ls < L2 < L3 < L4
Lp = ft. > Do
Do = 6 ft.
L = 6 ft.
WLs = 479 psf x 6 ft
WLs = 2874 lbs/ft Ws
Direction of Traffic
1 ft.
So we have all these pressures, and we must take and multiply them by the appropriate length to determine the live load in lbs/ft.
Remember, that in this case we take the lesser of the spread length versus the outside diameter. The spread length of the passing wheels is ft > 6 ft, since the length from the passing wheels is the shortest length, we know all the lengths are greater than the outside diameter of the pipe. Thus, O.D. will be used in each case. Therefore, we can simply take the maximum pressure and multiply it by the pipe O.D. to get the governing single axle live load in lbs/ft. Ls Do
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73. Four Lanes - Tandem Wt Passing Wheels Single Lane Lp
Direction of Traffic
Now we need to go back and check what occurs with tandem axles.
We have the same lane scenarios that we considered for the single axle, so all of the lengths are the same as before. Ls
Single Lane
Note: Check 2, 3, and 4 lanes as well.
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74. Calculate the Load Areas for Tandem Axles
ALLtp = Ws x Lp = ft x ft = ft2
ALLt = Ws x Ls = ft x ft = ft2
ALLt2 = Ws x L2 = ft x ft = ft2
ALLt3 = Ws x L3 = ft x ft = ft2
ALLt4 = Ws x L4 = ft x ft = ft2
We have slightly larger live load areas for the tandem axle configurations, but remember that we also have larger live loads.
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75. ( ) ( ) ( ) ( ) Live Load Pressures at Top of Pipe (Tandem Axles)
Single Lane
Passing Wheels ( ) ( ) IM IM P
1 +
(m) P
1 +
(m)
100
100
PLtp =
PLt =
ALLtp
ALLt ( )
16.5 ( )
50000
1 +
(1.0)
16.5
50000
100
1 +
(1.2)
For tandem axles, we have two 25 kip axles to deal with, so the total load is 50 kips for a single lane. Once again, there is the same amount of wheels from passing wheels overlapping as there is for single lane wheels overlapping, so we 50 kips of load for the passing wheels as well.
Once again, the live load pressure for the single lane condition governs our evaluation of the tandem axles because of the higher multiple presence factor used for the single lane.
100
PLtp =
PLt =
125.37
147.23
PLt = 475 psf
PLtP = 465 psf
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76. ( ) ( ) ( ) ( ) Live Load Pressures at Top of Pipe (Tandem Axles)
Two Lanes
Three Lanes ( ) ( ) IM IM P
1 +
(m) P
1 +
(m)
100
100
PLt3 =
PLt2 =
ALLt3
ALLt2 ( ) ( )
16.5
16.5
3 x 50000
1 +
(0.85)
2 x 50000
1 +
(1.0)
100
We can check multiple lanes for tandem axles as well.
Same result as for single axles. The single lane condition governs.
100
PLt3 =
PLt2 =
365.83
256.53
PLt2 = 454 psf
PL3 = 406 psf
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77. For Concrete Pipe, Load must be in
Terms of lbs/ft
WLt = PLtx * L
L = Smaller of Lx or Do
Lp < Ls < L2 < L3 < L4
Lp = ft. > Do
Do = 6 ft.
L = 6 ft.
WLt = 475 psf x 6 ft
WLt = 2850 lbs/ft Wt
Direction of Traffic
1 ft.
As mentioned a few slides ago, the live load spread lengths for tandem axles are the same as they are for the singe axle condition. They are all greater than the OD of the pipe, so simply multiply the highest pressure by the OD of the pipe to get the governing live load for the tandem axle application. Ls Do
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78. Governing Live Load
Live Load is the Maximum of the Single Axle or Tandem Load
WLs = 2874 lbs/ft
WLt = 2850 lbs/ft
WL = 2874 lbs/ft
We have found the governing live load from the single axle condition and the governing live load from the tandem axle condition. Now we take the maximum of these two and use it for our design.
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79. Determine the Live Load Bedding Factor
Table c-1
Pipe
Diameter, in
Fill Height, ft
< 2 ft
> 2 ft 12
3.2
2.4 18 24
30 and larger
2.2
We have a 60 inch pipe, so regardless of the depth, the live load bedding factor is 2.2.
BfLL = 2.2

80. Dead Load Values (Assuming Type 2 Installation)
WE = 4032 lbs/ft
WF = 1225 lbs/ft
Bfe = 2.83
Just so we have some values to complete our D-load design, I have provided the soil load, fluid load, and earth load bedding factors for a Type 2 Installation.
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81. ( ) ( ) Determine the D-Load D0.01 = 633 lbs/ft/ft 12
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Determine the D-Load ( ) ( ) 12
4032 lbs/ft lbs/ft
2874 lbs/ft
D = + 60
2.83
2.2
The D-load resulting from all of this is 633 lbs/ft.
So if you are 4 feet deep, a Class I pipe would be sufficient for live load when the direction of traffic is perpendicular to the span of the pipe.
The parallel direction may be a little more or a little less. I believe at this fill height for this particular pipe, the D-loads are very similar for both directions.
D0.01 = 633 lbs/ft/ft
Example Problem 1

82. Rigid Rugged Resilient
The ACPA fill height tables account for live load in either direction (parallel or perpendicular to the span) and take the worst case so that the user will not have to worry about the direction of traffic when using the tables.
We came up with a value of 633 lbs/ft in our example, while the fill height table has a value of 650 lbs/ft. This is easily explainable when we remember that the fill height tables used C-wall pipe and not B-wall, and the slightly larger OD of the pipe will result in a slightly larger live load on it. Additionally, the fill height table does not tell you which direction of traffic governed the value placed in the table, and it may be that the condition with traffic parallel to span governed.
In actuality, the live load for HL-93 traffic running parallel to the span of the pipe for a 60 inch C-wall pipe under 4 feet of fill is 650 lbs/ft and the live load for traffic running perpendicular to the same pipe is 644 lbs/ft; so the parallel condition governed in this case.
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83. Rigid Rugged Resilient
Checking the fill height table can give you a check to see if you are in the ballpark.
If you want a more exact check of your live load value, you can use Eriksson Pipe.
In this case we will check our 60 inch pipe with a 6 inch “B” Wall.
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84. Rigid Rugged Resilient
We have to choose the 7th Edition when analyzing the live load, even though we are designing for the 8th Edition. Eriksson Pipe was ahead of its time when incorporating the live loads.
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85. Rigid Rugged Resilient
If we are going to evaluate the condition where the pipe is traveling “perpendicular to the span”, then we will choose the direction of traffic “ALONG PIPE AXIS”, in Eriksson Pipe, since it uses a slightly different nomenclature, based on what PIPECAR had used previously.
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86. Rigid Rugged Resilient
The resulting live load is 2,875 lbs/ft, which matches our value of 2,874 lbs/ft on slide 78.
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87. The End
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88. The Latest NCHRP Live Load Research, 2010