Core Concepts for the Civil PE Exam:
Transportation Depth
Civil Morning Breadth and Transportation Depth Practice Problems and Quick Reference Manual
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PE Exam Transportation Depth

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40 Transportation Depth practice problems with detailed solutions!

Breakdown of relevant topics and example problems for all NCEES listed codes including AASHTO, AI, MUTCD, and HCM

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Civil PE Transportation Depth Online Study Guide
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Traffic Engineering
Sampling and Testing
First, we will discuss the layers of soil beneath the pavement. Below the top layer of either a wearing surface or rigid pavement is a layer called subbase. Subbase often consists of crushed stone material. The load is transferred through the subbase to the subgrade. Which is the soil native to the area. To effectively design the pavement, we must understand the characteristics of the subgrade.
The soil resilient modulus is essentially the modulus of elasticity of the soil. It can be determined either through lab tests, using samples, or estimated through soil strength parameters. There are two types of soil strength parameters, the California Bearing Ratio (CBR) and the Soil Resistance Factor (R). These can be correlated to the resilient modulus by the following equations from the AASHTO GDPS
MR=1500(CBR)
MR=1000+555R
Soil Stabilization Techniques
During the construction or rehabilitation of roadway projects, there is often a significant amount of grade change that may result in cut or fill volumes. Mass Diagrams are a graphical representation of the excavation or fill along a baseline. The cumulative volume in either cut or fill is shown on the Yaxis as a function of the length along the baseline. The mass diagram is often paired with or proceeded by a profile diagram. This is an elevation graph along the length of the baseline showing the existing and proposed profile. It is often useful to identify the points along a mass diagram in which the cumulative volume is zero. This represents a point where the cut and fill are equal cumulatively to that point. These points are called balance points.
Design Traffic Analysis and Pavement Design Procedures
The driving surface for vehicles must be durable so that it can handle the constant daily load from vehicle traffic. There are two types of pavement: flexible and rigid.
Flexible pavement is as the name suggests, a more elastic material to handle deformations due to loading and temperature changes. Bituminous pavement, or more commonly named asphalt, is the most common type of flexible pavement. It is mixed with aggregate similar to that of concrete with a bituminous binder. Bituminous can flex more under loading conditions making it more ideal in areas of less desirable subgrades. To design flexible pavement, the AASHTO Guide for the Design of Pavement Structures (GDPS) has the following layer thickness equation to determine the Structural Number. This is a number which encompasses all the properties and thicknesses of the pavement and subbase layers:
D = Layer thickness
a = Layer or strength coefficients
m = Drainage coefficients
The design of flexible pavement can also be determined from the AASHTO GDPS Figure 3.1
Rigid pavement is most often concrete. This type does not have the elasticity of the flexible pavement but is often provides more strength and durability. The AASHTO GDPS also has requirements for the design of rigid pavement. The equation for the design thickness is overly complicated for the exam and is often computed using computer models. AASHTO does however provide Figure 3.7, which has a flow chart for the design slab thickness based on a number of variables.
Pavement Evaluation and Maintenance Measures
Skid resistance is the ability of pavement to resist sliding of the tires for a vehicle. Skid resistance can often be quantified by using a Skid Number from the following equation:
F = Frictional resistance
W = Weight
Horizontal Design
Basic Curve Elements
Sight Distance Considerations
There are three types of sight distance for consideration:
Stopping sight distance is the distance it takes a driver to react to the need to stop and to apply the brakes. This is covered in detail in the morning session. AASHTO GDHS however does provide table 31 for quick reference based on standard values for perception reaction time and eye height.
Decision sight distance is, as it sounds, a distance required for the driver to make a decision to avoid an obstacle which has been recognized. This may involve changing lanes or going into the recoverable slope. These variables must be identified and can be classified by the GDHS into maneuver categories A through E. Table 33 provides decision sight distances based on the design speed and avoidance maneuver. The table values are from the following equations:
The last type is passing sight distance. This is the amount of distance for a vehicle to speed past a slower moving vehicle. GDHS provides Table 34 to determine the required distance based on design, slower, and faster vehicle speeds.
Objects or buildings which fall within a horizontal curve must be analyzed to ensure the sightline of the driver to a point further along the curve is not obstructed. This ensures appropriate horizontal clearance. The horizontal offset of a curve to an object is given by the following equation:
H = Offset
S = Horizontal sight distance
R = Radius of the curve
Superelevation
When a vehicle travels along a horizontal curve, there is a centrifugal force acting radially out on the vehicle. Roadways along a straight alignment are sloped away from the centerline. If the cross section remains the same along a curve, the combination of the radial force and the downslope may cause cars to tip or slide off the road. To counteract this, the crosssection transitions on the outside of the curve from having a downslope to having an upslope. This sloping is called superelevation. The rate of slope necessary to safely allow the car to cross the horizontal curve is the following equation:
e = Rate of superelevation
v = Velocity
R = Radius of curve
f = Friction factor
The transition to a fully superelevated section consists of two parts. The crown runoff (tangent runout) is the length over which the roadway transitions from its normal cross section to a flat grade. The second is the superelevation runoff which is the length over which the roadway transitions from flat to super elevated. The length of the superelevation runoff can be determined from the following equation:
W = Width of one lane
NL = Number of lanes
e = Rate of superelevation
Δ = Maximum relative gradient (GDHS Table 315)
bw = Lane adjustment factor (GDHS Table 316)
Special Horizontal Curves
Compound curves combine two horizontal curves together. To analyze, understand that the end of the first curve is the beginning of the second. Therefore:
PT1 = PC2 = PCC
The point in common is also called the Point of Continuing Curve (PCC)
Vertical Design
Sampling and Testing
First, we will discuss the layers of soil beneath the pavement. Below the top layer of either a wearing surface or rigid pavement is a layer called subbase. Subbase often consists of crushed stone material. The load is transferred through the subbase to the subgrade. Which is the soil native to the area. To effectively design the pavement, we must understand the characteristics of the subgrade.
The soil resilient modulus is essentially the modulus of elasticity of the soil. It can be determined either through lab tests, using samples, or estimated through soil strength parameters. There are two types of soil strength parameters, the California Bearing Ratio (CBR) and the Soil Resistance Factor (R). These can be correlated to the resilient modulus by the following equations from the AASHTO GDPS
MR=1500(CBR)
MR=1000+555R
Soil Stabilization Techniques
During the construction or rehabilitation of roadway projects, there is often a significant amount of grade change that may result in cut or fill volumes. Mass Diagrams are a graphical representation of the excavation or fill along a baseline. The cumulative volume in either cut or fill is shown on the Yaxis as a function of the length along the baseline. The mass diagram is often paired with or proceeded by a profile diagram. This is an elevation graph along the length of the baseline showing the existing and proposed profile. It is often useful to identify the points along a mass diagram in which the cumulative volume is zero. This represents a point where the cut and fill are equal cumulatively to that point. These points are called balance points.
Design Traffic Analysis and Pavement Design Procedures
The driving surface for vehicles must be durable so that it can handle the constant daily load from vehicle traffic. There are two types of pavement: flexible and rigid.
Flexible pavement is as the name suggests, a more elastic material to handle deformations due to loading and temperature changes. Bituminous pavement, or more commonly named asphalt, is the most common type of flexible pavement. It is mixed with aggregate similar to that of concrete with a bituminous binder. Bituminous can flex more under loading conditions making it more ideal in areas of less desirable subgrades. To design flexible pavement, the AASHTO Guide for the Design of Pavement Structures (GDPS) has the following layer thickness equation to determine the Structural Number. This is a number which encompasses all the properties and thicknesses of the pavement and subbase layers:
D = Layer thickness
a = Layer or strength coefficients
m = Drainage coefficients
The design of flexible pavement can also be determined from the AASHTO GDPS Figure 3.1
Rigid pavement is most often concrete. This type does not have the elasticity of the flexible pavement but is often provides more strength and durability. The AASHTO GDPS also has requirements for the design of rigid pavement. The equation for the design thickness is overly complicated for the exam and is often computed using computer models. AASHTO does however provide Figure 3.7, which has a flow chart for the design slab thickness based on a number of variables.
Pavement Evaluation and Maintenance Measures
Skid resistance is the ability of pavement to resist sliding of the tires for a vehicle. Skid resistance can often be quantified by using a Skid Number from the following equation:
F = Frictional resistance
W = Weight
Intersection Geometry
Hydrology
The rational method can be used to determine the flow rate from runoff of a drainage area. The equation is:
Q = ACi
Q = Flow Rate (cfs)
A = Drainage Area (Acres)
C = Runoff Coefficient
i = Rainfall Intensity (in/hr)
NRCS/SCS Runoff Method
This is an alternative method for determining runoff:
S = Storage Capacity of Soil (in.)
CN = NRCS Curve Number
Q = Runoff (in.)
Pg = Gross Rain Fall (in.)
Hydrograph development and applications, including synthetic hydrographs
Hyetographs – Graphical representation of rainfall distribution over time
Hydrograph – Graphical representation of rate of flow vs time past a given point often in a river, channel, or conduit. The area under the hydrograph curve is the volume for a given time period
Parts of a Hydrograph are shown graphically:
Unit Hydrographs can be determined by dividing the points on the typical hydrograph by the average excess precipitation.
Synthetic Hydrographs are created if there is insufficient data for a watershed. This method uses the NRCS curve number and is a function of the storage capacity.
tR = Storm duration (time)
Lo = Length overland (ft)
SPercentage = Slope of land
The equation for peak discharge from a synthetic hydrograph then is:
Hydraulics
Pressure conduits refer to closed cross sections that are not open to the atmosphere such as pipes:
The Darcy Equation is used for fully turbulent flow to find the head loss due to friction. The equation is:
hf = Head Loss due to friction (ft)
f = Darcy friction factor
L = Length of pipe (ft)
v = Velocity of flow (ft/sec)
D = Diameter of pipe (ft)
g = Acceleration due to gravity, (Use 32.2 ft/sec2)
The HazenWilliams equation is also used to determine head loss due to friction. Be aware of units as this equation may be presented in different forms. The most common is the following:
hf = Head Loss due to F\friction (ft)
L = Length (ft)
V = Velocity (gallons per minute)
C = Roughness coefficient
d = Diameter (in)
Openchannel flow
For open channel flow use the ChezyManning equation:
Q = Flow Rate (cfs)
n = Roughness Coefficient
A = Area of Water (ft2)
R = Hydraulic Radius (ft)
S = Slope (decimal form)
The hydraulic radius is the area of water divided by the wetted perimeter which is the perimeter of the sides of the channel which are in contact with water.
Hydraulic energy dissipation
A weir is a low dam used to control the flow of water. Weirs have shaped outlets notched into the top of the dam to allow water to flow out. The most common shapes are triangular and trapezoidal:
Triangular Weir
H = Height of water (ft)
θ = Weir angle
Trapezoidal Weir
b = Width of base (ft)
Broad Crested Weirs (Spillways)
Spillways are used to control the flow of excess water from a dam structure. Essentially they are large weirs and therefore can be called broad crested weirs. The calculation of discharge for spillways is taken as:
Cs = Spillway coefficient
There are many components used in the collection of stormwater. Some examples include:
Culverts: A pipe carrying water under or through a feature. Culverts often carry brooks or creeks under roadways. Culverts must be designed for large intensity storm events.
Stormwater Inlets: Roadside storm drains which collect water from gutter flow or roadside swales.
Gutter/Street flow: Flow which travels along the length of the street. Gutter flow can be approximated often by an adaptation of the Manning Equation:
Roadside and Cross Section Design
Forgiving Roadside Concepts
Drivers, for a number of reasons, may veer off the road whether it be distraction, fatigue, or to avoid collision. For proper roadway design, there needs to be a minimum horizontal distance so that the driver can safely return to the roadway unharmed. This horizontal distance which begins at the edge of the roadway is called the clear distance. The AASHTO Roadside Design Guide (RSDG) provides guidelines on the safety of cars which have traveled off of the roadway.
The land just outside of the roadway may not always be flat. The slope of the clear distance has an effect on the cars ability to safely recover. Slopes less than 1 Vertical to 4 Horizontal are considered recoverable slopes since the car’s ability to stop or maneuver will not be greatly affected by the slope. A nonrecoverable slope is one which is steeper than 1:4. If a nonrecoverable slope is present, the bottom of the slope must have a vehicle runout area which will allow the vehicle to stop. Table 31 of the AASHTO RSDG can be used to determine minimum clear distances based on slopes and design speeds.
When traveling on a horizontal curve, the cars traveling along the outside of the curve will struggle to recover moreso than a straight roadway due to the centrifugal force. Therefore, an adjustment factor needs to be applied to the clear zone on the outside of the curve only. The adjustment factor is found in table 32 of the AASHTO RSDG.
Barrier Design
Often objects outside of the roadway must fall within the clear zone. A barrier must be provided to both protect the object and prevent the vehicle from a collision. An appropriate barrier will minimize the damage to the vehicle and safely redirect it onto traffic. The runout length, LR, is the minimum distance away from an object that a vehicle may leave the roadway and strike the object. This will define the length of barrier needed. AASHTO RSDG Table 510b provides minimum values based on volume and design speeds. Barriers which are too close to the roadway may be troublesome to drivers and cause them to slow down. To prevent this, a minimum shy distance is provided in RSDG Table 57. The geometry of a barrier must be determined for a safe condition by the following equations:
LA = Distance from edge of road to back edge of object
b = Rise of taper slope
a = Run of taper slope
L1 = Length from object to beginning of flare
L2 = Distance from edge of road to face of barrier
LR = Runout Length
Crash attenuators can be used to prevent vehicles from crashing directly into an object or from entering an area which would be unsafe for the driver or pedestrians. When the vehicle strikes the attenuator, it begins to decelerate at a rate of the following equation:
F = Stopping force (lbs)
w = weight of vehicle (lbs)
d = Deceleration rate
g = Force due to gravity (32.2 ft/s2)
SF = Safety factor
Cross Section Elements
While a roadway often has to fit the area and purpose of its proposed location, the geometric features must meet certain minimum and maximum values. The Policy on Geometric Design of Highways and Streets provides a large number of requirements for the design of a roadway or walkway cross section. For the PE exam it is best to become familiar with the location of these requirements and most importantly be able to find them quickly since it is unreasonable to be expected to memorize all values.
ADA Design Considerations
The American Disabilities Act of 1990 outlines the requirements for structures to ensure proper treatment of individuals with disabilities. The guidelines outline many topics including parking, ramps, egress and others and the requirements which must be met to ensure the proper accessibility and safety. For the PE exam you will likely be asked a question or two requiring you to lookup certain aspects of the code. You should not spend excessive amounts of time reading the code but be familiar with the sections and be able to navigate and find information quickly.
Signal Design
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Traffic Control Design
Sampling and Testing
First, we will discuss the layers of soil beneath the pavement. Below the top layer of either a wearing surface or rigid pavement is a layer called subbase. Subbase often consists of crushed stone material. The load is transferred through the subbase to the subgrade. Which is the soil native to the area. To effectively design the pavement, we must understand the characteristics of the subgrade.
The soil resilient modulus is essentially the modulus of elasticity of the soil. It can be determined either through lab tests, using samples, or estimated through soil strength parameters. There are two types of soil strength parameters, the California Bearing Ratio (CBR) and the Soil Resistance Factor (R). These can be correlated to the resilient modulus by the following equations from the AASHTO GDPS
MR=1500(CBR)
MR=1000+555R
Soil Stabilization Techniques
During the construction or rehabilitation of roadway projects, there is often a significant amount of grade change that may result in cut or fill volumes. Mass Diagrams are a graphical representation of the excavation or fill along a baseline. The cumulative volume in either cut or fill is shown on the Yaxis as a function of the length along the baseline. The mass diagram is often paired with or proceeded by a profile diagram. This is an elevation graph along the length of the baseline showing the existing and proposed profile. It is often useful to identify the points along a mass diagram in which the cumulative volume is zero. This represents a point where the cut and fill are equal cumulatively to that point. These points are called balance points.
Design Traffic Analysis and Pavement Design Procedures
The driving surface for vehicles must be durable so that it can handle the constant daily load from vehicle traffic. There are two types of pavement: flexible and rigid.
Flexible pavement is as the name suggests, a more elastic material to handle deformations due to loading and temperature changes. Bituminous pavement, or more commonly named asphalt, is the most common type of flexible pavement. It is mixed with aggregate similar to that of concrete with a bituminous binder. Bituminous can flex more under loading conditions making it more ideal in areas of less desirable subgrades. To design flexible pavement, the AASHTO Guide for the Design of Pavement Structures (GDPS) has the following layer thickness equation to determine the Structural Number. This is a number which encompasses all the properties and thicknesses of the pavement and subbase layers:
D = Layer thickness
a = Layer or strength coefficients
m = Drainage coefficients
The design of flexible pavement can also be determined from the AASHTO GDPS Figure 3.1
Rigid pavement is most often concrete. This type does not have the elasticity of the flexible pavement but is often provides more strength and durability. The AASHTO GDPS also has requirements for the design of rigid pavement. The equation for the design thickness is overly complicated for the exam and is often computed using computer models. AASHTO does however provide Figure 3.7, which has a flow chart for the design slab thickness based on a number of variables.
Pavement Evaluation and Maintenance Measures
Skid resistance is the ability of pavement to resist sliding of the tires for a vehicle. Skid resistance can often be quantified by using a Skid Number from the following equation:
F = Frictional resistance
W = Weight
Geotechnical and Pavement
Hydrology
The rational method can be used to determine the flow rate from runoff of a drainage area. The equation is:
Q = ACi
Q = Flow Rate (cfs)
A = Drainage Area (Acres)
C = Runoff Coefficient
i = Rainfall Intensity (in/hr)
NRCS/SCS Runoff Method
This is an alternative method for determining runoff:
S = Storage Capacity of Soil (in.)
CN = NRCS Curve Number
Q = Runoff (in.)
Pg = Gross Rain Fall (in.)
Hydrograph development and applications, including synthetic hydrographs
Hyetographs – Graphical representation of rainfall distribution over time
Hydrograph – Graphical representation of rate of flow vs time past a given point often in a river, channel, or conduit. The area under the hydrograph curve is the volume for a given time period
Parts of a Hydrograph are shown graphically:
Unit Hydrographs can be determined by dividing the points on the typical hydrograph by the average excess precipitation.
Synthetic Hydrographs are created if there is insufficient data for a watershed. This method uses the NRCS curve number and is a function of the storage capacity.
tR = Storm duration (time)
Lo = Length overland (ft)
SPercentage = Slope of land
The equation for peak discharge from a synthetic hydrograph then is:
Hydraulics
Pressure conduits refer to closed cross sections that are not open to the atmosphere such as pipes:
The Darcy Equation is used for fully turbulent flow to find the head loss due to friction. The equation is:
hf = Head Loss due to friction (ft)
f = Darcy friction factor
L = Length of pipe (ft)
v = Velocity of flow (ft/sec)
D = Diameter of pipe (ft)
g = Acceleration due to gravity, (Use 32.2 ft/sec2)
The HazenWilliams equation is also used to determine head loss due to friction. Be aware of units as this equation may be presented in different forms. The most common is the following:
hf = Head Loss due to F\friction (ft)
L = Length (ft)
V = Velocity (gallons per minute)
C = Roughness coefficient
d = Diameter (in)
Openchannel flow
For open channel flow use the ChezyManning equation:
Q = Flow Rate (cfs)
n = Roughness Coefficient
A = Area of Water (ft2)
R = Hydraulic Radius (ft)
S = Slope (decimal form)
The hydraulic radius is the area of water divided by the wetted perimeter which is the perimeter of the sides of the channel which are in contact with water.
Hydraulic energy dissipation
A weir is a low dam used to control the flow of water. Weirs have shaped outlets notched into the top of the dam to allow water to flow out. The most common shapes are triangular and trapezoidal:
Triangular Weir
H = Height of water (ft)
θ = Weir angle
Trapezoidal Weir
b = Width of base (ft)
Broad Crested Weirs (Spillways)
Spillways are used to control the flow of excess water from a dam structure. Essentially they are large weirs and therefore can be called broad crested weirs. The calculation of discharge for spillways is taken as:
Cs = Spillway coefficient
There are many components used in the collection of stormwater. Some examples include:
Culverts: A pipe carrying water under or through a feature. Culverts often carry brooks or creeks under roadways. Culverts must be designed for large intensity storm events.
Stormwater Inlets: Roadside storm drains which collect water from gutter flow or roadside swales.
Gutter/Street flow: Flow which travels along the length of the street. Gutter flow can be approximated often by an adaptation of the Manning Equation:
Drainage
Hydrology
The rational method can be used to determine the flow rate from runoff of a drainage area. The equation is:
Q = ACi
Q = Flow Rate (cfs)
A = Drainage Area (Acres)
C = Runoff Coefficient
i = Rainfall Intensity (in/hr)
NRCS/SCS Runoff Method
This is an alternative method for determining runoff:
S = Storage Capacity of Soil (in.)
CN = NRCS Curve Number
Q = Runoff (in.)
Pg = Gross Rain Fall (in.)
Hydrograph development and applications, including synthetic hydrographs
Hyetographs – Graphical representation of rainfall distribution over time
Hydrograph – Graphical representation of rate of flow vs time past a given point often in a river, channel, or conduit. The area under the hydrograph curve is the volume for a given time period
Parts of a Hydrograph are shown graphically:
Unit Hydrographs can be determined by dividing the points on the typical hydrograph by the average excess precipitation.
Synthetic Hydrographs are created if there is insufficient data for a watershed. This method uses the NRCS curve number and is a function of the storage capacity.
tR = Storm duration (time)
Lo = Length overland (ft)
SPercentage = Slope of land
The equation for peak discharge from a synthetic hydrograph then is:
Hydraulics
Pressure conduits refer to closed cross sections that are not open to the atmosphere such as pipes:
The Darcy Equation is used for fully turbulent flow to find the head loss due to friction. The equation is:
hf = Head Loss due to friction (ft)
f = Darcy friction factor
L = Length of pipe (ft)
v = Velocity of flow (ft/sec)
D = Diameter of pipe (ft)
g = Acceleration due to gravity, (Use 32.2 ft/sec2)
The HazenWilliams equation is also used to determine head loss due to friction. Be aware of units as this equation may be presented in different forms. The most common is the following:
hf = Head Loss due to F\friction (ft)
L = Length (ft)
V = Velocity (gallons per minute)
C = Roughness coefficient
d = Diameter (in)
Openchannel flow
For open channel flow use the ChezyManning equation:
Q = Flow Rate (cfs)
n = Roughness Coefficient
A = Area of Water (ft2)
R = Hydraulic Radius (ft)
S = Slope (decimal form)
The hydraulic radius is the area of water divided by the wetted perimeter which is the perimeter of the sides of the channel which are in contact with water.
Hydraulic energy dissipation
A weir is a low dam used to control the flow of water. Weirs have shaped outlets notched into the top of the dam to allow water to flow out. The most common shapes are triangular and trapezoidal:
Triangular Weir
H = Height of water (ft)
θ = Weir angle
Trapezoidal Weir
b = Width of base (ft)
Broad Crested Weirs (Spillways)
Spillways are used to control the flow of excess water from a dam structure. Essentially they are large weirs and therefore can be called broad crested weirs. The calculation of discharge for spillways is taken as:
Cs = Spillway coefficient
There are many components used in the collection of stormwater. Some examples include:
Culverts: A pipe carrying water under or through a feature. Culverts often carry brooks or creeks under roadways. Culverts must be designed for large intensity storm events.
Stormwater Inlets: Roadside storm drains which collect water from gutter flow or roadside swales.
Gutter/Street flow: Flow which travels along the length of the street. Gutter flow can be approximated often by an adaptation of the Manning Equation:
Engineering Economics
LAUFENDE STEUERBERATUNG