Civil Professional Engineer Study Guides

Quantity Take off Methods

Quantity take-off methods are a means for estimating the cost of each aspect of a project. A project consists of many activities and materials all of which are accounted for as items of a project. For example, a project may involve the construction of a retaining wall. There are many activities and materials associated to complete this. Some include excavation, formwork, concrete for the wall, reinforcing steel etc. When contract drawings and specifications are developed, all of these items must be identified. All items also must include a quantity associated it's them to indicate the amount or extent of work for the item. These quantities must be defined by a particular unit of measure which must be appropriate for the action or material. Taking excavation as an example of an item, there must be an amount of excavation associated with it. Since excavation involves removing a volume of material, the most appropriate unit is cubic yard or cubic feet. To estimate the cost of the project, each item has a price per unit associated with it. This price is determined by previous similar work and taking into account the specifics of the particular project. Below is an example of the breakdown of some items associated with an example retaining wall project:

Cost Estimating

Project Schedules

Project schedules must be set and maintained to ensure it remains on time and on budget. To determine a project schedule, all tasks must be identified and the length of time (durations) for each task must be estimated. These tasks can then be sequenced by determining what the appropriate order of tasks are. Some tasks must be completed before others can begin. These tasks are defined as predecessors. See the example chart below indicating identified tasks, durations, and predecessors: This information can then be visualized by producing and activity diagram. First begin by drawing tasks. Start with A: Then determine which tasks have A as a predecessor. Draw these tasks as well with arrows indicating these tasks are connected: Continue in the same manor with each task. The final chart is as follows: Then you can determine the critical path of the project. The critical path is defined as the sequence of tasks which would yield the shortest amount of time to complete the project. If the duration of any task on the critical path is changed, the duration of the entire project will change. In the example above you can determine the critical path by identifying all paths and the critical one is the longest sum of duration. Therefore the possible paths are A-B-D, A-B-E, and A-C-E which have total durations of 6, 7, and 6. Therefore the critical path is A-B-E. A change in duration of non-critical tasks will only change the project duration if the change creates a longer path than the existing critical one.

Activity Identification and Sequencing

The appropriate steps in the proper sequence need to be identified to complete a project. This involves understanding all the tasks involved in a specific project type and providing a timeline of events to properly facilitate the successful completion of the project. There are many types of projects and the specifics can vary. For the purposes of the PE Exam, it is important to have a general knowledge of common construction tasks and sequences. Below are some examples of design and construction tasks divided by when they occur in certain project phases: Pre-Design/Design/Project Award - Owner initiates project - Owner hires Architect/Engineer or uses In-House Architect/Engineer - Contract documents and specifications are developed - Contractors bid on the project - Project is awarded Pre-Construction - Contractor submittals are reviewed and approved - Sub-Contractors hired - Site survey, staking, and layout - Procurement of materials Construction - Traffic Control, water handling, etc. installed if necessary - Crane set up and positioning - Temporary earth retaining systems installed if necessary - Excavation - Formwork or Erection - Testing of materials - Installation of rebar - Pouring of concrete - Concrete curing - Backfill Post-Construction - Semi Final/Final Inspections - Open road to traffic - Punch-Lists - As-Built drawings

Construction Loads

Construction loads are temporary loads, occurring within the duration of a project, imposed on a structure which may be partially or fully complete. This may include materials, personnel, equipment, or temporary structures. The concern for construction loads is to understand the different types of stresses they may impose on members as opposed to the final in-place condition of those members and ensure they are designed to handle these forces. Materials: Storage of materials is an often overlooked aspect of a project. Rebar, excavated materials, or other building materials need to be stored in an accessible location and will often impose a large additional dead load on the structure. Temporary Structures: Temporary structures may often be needed to either provide additional support to unstable members or access for personnel to continue the erection process. Temporary structures may also be for the housing of materials or personnel. Equipment: Equipment is often needed for various construction activities such as welding or painting procedures. The weight and distribution of these loads should be accounted for. Cranes: Cranes can also be considered equipment however special attention should be given to the sequencing of erection based on the cranes reach. Members in Temporary Conditions: Along with additional dead load, construction can introduce stresses into members for which they are not designed. Some examples include the erection of a precast member such as a wall panel which may be designed for compression but will see some flexure about its weak axis while it is being picked and placed. Also, the first steel girder in a bridge before it is connected to the others through diaphragms will be unstable and must be temporarily supported. In these conditions, design measures need to be taken even though they are not required for the final condition.

Construction Methods

Steel: Strong and durable material. Steel has the capabilities to be used for long span bridges and high rise buildings. Steel members are manufactured using either the hot-rolled or cold-formed methods. Steel members are provided in predetermined shapes. Some examples include W-, S-, C, and HSS-shapes. Steel is connected and constructed by the use of bolted or welded connections. The advantages of steel are again the ability to span long distances and the weight of the members compared to the strength is relatively low. Some disadvantages include the high cost, lack of ability to form unique shapes, and tendency of the material to corrode. When steel is exposed to salts, a chemical reaction occurs causing the steel to rust and even loose section properties. To counteract corrosion some preventive measures are paint systems, coating systems such as galvanizing, or weathering steel. Reinforced Concrete: Concrete is strong in compression but weak in tension. However it has the ability to bond to reinforcing steel to appropriately resist tension. Reinforced concrete is used in buildings and shorter span bridges or certain components of bridges. Some common applications are foundation elements, bridge decks and parapets, or retaining walls. The advantage of concrete is it can be formed to any shape or aesthetic look with proper formwork and is strong in compression. The disadvantages however are that concrete has a high self-weight, will likely crack, and has a limited span length. The reinforcing in concrete can also corrode and cause pop-outs or spalls. Precast/Prestressed/Post-Tensioned Concrete: Precast concrete is concrete which is cast somewhere other than its final location, either at a plant or another area on the construction site, and is then stripped from its forming, transported to the site, and erected. Prestressed concrete is precast concrete which has been pre-compressed using steel strands with high elasticity. The strands are tensioned to a design force before the concrete is cast. Then the concrete mix is placed and cured. The strands are then cut at the ends. Since the strands have a high elasticity, they will try to return to their original state. However since the stands are now bonded to the concrete, there is a compressive force transferred to the concrete. This force will oppose the stresses caused by bending. Post-Tensioned concrete uses the same concept as prestressed concrete. However, the concrete member is cast first and the strands are tensioned through the member using plastic tubes embedded along the length of the member. The tube is then grouted and the strands are cut to transfer the force. Precast Concrete will have the lowest tensile capacity and therefore is used for the lowest spans. Precast is often used for compression members or bridge deck units. Prestressed Concrete is be able to span larger distances and is used for floor members. It is common in parking garages as double-tee shapes for floor members or for long span bridges with common shapes such as prestressed bulb tees. Post tensioned concrete is not as common and is used for much larger spans. Precast concrete advantages are the quality of concrete is often better under plant controlled conditions and the construction is much quicker. The disadvantages are there is a higher cost than reinforced concrete due to shipping and erection expenses and the tendons also are susceptible to corrosion. Wood: Relatively low strength material. Wood is often used in residential applications or for very small span bridges. Wood is extremely cheap and lightweight for erection. In addition to the low strength, wood also will deteriorate due to rot and is highly sensitive to fire damage. Masonry: Can be reinforced or unreinforced. Masonry is also strong in compression but weak in tension. Only used in small retaining wall applications and some older bridges still are composed of masonry components.

Temporary Structures

Structures which are built for a specific purpose, often to facilitate an aspect of a construction project, and are removed before the conclusion of the project are temporary structures. Some examples include: - Temporary Buildings: May be used for storage or offices during construction. - Scaffolding: Temporary elevated platforms which provide access to perform certain tasks. - Temporary Supports and Shoring: Often forces are introduced during construction which are not the same as the final in-place conditions. In these situations temporary supports are needed to keep structural members stable until the construction can be complete. - Temporary earth retaining systems: When excavation is needed, there is often not enough room to safely dig to the required depths. There may be a need to support traffic or adjacent facilities during the excavation. In these cases temporary earth retaining is required. Some examples include sheet piles, concrete blocks, or trench boxes. - Formwork: Concrete formwork is used to place concrete to the desired shape and will remain in place until the mix has cured to the desired strength. -Cofferdams: A wall constructed to prevent the flow of water to a specific area. Can be made of sandbags, sheet piling, or other materials.

Lateral Earth Pressure

Soil Consolidation

Settlement is when the soil supporting the foundation consolidates which causes a decrease in volume and a drop in elevation. This causes the foundation to no longer be fully supported and will introduce additional stress. There are three phases of settlement: 1. Immediate Settling or Elastic Settling: This settlement occurs immediately after the structure is built. The load from the structure causes instant consolidation of the soil. This is the main component of settlement in sandy soil conditions. 2. Primary Consolidation: A more gradual consolidation which is due to water leaving the voids over time. This is mostly a factor only in clayey soils. 3. Secondary Consolidation: Also occurs at a very gradual rate. This is due to the shifting and readjustment of soil grains. Most often this is the lowest magnitude of consolidation phases.

Effective Stress

Bearing Capacity

For shallow foundations, the soil below must be suitable to support the load transferred through the footing. Different types of soils have different bearing capacities. Sand is often a good foundation material. Sand undergoes some small immediate settlement and then stabilizes since it drains quickly. Clay generally is poor in bearing capacity. Clays do not drain quickly and will retain water for longer periods of time leading to long-term settlements. Most soils in reality are some combination of sands, clays, and silts which will behave somewhere in-between sand and clay. Exceeding the allowable bearing capacity of a soil will cause shear failure or excessive settlements. Bearing capacity is determined using the Terzaghi-Meyerhof equation:

Slope Stability

Dead and Live Load

Dead Loads: Loads which are permanent in the final condition of the structure. Examples include self weight and additional permanent loads (such as pavement). Dead load factors are often lower than other types of loads. This is due to the higher level of reliability being able to predict the magnitude and character of these loads. Live Loads: Loads which will or may change over time. In general live loads represent pedestrian or vehicle loads. The load factor for live loads is often much higher due to the unpredictability. In LRFD different types of loads are factored to represent a safety factor based on the reliability of our ability to accurately predict certain loading conditions. If only Dead and Live loads are present, the likely load combination is: 1.2D + 1.6L

Trusses

Trusses are structural members used to span long distances. Trusses are built up by members which are only in axial tension or axial compression. They can be analyzed by the method of joints as illustrated below. Consider the example truss with nodes labeled. To design, the axial force in each member must be determined. If we wanted to find the force in member BD, first like a typical beam, the reactions at A and B can be found by summing forces. Then take a free body diagram of only the joint at A. This is shown below. In summing vertical reactions and since the reaction at A was found, the force in AC can be determined. Then there are only 2 horizontal forces and the force in AB can be found: Then take a free body diagram of Joint B as shown below. Since there are only two horizontal forces, the axial force in member BD can then be determined: The remainder of the truss can be analyzed similarly. Zero force members: When determining how many 0-Force members a truss has, analyze each joint individually as a free body diagram and follow these guidelines: In a joint with 2 members and no external forces or supports, both members are 0-force In a joint with 2 members and external forces, If the force is parallel to one member and perpendicular to the other, then the member perpendicular to the force is a 0-force member. In a joint with 3 members and no external forces, if 2 members are parallel then the other is a 0-force member All other members are non-zero.

Bending Stress

Bending Stress Mc/I M = Applied Moment c = Distance from the Centroid of the Cross Section to the Desired Location of Stress I = Moment of Inertia of the Cross Section

Shear Stress

Shear stress at any point along a beam is the shear at that point over the area. t = V/A V = Shear at the point of interest A = Cross sectional area There is also horizontal shear stress due to bending Horizontal shear stress t = VQ/Ib V = Applied Shear Force (kips) Q = First Moment of the Desired Area = ay. a = Cross Sectional Area from Point of Desired Shear Stress to Extreme Fiber (in2) y = Distance from Centroid of Beam to Centroid of Area “a” (in) I = Moment of Inertia of Beam (in3) b = Width of Member (in)

Axial Stress

Axial Stress: P/A P = Applied Force A = Cross Sectional Area

Deflection

Deflection is the degree to which an element is displaced under load. Common equations for the maximum deflection of beams can be found in the Beam Chart

Beams

The chart below shows reactions, moments, and max deflections for common beam types: Shear and Moment Diagrams Shear and moment diagrams are a graphical representation of the forces applied along the length of a beam. The following rules are used to develop shear diagrams: -A concentrated force causes a jump In the shear diagram of equal magnitude -A distributed load causes a line in the diagram with slope equal to the distributed load -Forces up are positive and down is negative This is depicted graphically below: The following are rules for construction of a moment diagram: -The moment at any point on the graph is equal to the area under the shear diagram up to this point -An isolated moment causes a jump in the diagram of equal magnitude -The shear at any point in the beam is equal to the slope of the same point on the moment diagram -A distributed load will cause a parabolic moment diagram curve

Columns

Slabs

One way slabs: Slabs are structural elements whose length and widths are large compared to the thickness. Slabs are often used as floors or as foundation elements. Flexure: Slabs must be analyzed by simplified methods due to the indeterminacy of a full analysis. The most common of which is to analyze as a 1- foot wide strip and treat the span length as a beam. Transverse reinforcement is necessary to control temperature and shrinkage. Shear: Shear in slabs is also determined by taking one foot wide sections to analyze as a beam. However often shear will not control.

Footings

Retaining Walls

Retaining walls are built to facilitate an immediate change in elevation. Some uses are to support roadways or a need for a wide, level area to be formed from a sloping existing grade. Retaining walls are designed to resist lateral loads from active earth pressure (see geotechnical section for computation of these loads) and surcharge loads which is any additional load imposed on the soil above, which when close enough will cause an additional pressure on the load due to the distribution of this load through soil. The stem of retaining walls can be analyzed as a cantilever beam extending vertically from the footing. The footing is composed of the toe which is the portion on the side of the lower elevation of soil and the heel which is portion on the side of the higher elevation of soil. Retaining walls are analyzed on a per foot width: Moment at base of stem= Mstem=Rahya Rah = Horizontal Active Earth Pressure per ft Width ya = Eccentricity of Horizontal Active Earth Pressure For shear, the critical section is a distance, d, from the base of the stem where d is the distance from the main flexural reinforcement (Heel side) to the extreme compression face (Toe side): Vstem=Rah

Open Channel Flow

For open channel flow use the Chezy-Manning equation: Q = Flow Rate (cfs) n = Roughness Coefficient A = Area of Water R = Hydraulic Radius 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.

Stormwater Collection

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 or gutter. Storm Sewer Pipes: Pipes installed under the road which carry the water from inlets to a suitable outlet. The principle of Conservation of Flow is often applicable when analyzing drainage. It states that the flow in must equal a flow out and therefore: Q1 + Q2 = Q3

Storm Characteristics

Storm characteristics include duration, total volume, and intensity. Duration: The length of time of a storm. Often measured in days and hours. Total Volume: The entire amount of precipitation throughout the duration of the storm in a defined area. Storm Intensity: Total volume of the storm divided by the duration of the storm event. Intensities can be averaged over the entire storm or at shorter intervals to provide instantaneous high intensity portions of the storm. Hyetographs are bar graphs used to measure instantaneous rainfall intensities over time. A design storm must be specified when performing any calculations. The design storm is defined by its recurrence interval which is the given amount of time it is likely to see a storm of a certain intensity. Design storms are often 10, 20, 50, or 100-year storms meaning a storm of a certain intensity would only occur once within the given duration. 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. Parts of a Hydrograph are shown graphically:

Runoff Analysis

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) For total flow from multiple areas to a single outlet the conservation of flow principle is applied and the total is the sum of all flow into the outlet. Time of Concentration, tc: The time of travel for water to move from the hydraulically most remote point in a watershed to the outlet. The time of concentration is the sum of three components: tc=tsheet+tshallow+tchannel For approximately the first 300 ft, water moves as sheet flow:

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.)

Detention and Retention Ponds

Detention and retention ponds are often used to collect water for flood control and stormwater runoff treatment. Detention Ponds: Also known as dry ponds. These are ponds which are often kept dry except during flood events. The pond will fill up during increased precipitation to control the flow intensity. This is common in dry, arid or urban areas to prevent excessive flooding. The ponds typically will be designed to hold water for about 24 hours. Detention ponds also controls the amount of sediment since it is captured in the pond and then typically becomes accessible after the pond has dried. Retention Ponds: Also called wet ponds since they contain a volume of water at all times. The elevation of the water will vary depending on precipitation but will always maintain a permanent amount of water based on low flow conditions. This allows sediment control since the deposits will settle to the bottom and allow for collection.

Pressure Conduits

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 Hazen-Williams 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 Friction (ft) L = Length (ft) V = Velocity (gallons per minute) C = Roughness Coefficient d = Diameter (ft) In addition to these losses, there is also what is called minor losses of energy due to friction Minor Losses – Friction losses due to fittings in the line, changes in the dimensions of the pipe, or changes in direction Minor losses can be calculated as per the Method of Loss coefficients. Each change in the flow of pipe is assigned a loss coefficient, K Loss coefficients for fittings are most often determined and provided by the manufacturer Loss coefficients for sudden changes in area must be determined: For Sudden Expansions: For Sudden Contractions: D1=Smaller diamter pipe Loss coefficients are then multiplied by the kinetic energy to determine the loss.

Bernoulli Energy Equation

The Bernoulli equation for the conservation of energy states that the total energy is equal to the sum of the pressure + kinetic energy + potential energy and is conserved at any point in the system. Therefore: Epr = Pressure = p Ev = Kinetic Energy = v2/2g v = Velocity (ft/s) g = Acceleration Due to Gravity (32.2 ft/s2) Ep = Potential Energy = z = Height above point of interest to surface of water (ft)

Horizontal Curves

Vertical Curves

Traffic Volume

The following are traffic volume factors. It is important to note for how many lanes and directions the values represent: Average Daily Traffic, ADT: Average number of vehicles per day over a given time period. Average Annual Daily Traffic, AADT: Average number of vehicles per day over a year. Typically it is calculated by dividing the total volume of vehicles in a year by 365 days. Average Daily Truck Traffic, ADTT: Average number a trucks per day in a given time period. Design Hour Volume, DHV: The hour of volume used in design. K-factor, K: The ratio of the Design Hour Volume to the Average Annual Daily Traffic (DHV/AADT). Directional Factor, D: Percentage of volume for the dominant direction of traffic during peak flow. Directional Design Hour Volume, DDHV: The product of the Directional Factor and the Design Hour Volume. Rate of Flow, v: Equivalent hourly rate at which vehicles pass a given point during a given time interval. The time frame is often taken as 15 min. Design Capacity: Maximum volume a given roadway can handle. Ideal Capacity, c: Ideal amount of volume for a given roadway. For freeways this is often taken as 2400 passenger cars per hour per lane (pcphpl). Volume to capacity ratio: Volume over capacity, v/c Peak Hour Factor, PHF: Ratio of the peak hour volume to the peak rate of flow in that hour:

Vehicle Dynamics

The distance it takes a driver to stop after recognizing an obstruction is the sum of two components. The first is before breaking and the second is after breaking. This is represented in the following equation: The first component assumes the velocity is constant during the perception reaction time which is the time it takes the driver to recognize the obstruction and begin the breaking process. This is calculated by: vtp where v = Velocity (ft/s) tp = Perception Reaction Time (seconds) The stopping distance during the breaking process is the following: sb = v2mph/(30(f+G)) v = Velocity (miles per hour) f = Friction Factor with the Pavement G = slope (positive for uphill and negative for downhill) To convert the velocity from ft/s to mi/hour where applicable multiply by: (3600 s/hr)/(5280 ft/mi)

Soil Classification

Soil Properties

The strength of soil is often determined by the standard penetration test. This measures the resistance to penetration using a standard split spoon sampler which is hit by a 140 lb hammer dropped from 30” high. The number of blows required to drive the sampler 12” after an initial penetration of 6” is referred to as the N-Value. Permeability of a soil is a measure of continuous voids. The flow rate of water through soil depending on its permeability can be measured by Darcy’s Law:

Concrete Properties

Concrete consists of cement, coarse aggregate, fine aggregate, and water. Additionally concrete may contain admixtures to enhance a certain desirable aspect of the target product. Some properties of concrete include: Concrete Strength, f’c,: The design compressive strength of the concrete. In general this will range from 3000 to 6000 psi. However strengths can be much higher such as 20,000 psi with proper mixing and additives. sqrt = square root Modulus of Elasticity (Normal weight concrete), Ec = 57,000 sqrt(f'c) Modulus of Rupture or the tensile strength, fr = 7.5sqrt(f'c) While the tensile strength of concrete is ignored in flexure, this is often used in cracking analysis. Water to Cement ratio, w/c, is the amount of water to the amount of cement in a given mix. In general the w/c ratio is inversely proportional to the strength since the higher amount of cement, the stronger the mix. Cement Types: Type I – General use cement. When special properties are not desired Type I can be used. Type II – Used in areas where sulfate attack is a concern. This is often in areas exposed to groundwater such as drainage structures. Type II will cure at a slower rate and therefore produce less heat than other types and gain strength at a slower rate. Type III – High early strength concrete. As opposed to type II or IV, a large amount of heat is released quickly and therefore is not suitable for mass-type pours. Type III is used in concrete where rapid strength gain is desirable such as precast concrete. Type IV – Low heat of hydration. Gains strength slowly and generates a low amount of heat. Often used for mass-pours such as mat foundations or large retaining walls.

Structural Steel

Yield Strength, Fy: Stress at which the steel will yield and begin to cause permanent deformations. Ultimate Strength, Fu: Stress at which the steel will fracture or fail in brittle behavior. Modulus of Elasticity, Es = The tendency of a material to deform when subjected to forces. Also is the ratio of stress over strain. Often in structural steel it is assumed to be taken as 29,000 ksi Ductility: Measure of a materials ability to deform before failure. Ductility is the ratio of ultimate failure strain to yielding strain. Toughness: The ability to withstand high stresses without fracturing. Hardness: The ability of a material to resist surface deformation.

Material Test Methods and Spec Conformance

Concrete: Strength tests: Most often strength is determined by loading cylinders often 6” in diameter to failure and recording the results. Slump Test: Measure of the consistency and workability of a batch of concrete. A cone about 6” in diameter on the wide end and 12” tall is filled with concrete. The filled cone is placed on the ground and then removed to allow the concrete to naturally disperse. The remaining height and diameter of the concrete mix is measured and recorded. Steel: Tensile Test: Axially loading a steel member to recorded the strain in the member as the load increases. From this test the yield strength, ultimate strength, and stress strain curve can be determined. When the applied stress exceeds the yield strength, the member will undergo plastic deformation and the cross sectional area will reduce until the member fractures. This is known as necking. Fatigue Testing: Fatigue is damage caused by repeated cycles of loading. Even though the stress in fatigue is less than the yield strength of the member, the repetition over a long period of time can cause failure. A fatigue test measures the ability of a member to resist repeated cycles of stress at a given magnitude. Scratch Hardness Test: Also known as Mohs Test. Compares the hardness of a material to that of minerals. Minerals of known and increasing hardness are used to scratch the sample and results are observed. Charpy V-Notch Test: Measure of a member’s toughness. A member is given a 45 degree notch and a pendulum is used to hit the opposite side of the member. This is performed at different heights and magnitudes until the member fails.

Compaction

Compaction is the reduction of voids in a mass of soil. The more compacted a mass of soil is, the more stable and stronger it is to support a structure. Compaction is done by placing soil in layers called lifts and using equipment to mechanically apply weight and potentially vibration to the lifts. Some types of compaction equipment are Grid Rollers for rocky soil, sheep foot rollers for cohesive soils, or roller compactors with vibration capabilities for cohesion less soils. When soil is compacted, the volume decreases. This is referred to as shrinkage. To calculate the compacted volume of a soil mass from its volume in its natural state use the following equation:

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Excavation

The most common method for determining the volume of excavation for cut and fill is the average end area method: V = L(A1+A2)/2 L = Distance Between Area 1 and 2 (ft) A1 and A2 = Respective Cross-Sectional Areas (ft2)

Construction Site Layout

Construction sites are surveyed and markers are placed to indicate measurements and control points. These points are designated in the field by the use of stakes. These stakes can be called construction stakes, alignment stakes, offset stakes, grade stakes, or slope stakes depending on what they are meant to indicate. The accuracy of dimensions depends on the intent. Some accuracy requirements are shown below:

Soil Erosion and Sediment Control

During construction activities involving excavation, there can be a significant amount of soil erosion leading to a dispersion of sediment. This needs to be controlled to prevent a negative impact to the surrounding areas. There are a number of options for sediment control: Silt Fences: Fences consisting of a geotextile fabric and posts which allow the passing of runoff water but will catch the suspended sediment. They will be placed at the bottom of slopes and/or at the perimeter of the job sites at low points. Hay Bales: Placed at the toe of slopes to help control runoff. Bales should be embedded in the ground and anchored securely with wooden posts. Erosion Control Fabric: Geotextile fabric used for the control of erosion on steep slopes. Often these are used on piles of excavated material. Temporary Seeding and Mulch: This involves seeding and mulching slopes to create growth that can control erosion due to the roots holding together soil. This is often used as a permanent measure for cut slopes. Slope drain: A drain constructed to direct water to a specified area. The drain can be constructed with numerous materials such as plastic or metal pipes and concrete or asphalt. Drains must be properly anchored to resist forces from the flow of water. The outlet often is required to slow the flow of water by using energy dissipaters such as riprap. Sediment Structure: An energy dissipating structure often made of rocks used to slow the flow of water and catch sediment. Temporary Berm: A hill constructed of compacted soil to prevent runoff flowing in a specific direction. Berms are placed either at the top or bottom of slopes. Impact of Construction on Adjacent Facilities Construction can have a negative effect on surrounding properties and areas. These issues need to be anticipated and mitigated as possible. Some of the concerns include: Construction Noise: OHSA sets maximum decibel limits on daily sound exposure. In the United States, this is typically 90 dBA for the eight hour noise level. Runoff and Sediment: Construction sites, especially those involving excavation, can change the dynamics of runoff and drainage. See the section on Soil Erosion and Sediment Control for more details. View: Construction projects often change the landscape of the affected area. This may have an impact on the look and feel of an area. The needs of adjacent properties may need to be considered for these changes. Rights of Way: Often, land which is not owned by the owner of the project is necessary for the final or temporary conditions. In these cases land needs to be acquired temporarily or permanently to complete the work. The owner of the project and of the land must come to an agreement to allow use of the property. Economic or social impact: Construction during and after may impact the access or desirability of a business or residential area. Consideration should be taken to limit the impacts to businesses or residents. For example, a bridge detour may cut off access to a restaurant which collects patrons mostly from tourists passing the effected route. The owner would then be compensated for the loss of business.

Safety

Safety is extremely important for construction sites. The OSHA CFR 29 Part 1910 and Part 1926: Occupational Safety and Health provides requirements for all types of construction situations and is recommended to use for the exam. Some of the highlights which you should further familiarize yourself with include:

• Excavation Safety: Except for excavations in rock, anything deeper than 5 ft must be stabilized to prevent cave-in. This may be achieved by providing appropriate earth retention systems or sloping at appropriate rates. This is determined by the depth of excavation, soil type, and other requirements.

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Uninterrupted Flow

The capacity of a roadway, for a given stretch of road with defined characteristics, is a measure of the amount of traffic it can handle to maintain design speeds. The Highway Capacity Manual (HCM) is used for guidelines on the analysis of roadway capacity. Roadways must first be classified into one of two categories: Uninterrupted or interrupted flow. As the name suggests, uninterrupted flow includes roads where there is no disruption of the traffic from intersections or traffic control measures. These are typically highways or freeways. Interrupted flow is the opposite in which there are locations in which the traffic is controlled. Interrupted flow will be discussed in the next section below. To classify roads by how they perform, the HCM has established a metric called Level of Service. A roadway can be rated from A being the best to F being the worst. The level of service is determined from charts in the HCM and is a function of the calculated density of the roadway. For freeways and multilane highway segments use HCM exhibit 12-15. The heavy vehicle factor converts flow of trucks and buses into passenger car equivalents. The calculation of the variables is based on the characteristics of the roadway. They can be classified into either general terrain segments or individual segments. The general terrain is applicable for grades up to 3% for lengths of 0.25 to 1.0 miles. The terrain is then classified as level or rolling. ET is then determined in exhibit 12-25. PT is the proportions of trucks and buses. Free flow speed is the speed of the traffic flow when the volume is low enough to not impede the speed of the vehicles. This can be calculated off of a Base Free Flow Speed. This is the speed of a roadway under perfect geometric conditions:

Interrupted Flow

Interrupted flow conversely to uninterrupted flow contains some restriction for the analysis of the capacity of a segment of roadway. This includes intersections both signalized and unsignalized, roundabouts, urban street flow, and pedestrians. Because of these restrictions the traffic can often not reach the free flow speed and instead can only reach a running speed. This is the speed at which a vehicle is able to travel when accounting for the factors created by the interruption of flow. This speed can be calculated from the following equation HCM 18-48:

Intersection Capacity

Traffic Analysis

Volume studies as the name indicates is an analysis of a roadway or intersection by field measurements. The study most often consists of observers on site counting traffic volumes and recording the numbers. The parameters of the study need to be determined by engineering judgement based on the intention of the study. The range and duration of the study can vary to achieve these intentions. The results of the study can be used to calculate parameters used in analyses such as average daily traffic, intersection volumes, and observed speeds. It is important to set the limits of the segment in which the speed is to be recorded. This segment needs to be determined by judgement based on the intention of the study. The average speed over a given segment can be calculated by the following equation: Savg = Average speed for the given segment L = Length of segment Nt = Number of cars observed t = Observed time of each vehicle Modal split is the measure of the percentages of different modes of transportation for an observed stretch. The modes often include cars, buses, trucks, bikes and pedestrians and any other uncommon mode. It is a good representation of the distribution of traffic for a given location or stretch of roadway.

Trip Generation

Trips are the act of a type of modal transportation leaving an origin and arriving at a destination. It is important to characterize the amount and type of trips which occur in a given area. This is a trip generation analysis. This is often used to characterize trips and observations are classified as data points for a given type of trip. These data points are then charted and fit to an equation to help approximate anticipated trips. The best fit equation can be linear or nonlinear: T=y+bx linear lnT=y+blnX (nonlinear) T = Number of trips y = y-intercept b = Slope of best fit line X = Trip generation parameter

Accident Analysis

When traffic movements create a potential for a crash, these can be reviewed as a part of a conflict analysis. This identifies all of the potential movements for an intersection or roadway and determines where there is the possibility for a crash. Conflict diagrams show all movements and the types of conflicts associated with other movements. This can be used to see where there are troublesome areas and the potential for improvements to avoid undesirable conflicts. Accident analysis is, as the name suggests, an evaluation of the number of crashes for a given intersection or segment. This information can be used to evaluate if improvements are required. The accident rate is a ratio of the number of crashes to the exposure, which is the number of vehicles for a defined time or length of roadway:

Nonmotorized Facilities

The analysis of pedestrians is important to the flow of vehicle traffic, to ensure the area can handle the number of pedestrians, and to ensure safety. Just as with vehicles we can calculate the pedestrian flow rate at a given location: SP = Walking speed DP = Pedestrian density It is important to note the speed of pedestrians will decrease as the density is increased. This is because people have more trouble maneuvering and walking at a normal pace if they are obstructed by other people. The Highway Capacity Manual has a number of graphs which show the relationship between density, speed, space, and flow in exhibits 4-14/15/16/17. A walkway or sidewalk has a certain width. However, there are often objects in the walkway which will reduce the effective width. The reduction in the original walkway width is the sum of the shy distances. Typical values for reductions can be found in HCM exhibit 24-9. Just as in the analysis of vehicular traffic, the performance for pedestrian flow at a particular walkway or intersection can be classified by a Level of Service. The flow of pedestrians can be uninterrupted or interrupted. The unit flow rate is the determining variable for the LOS but is most often taken at 15 min intervals. The 15 min pedestrian flow rate is (HCM Eq. 24-3): The LOS for average walkways can be determined from HCM exhibit 24-1. There is also platoon level of service. This accounts for the fact that pedestrians will often travel in groups. Platoon LOS can be determined from HCM exhibit 24-2.

Traffic Forecast

Predicting traffic is important for allocating funds and prioritizing projects for the future. Often traffic can be estimated using historical data to obtain a growth rate. Future traffic can be predicted using the following equation: P = Growth rate (decimal) n = Number of years

Highway Safety

The AASHTO Highway Safety Manual (HSM) provides guidelines for the prediction of crashes for a given segment or location. The frequency of crashes can be predicted by using equations called Safety Performance Functions (SPF) based on the characteristics of the roadway and the desired time period. The equations must be determined through statistical modeling and are most often based on annual traffic volume and segment length but may also include other roadway characteristics. These SPF’s are used to determine a predicted crash frequency which can then be adjusted to determine the actual predicted frequency from the following equation: C = Calibration factor CMF = Product of all Crash Modification Factors The Crash Modification Factors (CMF) are based on proposed modifications to a site. It is the ratio of the expected crash frequency of the changed site to the crash frequency of the original condition: CMF= Modified Crash Frequency/Original Crash Frequency

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 3-1 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 3-3 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 3-4 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 cross-section 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 3-15) bw = Lane adjustment factor (GDHS Table 3-16)

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 Curve Geometry

Stopping and Passing Sight Distance

For vertical curves, the slopes will have an impact on the cars ability to recognize an object and stop or properly pass. The length of the curve must be adequate for these conditions. There are two methods of determining this minimum length and their use is dependent on the variables provided. The first method is the use of the K-value. The factor K is the ratio of the length of curve to the absolute difference in grades: K can also be determined from the design speed by the charts in the AASHTO Policy on the Geometric Design of Highways and Streets Table 3-34/35/36. The AASHTO GDHS also provides equations correlating the stopping sight distance to the curve length and the difference in grade. The appropriate equation can be used depending on the curve type, stopping or passing distance, and if the stopping distance is greater than the curve length.

Vertical Clearence

Vertical clearance is the height from the roadway to an obstruction, often a bridge above. There are two concerns when analyzing a vertical curve for clearance issues. The first is to ensure the object above the road does not inhibit the necessary sight distance. The second is to ensure the height of vehicle can safely pass under the obstruction. The required length of curve for a required clearance can be determined from the following equations: S = Sight distance (ft) C = Clearance (ft) h1 = height to driver eye h2 = Height to object A = Algebraic difference in grade

Intersection Sight Disctance

When a vehicle is approaching or is stopped at an intersection, they must have an adequate line of sight along the perpendicular roadway to be able to safely stop or maneuver if necessary. This sight distance can be approximated by sight triangles where the hypotenuse is the required sight distance and the base is the required stopping distance. The diagram below exhibits this where X is the stopping distance of the vehicle on the major road and H is the sight distance:

Interchanges

An interchange is a grade-separated crossing of 2 or more roadways in which ramps are used in such a manner so that the flow of traffic is not interrupted. On ramps and off ramps need to be designed such that there is enough length for acceleration and sight distance for the seamless merging of traffic. Mostly the design lengths can be determined from the appropriate tables in the GDHS. There are a number of types of interchanges which have advantages and disadvantages based on the site constraints. Some examples include trumpet, diamond, partial and full cloverleaf, or fully directional As with traffic signals, GDHS provides warrants for the consideration of the use of interchanges. These include: 1. Design Designation 2. Bottleneck or Spot Congestion Relief 3. Safety Improvements 4. Topography 5. User Benefits 6. Traffic Volume

At Grade Intersection Layout

Intersections must be detailed to minimize disruption of traffic and to ensure a safe driving condition. To achieve this, the layout must facilitate both proper sight distances and maneuverability. Acute angles at intersections provide difficulties for both of these aspects and should be avoided as much as possible. The AASHTO Policy on the Geometric Design of Highways and Streets (GDHS) provides a wide range of tables and figures. Chapter 2 focuses on vehicle dimensions and the ability to make turns. Chapter 9 provides guidance on the geometry of the traveled way and intersections to account for minimum turning requirements.

Forgiving Roadside Concepts

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 5-10b 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 5-7. 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: d = Deceleration rate (ft/s2) v = Velocity (ft/s) L = Length of attenuator (ft) x = Attenuation efficiency factor The stopping force then is: 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 Timing

Traffic signals must be designed to allow enough time for each traffic movement at the intersection to handle the volume in that direction. Each individual set of traffic movements are grouped together by movements which can safely coexist. The signal then changes and another group of movements is allowed to proceed. The time for each group is a phase. The time it takes to go through all phases, is the cycle. The phase length is the following equation (HCM Eq. 19-2): l1 = Time for drivers to react to green gs = Time required to clear the queue ge = Time extension for random vehicles Y = Yellow light time Rc = Red light clearance time The effective green or the time in which vehicles are actually flowing can be taken as (HCM Eq. 19-3): e = Effective green extension (often taken as 2 seconds) The capacity of pedestrians entering a signalized intersection must be determined to ensure there is sufficient time to handle the volume of people. The number of pedestrians which can cross at a single cross walk during a single cycle is determined from the following (HCM Eq. 19-66): C = Cycle length (s) g = Green time (s) v = Pedestrian volume (People/s) The time to have a cross walk cleared can be determined from (HCM Eq. 19-64): L = Length of crossing (ft) Sp = Pedestrian design speed (ft/s) W = Width of cross walk (ft)

Signal Warrents

Intersections which do not include traffic signals may be analyzed to determine if one is required. The Manual on Uniform Traffic Control Devices (MUTCD) provides eight different scenarios which can be used to identify intersections which may require a signal to be installed. The following are the eight warrants:

• Warrant 1, Eight-Hour Vehicular Volume
• Warrant 2, Four-Hour Vehicular Volume
• Warrant 3, Peak Hour
• Warrant 4, Pedestrian Volume
• Warrant 5, School Crossing
• Warrant 6, Coordinated Signal System
• Warrant 7, Crash Experience
• Warrant 8, Roadway Network
• Warrant 9, Intersection Near a Grade Crossing

Signs and Pavement Markings

MUTCD Chapter 3 provides requirements for signs and pavement markings. As with cross sectional elements, become familiar with this chapter and how to locate requirements quickly.

Temporary Traffic Control

When work in the roadway is necessary, traffic must be shifted and directed away from the work zone in a safe manner for both the flow of traffic and the workers in the zone of construction. Tapered traffic control devices are used to direct traffic away from the work zone. MUTCD provides equations for the suggested taper length. W = Width of work zone S = Design speed (mph) However, the length L must be adjusted depending on the type of taper as per MUTCD Table 6C-3.

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 Y-axis 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

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. To develop the synthetic hydrograph, you must calculate the time to peak flow: 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 Hazen-Williams 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) Open-channel flow For open channel flow use the Chezy-Manning 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 Often, the weir can be approximated by taking Cd, the discharge coefficient = 0.63 and the equation is simplified as: 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: However, often in a dam situation the approach velocity can be taken as zero since it is so small and the equation becomes: 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:

Economic Analysis

The PE exam will potentially provide examples of engineering economics which are geared towards assets in Transportation. For these questions refer to the morning session equations for engineering economics.

Select from the Categories Above for More Information

Uninterrupted Flow

The capacity of a roadway, for a given stretch of road with defined characteristics, is a measure of the amount of traffic it can handle to maintain design speeds. The Highway Capacity Manual (HCM) is used for guidelines on the analysis of roadway capacity. Roadways must first be classified into one of two categories: Uninterrupted or interrupted flow. As the name suggests, uninterrupted flow includes roads where there is no disruption of the traffic from intersections or traffic control measures. These are typically highways or freeways. Interrupted flow is the opposite in which there are locations in which the traffic is controlled. Interrupted flow will be discussed in the next section below. To classify roads by how they perform, the HCM has established a metric called Level of Service. A roadway can be rated from A being the best to F being the worst. The level of service is determined from charts in the HCM and is a function of the calculated density of the roadway. For freeways and multilane highway segments use HCM exhibit 12-15. The heavy vehicle factor converts flow of trucks and buses into passenger car equivalents. The calculation of the variables is based on the characteristics of the roadway. They can be classified into either general terrain segments or individual segments. The general terrain is applicable for grades up to 3% for lengths of 0.25 to 1.0 miles. The terrain is then classified as level or rolling. ET is then determined in exhibit 12-25. PT is the proportions of trucks and buses. Free flow speed is the speed of the traffic flow when the volume is low enough to not impede the speed of the vehicles. This can be calculated off of a Base Free Flow Speed. This is the speed of a roadway under perfect geometric conditions:

Interrupted Flow

Interrupted flow conversely to uninterrupted flow contains some restriction for the analysis of the capacity of a segment of roadway. This includes intersections both signalized and unsignalized, roundabouts, urban street flow, and pedestrians. Because of these restrictions the traffic can often not reach the free flow speed and instead can only reach a running speed. This is the speed at which a vehicle is able to travel when accounting for the factors created by the interruption of flow. This speed can be calculated from the following equation HCM 18-48:

Intersection Capacity

Traffic Analysis

Volume studies as the name indicates is an analysis of a roadway or intersection by field measurements. The study most often consists of observers on site counting traffic volumes and recording the numbers. The parameters of the study need to be determined by engineering judgement based on the intention of the study. The range and duration of the study can vary to achieve these intentions. The results of the study can be used to calculate parameters used in analyses such as average daily traffic, intersection volumes, and observed speeds. It is important to set the limits of the segment in which the speed is to be recorded. This segment needs to be determined by judgement based on the intention of the study. The average speed over a given segment can be calculated by the following equation: Savg = Average speed for the given segment L = Length of segment Nt = Number of cars observed t = Observed time of each vehicle Modal split is the measure of the percentages of different modes of transportation for an observed stretch. The modes often include cars, buses, trucks, bikes and pedestrians and any other uncommon mode. It is a good representation of the distribution of traffic for a given location or stretch of roadway.

Trip Generation

Trips are the act of a type of modal transportation leaving an origin and arriving at a destination. It is important to characterize the amount and type of trips which occur in a given area. This is a trip generation analysis. This is often used to characterize trips and observations are classified as data points for a given type of trip. These data points are then charted and fit to an equation to help approximate anticipated trips. The best fit equation can be linear or nonlinear: T=y+bx linear lnT=y+blnX (nonlinear) T = Number of trips y = y-intercept b = Slope of best fit line X = Trip generation parameter

Accident Analysis

When traffic movements create a potential for a crash, these can be reviewed as a part of a conflict analysis. This identifies all of the potential movements for an intersection or roadway and determines where there is the possibility for a crash. Conflict diagrams show all movements and the types of conflicts associated with other movements. This can be used to see where there are troublesome areas and the potential for improvements to avoid undesirable conflicts. Accident analysis is, as the name suggests, an evaluation of the number of crashes for a given intersection or segment. This information can be used to evaluate if improvements are required. The accident rate is a ratio of the number of crashes to the exposure, which is the number of vehicles for a defined time or length of roadway:

Nonmotorized Facilities

The analysis of pedestrians is important to the flow of vehicle traffic, to ensure the area can handle the number of pedestrians, and to ensure safety. Just as with vehicles we can calculate the pedestrian flow rate at a given location: SP = Walking speed DP = Pedestrian density It is important to note the speed of pedestrians will decrease as the density is increased. This is because people have more trouble maneuvering and walking at a normal pace if they are obstructed by other people. The Highway Capacity Manual has a number of graphs which show the relationship between density, speed, space, and flow in exhibits 4-14/15/16/17. A walkway or sidewalk has a certain width. However, there are often objects in the walkway which will reduce the effective width. The reduction in the original walkway width is the sum of the shy distances. Typical values for reductions can be found in HCM exhibit 24-9. Just as in the analysis of vehicular traffic, the performance for pedestrian flow at a particular walkway or intersection can be classified by a Level of Service. The flow of pedestrians can be uninterrupted or interrupted. The unit flow rate is the determining variable for the LOS but is most often taken at 15 min intervals. The 15 min pedestrian flow rate is (HCM Eq. 24-3): The LOS for average walkways can be determined from HCM exhibit 24-1. There is also platoon level of service. This accounts for the fact that pedestrians will often travel in groups. Platoon LOS can be determined from HCM exhibit 24-2.

Traffic Forecast

Predicting traffic is important for allocating funds and prioritizing projects for the future. Often traffic can be estimated using historical data to obtain a growth rate. Future traffic can be predicted using the following equation: P = Growth rate (decimal) n = Number of years

Highway Safety

The AASHTO Highway Safety Manual (HSM) provides guidelines for the prediction of crashes for a given segment or location. The frequency of crashes can be predicted by using equations called Safety Performance Functions (SPF) based on the characteristics of the roadway and the desired time period. The equations must be determined through statistical modeling and are most often based on annual traffic volume and segment length but may also include other roadway characteristics. These SPF’s are used to determine a predicted crash frequency which can then be adjusted to determine the actual predicted frequency from the following equation: C = Calibration factor CMF = Product of all Crash Modification Factors The Crash Modification Factors (CMF) are based on proposed modifications to a site. It is the ratio of the expected crash frequency of the changed site to the crash frequency of the original condition: CMF= Modified Crash Frequency/Original Crash Frequency

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 3-1 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 3-3 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 3-4 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 cross-section 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 3-15) bw = Lane adjustment factor (GDHS Table 3-16)

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 Curve Geometry

Stopping and Passing Sight Distance

For vertical curves, the slopes will have an impact on the cars ability to recognize an object and stop or properly pass. The length of the curve must be adequate for these conditions. There are two methods of determining this minimum length and their use is dependent on the variables provided. The first method is the use of the K-value. The factor K is the ratio of the length of curve to the absolute difference in grades: K can also be determined from the design speed by the charts in the AASHTO Policy on the Geometric Design of Highways and Streets Table 3-34/35/36. The AASHTO GDHS also provides equations correlating the stopping sight distance to the curve length and the difference in grade. The appropriate equation can be used depending on the curve type, stopping or passing distance, and if the stopping distance is greater than the curve length.

Vertical Clearence

Vertical clearance is the height from the roadway to an obstruction, often a bridge above. There are two concerns when analyzing a vertical curve for clearance issues. The first is to ensure the object above the road does not inhibit the necessary sight distance. The second is to ensure the height of vehicle can safely pass under the obstruction. The required length of curve for a required clearance can be determined from the following equations: S = Sight distance (ft) C = Clearance (ft) h1 = height to driver eye h2 = Height to object A = Algebraic difference in grade

Intersection Sight Disctance

When a vehicle is approaching or is stopped at an intersection, they must have an adequate line of sight along the perpendicular roadway to be able to safely stop or maneuver if necessary. This sight distance can be approximated by sight triangles where the hypotenuse is the required sight distance and the base is the required stopping distance. The diagram below exhibits this where X is the stopping distance of the vehicle on the major road and H is the sight distance:

Interchanges

An interchange is a grade-separated crossing of 2 or more roadways in which ramps are used in such a manner so that the flow of traffic is not interrupted. On ramps and off ramps need to be designed such that there is enough length for acceleration and sight distance for the seamless merging of traffic. Mostly the design lengths can be determined from the appropriate tables in the GDHS. There are a number of types of interchanges which have advantages and disadvantages based on the site constraints. Some examples include trumpet, diamond, partial and full cloverleaf, or fully directional As with traffic signals, GDHS provides warrants for the consideration of the use of interchanges. These include: 1. Design Designation 2. Bottleneck or Spot Congestion Relief 3. Safety Improvements 4. Topography 5. User Benefits 6. Traffic Volume

At Grade Intersection Layout

Intersections must be detailed to minimize disruption of traffic and to ensure a safe driving condition. To achieve this, the layout must facilitate both proper sight distances and maneuverability. Acute angles at intersections provide difficulties for both of these aspects and should be avoided as much as possible. The AASHTO Policy on the Geometric Design of Highways and Streets (GDHS) provides a wide range of tables and figures. Chapter 2 focuses on vehicle dimensions and the ability to make turns. Chapter 9 provides guidance on the geometry of the traveled way and intersections to account for minimum turning requirements.

Forgiving Roadside Concepts

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 5-10b 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 5-7. 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: d = Deceleration rate (ft/s2) v = Velocity (ft/s) L = Length of attenuator (ft) x = Attenuation efficiency factor The stopping force then is: 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 Timing

Traffic signals must be designed to allow enough time for each traffic movement at the intersection to handle the volume in that direction. Each individual set of traffic movements are grouped together by movements which can safely coexist. The signal then changes and another group of movements is allowed to proceed. The time for each group is a phase. The time it takes to go through all phases, is the cycle. The phase length is the following equation (HCM Eq. 19-2): l1 = Time for drivers to react to green gs = Time required to clear the queue ge = Time extension for random vehicles Y = Yellow light time Rc = Red light clearance time The effective green or the time in which vehicles are actually flowing can be taken as (HCM Eq. 19-3): e = Effective green extension (often taken as 2 seconds) The capacity of pedestrians entering a signalized intersection must be determined to ensure there is sufficient time to handle the volume of people. The number of pedestrians which can cross at a single cross walk during a single cycle is determined from the following (HCM Eq. 19-66): C = Cycle length (s) g = Green time (s) v = Pedestrian volume (People/s) The time to have a cross walk cleared can be determined from (HCM Eq. 19-64): L = Length of crossing (ft) Sp = Pedestrian design speed (ft/s) W = Width of cross walk (ft)

Signal Warrents

Intersections which do not include traffic signals may be analyzed to determine if one is required. The Manual on Uniform Traffic Control Devices (MUTCD) provides eight different scenarios which can be used to identify intersections which may require a signal to be installed. The following are the eight warrants:

• Warrant 1, Eight-Hour Vehicular Volume
• Warrant 2, Four-Hour Vehicular Volume
• Warrant 3, Peak Hour
• Warrant 4, Pedestrian Volume
• Warrant 5, School Crossing
• Warrant 6, Coordinated Signal System
• Warrant 7, Crash Experience
• Warrant 8, Roadway Network
• Warrant 9, Intersection Near a Grade Crossing

Signs and Pavement Markings

MUTCD Chapter 3 provides requirements for signs and pavement markings. As with cross sectional elements, become familiar with this chapter and how to locate requirements quickly.

Temporary Traffic Control

When work in the roadway is necessary, traffic must be shifted and directed away from the work zone in a safe manner for both the flow of traffic and the workers in the zone of construction. Tapered traffic control devices are used to direct traffic away from the work zone. MUTCD provides equations for the suggested taper length. W = Width of work zone S = Design speed (mph) However, the length L must be adjusted depending on the type of taper as per MUTCD Table 6C-3.

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 Y-axis 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

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. To develop the synthetic hydrograph, you must calculate the time to peak flow: 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 Hazen-Williams 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) Open-channel flow For open channel flow use the Chezy-Manning 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 Often, the weir can be approximated by taking Cd, the discharge coefficient = 0.63 and the equation is simplified as: 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: However, often in a dam situation the approach velocity can be taken as zero since it is so small and the equation becomes: 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:

Economic Analysis

The PE exam will potentially provide examples of engineering economics which are geared towards assets in Transportation. For these questions refer to the morning session equations for engineering economics.

Select from the Categories Above for More Information

Uninterrupted Flow

The capacity of a roadway, for a given stretch of road with defined characteristics, is a measure of the amount of traffic it can handle to maintain design speeds. The Highway Capacity Manual (HCM) is used for guidelines on the analysis of roadway capacity. Roadways must first be classified into one of two categories: Uninterrupted or interrupted flow. As the name suggests, uninterrupted flow includes roads where there is no disruption of the traffic from intersections or traffic control measures. These are typically highways or freeways. Interrupted flow is the opposite in which there are locations in which the traffic is controlled. Interrupted flow will be discussed in the next section below. To classify roads by how they perform, the HCM has established a metric called Level of Service. A roadway can be rated from A being the best to F being the worst. The level of service is determined from charts in the HCM and is a function of the calculated density of the roadway. For freeways and multilane highway segments use HCM exhibit 12-15. The heavy vehicle factor converts flow of trucks and buses into passenger car equivalents. The calculation of the variables is based on the characteristics of the roadway. They can be classified into either general terrain segments or individual segments. The general terrain is applicable for grades up to 3% for lengths of 0.25 to 1.0 miles. The terrain is then classified as level or rolling. ET is then determined in exhibit 12-25. PT is the proportions of trucks and buses. Free flow speed is the speed of the traffic flow when the volume is low enough to not impede the speed of the vehicles. This can be calculated off of a Base Free Flow Speed. This is the speed of a roadway under perfect geometric conditions:

Interrupted Flow

Interrupted flow conversely to uninterrupted flow contains some restriction for the analysis of the capacity of a segment of roadway. This includes intersections both signalized and unsignalized, roundabouts, urban street flow, and pedestrians. Because of these restrictions the traffic can often not reach the free flow speed and instead can only reach a running speed. This is the speed at which a vehicle is able to travel when accounting for the factors created by the interruption of flow. This speed can be calculated from the following equation HCM 18-48:

Intersection Capacity

Traffic Analysis

Volume studies as the name indicates is an analysis of a roadway or intersection by field measurements. The study most often consists of observers on site counting traffic volumes and recording the numbers. The parameters of the study need to be determined by engineering judgement based on the intention of the study. The range and duration of the study can vary to achieve these intentions. The results of the study can be used to calculate parameters used in analyses such as average daily traffic, intersection volumes, and observed speeds. It is important to set the limits of the segment in which the speed is to be recorded. This segment needs to be determined by judgement based on the intention of the study. The average speed over a given segment can be calculated by the following equation: Savg = Average speed for the given segment L = Length of segment Nt = Number of cars observed t = Observed time of each vehicle Modal split is the measure of the percentages of different modes of transportation for an observed stretch. The modes often include cars, buses, trucks, bikes and pedestrians and any other uncommon mode. It is a good representation of the distribution of traffic for a given location or stretch of roadway.

Trip Generation

Trips are the act of a type of modal transportation leaving an origin and arriving at a destination. It is important to characterize the amount and type of trips which occur in a given area. This is a trip generation analysis. This is often used to characterize trips and observations are classified as data points for a given type of trip. These data points are then charted and fit to an equation to help approximate anticipated trips. The best fit equation can be linear or nonlinear: T=y+bx linear lnT=y+blnX (nonlinear) T = Number of trips y = y-intercept b = Slope of best fit line X = Trip generation parameter

Accident Analysis

When traffic movements create a potential for a crash, these can be reviewed as a part of a conflict analysis. This identifies all of the potential movements for an intersection or roadway and determines where there is the possibility for a crash. Conflict diagrams show all movements and the types of conflicts associated with other movements. This can be used to see where there are troublesome areas and the potential for improvements to avoid undesirable conflicts. Accident analysis is, as the name suggests, an evaluation of the number of crashes for a given intersection or segment. This information can be used to evaluate if improvements are required. The accident rate is a ratio of the number of crashes to the exposure, which is the number of vehicles for a defined time or length of roadway:

Nonmotorized Facilities

The analysis of pedestrians is important to the flow of vehicle traffic, to ensure the area can handle the number of pedestrians, and to ensure safety. Just as with vehicles we can calculate the pedestrian flow rate at a given location: SP = Walking speed DP = Pedestrian density It is important to note the speed of pedestrians will decrease as the density is increased. This is because people have more trouble maneuvering and walking at a normal pace if they are obstructed by other people. The Highway Capacity Manual has a number of graphs which show the relationship between density, speed, space, and flow in exhibits 4-14/15/16/17. A walkway or sidewalk has a certain width. However, there are often objects in the walkway which will reduce the effective width. The reduction in the original walkway width is the sum of the shy distances. Typical values for reductions can be found in HCM exhibit 24-9. Just as in the analysis of vehicular traffic, the performance for pedestrian flow at a particular walkway or intersection can be classified by a Level of Service. The flow of pedestrians can be uninterrupted or interrupted. The unit flow rate is the determining variable for the LOS but is most often taken at 15 min intervals. The 15 min pedestrian flow rate is (HCM Eq. 24-3): The LOS for average walkways can be determined from HCM exhibit 24-1. There is also platoon level of service. This accounts for the fact that pedestrians will often travel in groups. Platoon LOS can be determined from HCM exhibit 24-2.

Traffic Forecast

Predicting traffic is important for allocating funds and prioritizing projects for the future. Often traffic can be estimated using historical data to obtain a growth rate. Future traffic can be predicted using the following equation: P = Growth rate (decimal) n = Number of years

Highway Safety

The AASHTO Highway Safety Manual (HSM) provides guidelines for the prediction of crashes for a given segment or location. The frequency of crashes can be predicted by using equations called Safety Performance Functions (SPF) based on the characteristics of the roadway and the desired time period. The equations must be determined through statistical modeling and are most often based on annual traffic volume and segment length but may also include other roadway characteristics. These SPF’s are used to determine a predicted crash frequency which can then be adjusted to determine the actual predicted frequency from the following equation: C = Calibration factor CMF = Product of all Crash Modification Factors The Crash Modification Factors (CMF) are based on proposed modifications to a site. It is the ratio of the expected crash frequency of the changed site to the crash frequency of the original condition: CMF= Modified Crash Frequency/Original Crash Frequency

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 3-1 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 3-3 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 3-4 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 cross-section 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 3-15) bw = Lane adjustment factor (GDHS Table 3-16)

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 Curve Geometry

Stopping and Passing Sight Distance

For vertical curves, the slopes will have an impact on the cars ability to recognize an object and stop or properly pass. The length of the curve must be adequate for these conditions. There are two methods of determining this minimum length and their use is dependent on the variables provided. The first method is the use of the K-value. The factor K is the ratio of the length of curve to the absolute difference in grades: K can also be determined from the design speed by the charts in the AASHTO Policy on the Geometric Design of Highways and Streets Table 3-34/35/36. The AASHTO GDHS also provides equations correlating the stopping sight distance to the curve length and the difference in grade. The appropriate equation can be used depending on the curve type, stopping or passing distance, and if the stopping distance is greater than the curve length.

Vertical Clearence

Vertical clearance is the height from the roadway to an obstruction, often a bridge above. There are two concerns when analyzing a vertical curve for clearance issues. The first is to ensure the object above the road does not inhibit the necessary sight distance. The second is to ensure the height of vehicle can safely pass under the obstruction. The required length of curve for a required clearance can be determined from the following equations: S = Sight distance (ft) C = Clearance (ft) h1 = height to driver eye h2 = Height to object A = Algebraic difference in grade

Intersection Sight Disctance

When a vehicle is approaching or is stopped at an intersection, they must have an adequate line of sight along the perpendicular roadway to be able to safely stop or maneuver if necessary. This sight distance can be approximated by sight triangles where the hypotenuse is the required sight distance and the base is the required stopping distance. The diagram below exhibits this where X is the stopping distance of the vehicle on the major road and H is the sight distance:

Interchanges

An interchange is a grade-separated crossing of 2 or more roadways in which ramps are used in such a manner so that the flow of traffic is not interrupted. On ramps and off ramps need to be designed such that there is enough length for acceleration and sight distance for the seamless merging of traffic. Mostly the design lengths can be determined from the appropriate tables in the GDHS. There are a number of types of interchanges which have advantages and disadvantages based on the site constraints. Some examples include trumpet, diamond, partial and full cloverleaf, or fully directional As with traffic signals, GDHS provides warrants for the consideration of the use of interchanges. These include: 1. Design Designation 2. Bottleneck or Spot Congestion Relief 3. Safety Improvements 4. Topography 5. User Benefits 6. Traffic Volume

At Grade Intersection Layout

Intersections must be detailed to minimize disruption of traffic and to ensure a safe driving condition. To achieve this, the layout must facilitate both proper sight distances and maneuverability. Acute angles at intersections provide difficulties for both of these aspects and should be avoided as much as possible. The AASHTO Policy on the Geometric Design of Highways and Streets (GDHS) provides a wide range of tables and figures. Chapter 2 focuses on vehicle dimensions and the ability to make turns. Chapter 9 provides guidance on the geometry of the traveled way and intersections to account for minimum turning requirements.

Forgiving Roadside Concepts

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 5-10b 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 5-7. 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: d = Deceleration rate (ft/s2) v = Velocity (ft/s) L = Length of attenuator (ft) x = Attenuation efficiency factor The stopping force then is: 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 Timing

Traffic signals must be designed to allow enough time for each traffic movement at the intersection to handle the volume in that direction. Each individual set of traffic movements are grouped together by movements which can safely coexist. The signal then changes and another group of movements is allowed to proceed. The time for each group is a phase. The time it takes to go through all phases, is the cycle. The phase length is the following equation (HCM Eq. 19-2): l1 = Time for drivers to react to green gs = Time required to clear the queue ge = Time extension for random vehicles Y = Yellow light time Rc = Red light clearance time The effective green or the time in which vehicles are actually flowing can be taken as (HCM Eq. 19-3): e = Effective green extension (often taken as 2 seconds) The capacity of pedestrians entering a signalized intersection must be determined to ensure there is sufficient time to handle the volume of people. The number of pedestrians which can cross at a single cross walk during a single cycle is determined from the following (HCM Eq. 19-66): C = Cycle length (s) g = Green time (s) v = Pedestrian volume (People/s) The time to have a cross walk cleared can be determined from (HCM Eq. 19-64): L = Length of crossing (ft) Sp = Pedestrian design speed (ft/s) W = Width of cross walk (ft)

Signal Warrents

Intersections which do not include traffic signals may be analyzed to determine if one is required. The Manual on Uniform Traffic Control Devices (MUTCD) provides eight different scenarios which can be used to identify intersections which may require a signal to be installed. The following are the eight warrants:

• Warrant 1, Eight-Hour Vehicular Volume
• Warrant 2, Four-Hour Vehicular Volume
• Warrant 3, Peak Hour
• Warrant 4, Pedestrian Volume
• Warrant 5, School Crossing
• Warrant 6, Coordinated Signal System
• Warrant 7, Crash Experience
• Warrant 8, Roadway Network
• Warrant 9, Intersection Near a Grade Crossing

Signs and Pavement Markings

MUTCD Chapter 3 provides requirements for signs and pavement markings. As with cross sectional elements, become familiar with this chapter and how to locate requirements quickly.

Temporary Traffic Control

When work in the roadway is necessary, traffic must be shifted and directed away from the work zone in a safe manner for both the flow of traffic and the workers in the zone of construction. Tapered traffic control devices are used to direct traffic away from the work zone. MUTCD provides equations for the suggested taper length. W = Width of work zone S = Design speed (mph) However, the length L must be adjusted depending on the type of taper as per MUTCD Table 6C-3.

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 Y-axis 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

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. To develop the synthetic hydrograph, you must calculate the time to peak flow: 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 Hazen-Williams 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) Open-channel flow For open channel flow use the Chezy-Manning 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 Often, the weir can be approximated by taking Cd, the discharge coefficient = 0.63 and the equation is simplified as: 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: However, often in a dam situation the approach velocity can be taken as zero since it is so small and the equation becomes: 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:

Economic Analysis

The PE exam will potentially provide examples of engineering economics which are geared towards assets in Transportation. For these questions refer to the morning session equations for engineering economics.