Civil Professional Engineer Study Guides

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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.

Live Load

Snow Loads

Snow loads are determined from Chapter 7. There are 3 types of snow loads to know: ground, flat roof, and design roof. Pg = ground snow load. This is the snow load on the ground as per a specific geographic area. Pf = flat roof snow load = Pg(0.7CeCtIS) Ce = Exposure Factor from Table 7-2 Ct = Thermal Factor from Table 7-3 IS = Importance factor from 1-5.2 Ensure this is greater than the minimum = 20IS The design roof snow load Ps = CsPf Determine CS from Table 7-2c .

Snow Drift

Snow drift is additional load due to snow building up against a vertical wall from wind. The additional load is approximated by a triangular cross section of snow. Figure 7-8 depicts the necessary variables. To solve: First determine the density of snow: g = 0.13pg + 14 < 30 pcf Then using the density you can determine the height of the roof snow hb = ps/g hc = the vertical distance from the top of roof snow to upper roof = height to upper roof - hb If hc < 0.2hb, Snow drift does not need to be applied Then using figure 7-9 determine the drift height hd which will be the larger of: For Leeward drift use lu = the length of the upper roof For Windward use lu = the length of the lower roof and only use ¾ of the hd as determined from figure 7-9 Then calculate the width of the drift, w, for hd < hc w=4h, if hd > hc w = 4hd2/hc however w shall not be greater 8hc The variables are better depicted in the diagram below:

Site Classification and Occupancy

• From Table 20.3-1 the site classification can be determined

Site Coefficients and Spectural Response Factors

SDS = Design Spectural response acceleration parameter at short periods = 2/3SMS = 2/3FaSS SMS = The risk targeted maximum considered earthquake ground motion acceleration parameter (MCER) Spectural response acceleration parameter at short periods. Fa = Site coefficient defined in table 11.4-1 SS = Mapped (MCER) Spectural response acceleration parameter at short periods determined in accordance with section 11.4.1 SD1 = Design Spectural response acceleration parameter at a period of 1 s = 2/3SM1 = 2/3FvS1 SM1 = The risk targeted maximum considered earthquake ground motion acceleration parameter (MCER) Spectural response acceleration parameter at a period of 1 s. Fv = Site coefficient defined in table 11.4-1 S1 = Mapped (MCER) Spectural response acceleration parameter at a period of 1 sec as determined in accordance with section 11.4.1 From Table 20.3-1 the site classification can be determined Determine the Seismic design category based on short period response acceleration parameters from Table 11.6-1 Determine the Seismic design category based on 1-S period response acceleration parameters from Table 11.6-2

Effective Seismic Weight

Effective weight is the load which can be accounted for to offset horizontal seismic forces. This includes the dead load and any additional loading as outlined in section 12.7.2 such as: 1. In areas used for storage, a minimum of 25 percent of the floor live load (floor live load in public garages and open parking structures need not be included). 2. Where provision for partitions is required by Section 4.2.2 in the floor load design, the actual partition weight or a minimum weight of 10 psf (0.48 kN/m2) of floor area, whichever is greater. 3. Total operating weight of permanent equipment. 4. Where the flat roof snow load, Pf , exceeds 30 psf (1.44 kN/m2), 20 percent of the uniform design snow load, regardless of actual roof slope.

Seismic Base Shear and Force Distribution

Equivalent Lateral Force Procedure Section 12.8 The seismic base shear by the equivalent force method V = CsW CS = Seismic response coefficient = SDS/(R/Ie) Determine Ie from table 1.5-2 using the risk category R = response modification factor from table 12.2-1 The lateral seismic force at a given level shall be: Cvx = vertical distribution factor V = total design lateral force or shear at the base of the structure (kip or kN) wi and wx = the portion of the total effective seismic weight of the structure (W) located or assigned to Level i or x hi and hx = the height (ft) from the base to Level i or x k = an exponent related to the structure period as follows: for structures having a period of 0.5 s or less, k = 1 for structures having a period of 2.5 s or more, k = 2for structures having a period between 0.5 and 2.5 s, k shall be 2 or shall be determined by linear interpolation between 1 and 2

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Introduction to Bridges

Parts of a bridge include:

• Foundation – Structural members used to transfer load to the supporting soil.

• Substructure – Structural parts that support the horizontal span

• Superstructure – Structural parts which provide the horizontal span

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Limit States and Load Factors

Load factors and load combinations are handled differently in AASHTO. Different loading conditions are represented by Limit States. Some examples are Strength I, Strength III, and Service I. The load factors vary in magnitude depending on which limit state is applied. The load factors are then multiplied by the various types of loads. The Load Factors are found in Tables 3.4.1-1 and 3.4.1-2.

Live Load Distribution

Live load on bridges is not distributed evenly to girders. Live load distribution provides a more appropriate distribution based on girder spacing, deck thickness, type of bridge etc. The applicable cross sections are from Table 4.6.2.2.1-1 Then the appropriate equation on pages 4-37 through 4-45 determines the distribution of load. Be aware of the appropriate mode of failure and whether the beam is interior or exterior

Flexure

Moment capacity in concrete beams is based on the tension in the member being equal to the compression. The moment capacity then is the area of steel multiplied by the strength of steel multiplied by the distance from the steel centroid to the centroid of the compression block. Therefore: As = area of steel (in2) Fy = yield strength of steel (ksi) d = depth of tension steel (in) a = depth of compression block (in) And since Tension = Compression Asfy = 0.85f’cba, and therefore a = Asfy/(0.85f’cb) This is represented in the diagram below: The minimum reinforcing in a concrete beam is the larger of the following two equations: The maximum reinforcing does not have a simple equation but is a function of limiting the strain in the steel so that the mode of failure is not crushing of the concrete. This is done by setting the strain of steel to 0.005. Therefore:

Shear

The shear capacity of a concrete beam is the addition of the shear strength of the concrete and the reinforcing stirrups. Therefore: s = spacing of stirrups (in) Av = Area of vertical stirrups (in2). Note: the cross section for shear often includes multiple vertical bars. Av is the total area of all vertical legs Spacing shall not be greater than = Avfy/50bw

Two-Way Shear

Axial

Reinforcing Development and Details

Compression

The capacity of compression members are a function of the unbraced length. For non-doubly symmetric members there is a different capacity about each axis and it must be determined which is the controlling axis. To do this AISC Chapter 4 Tables provide the conversion factor to determine the equivalent unbraced length of the strong axis which is the ratio of the radii of gyration about each axis. Then the design axial capacity can be determined from the appropriate table for each structural shape.

Flexure

Flexural capacity of steel is determined by the length of lateral support. If a beam is fully laterally supported, the capacity is the plastic moment capacity: The plastic moment is the yield strength times the plastic section modulus: MP = FyZ The plastic section modulus is the summation of the areas in compression and tension multiplied by the distance from the center of gravity of each area to the plastic neutral axis. For a symmetric W shape, Z = 2(AfYf +Aw/2Yw) If a beam is not fully laterally supported, the capacity is a function of the unbraced length and will fail in lateral torsion buckling. For the purposes of this exam it is best to determine the capacity of a member from the design tables AISC 3-10. Find the intersection of the unbraced length and the applied load and then find the first dark line directly above this point to find the most efficient section.

Tension

A steel tension member needs to be checked for 2 modes of failure. Yielding of the gross area and rupture of the effective net area The gross area includes no holes The net area includes the holes. The diameter of the hole is obtained by adding 1/8” to the diameter of the bolt

Fatigue

Fatigue is covered in the specifications Appendix 3 of the AISC. The stress range is determined by the following equation: N is the fluctuations for the life of the structure Cf = Found from table A3.1 FTH = Table A3.1

Bolt Strength

Bolted connections fail in shear or bearing. For Shear: Fn = Shear strength of bolt from table J3.2. N is for threads included, X for threads excluded n = number of bolts Also note the capacity is multiplied by the number of shear planes on the bolt For Bearing: Lc = clear edge distance measured from edge of hole to edge of connected material Fu = ultimate strength of connected material t = thickness of connected material d = bolt diameter

Block Shear

The main concept to understand for block shear is that a component of the capacity comes from tension which is the length of perimeter perpendicular to the load and the other comes in shear from the portion which is parallel to the tension. Then simply fill in the equation Ubs = 1.0 if tension is uniform and 0.5 otherwise (Most often taken as 1.0) Anv = net area in shear (in2) Ant = net area in tension (in2) Agv = gross area in shear (in2) The diameter of the hole is 1/8” + diameter of the bolt

Welds

Sawn Lumber

Wood Design consists of finding the allowable design stress for each mode of failure by multiplying the reference stress by the appropriate adjustment factors to find the design allowable stress. The breakdown for sawn lumber and structurally glued members is in Tables 4.3.1 and 5.3.1 respectively.

Structural Glued Laminated

Connections

Connections are similar to other modes of failure in which the reference value is multiplied by adjustment factors to determine the design allowable stress. Dowel Type Fastener (bolts, lag screws, wood screws, nails, spikes, drift bolts, drift pins) stresses are determined from Table 11.3.1 For Lateral Loads: Z’ = Z x CD CM Ct Cg CD Ceg Cdi Ctn Withdrawal W’ = W x CDCM2CtCegCtn CD = Duration Factor 11.3.2 CM = Wet Service Factor 11.3.3 Ct = Temperature Factor 11.3.4 Cg = Group Action Factor 11.3.6 CD = Geometry Factor 12.5.1 Ceg = End Grain Factor 12.5.2 Cdi = Diaphragm Factor 12.5.3 Ctn = Toe Nail Factor 12.5.4

Bending

Compression

Prestressing Stresses

In addition to the stress from external forces, prestressed beams are subject to the stresses from the strands. There are 2 types of stress from the applied Prestressing force (P):

1. Compression stress due to the strands P/A
2. Bending due to the eccentricity of the strands Pe(c)/I

Prestressing Flexure

Shipping and Handling

• Precast/prestressed members need to transported. This introduces stresses which may be different from the in-place design conditions.
• PCI provides provisions for the handling of precast members to limit cracking.
• The modulus of rupture of the section must be greater than applied stress due handling.
• Modulus of Rupture, fr = 7.5sqrt(f'c)
• PCI provides equations for the moments during lifting of typical pick point configurations. This can be found in Figure 8.3.1.
• The situation in which lifting or transportation occurs requires an additional multiplier as outlined in Table 8.3.1.

General Requirements

Some main concepts 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. 1926 Subpart P – Excavations

Loads and Load Combinations

Load combinations as per IBC are: Section 1605.2

• 1.4(D +F) (Equation 16-1)
• 1.2(D + F) + 1.6(L + H) + 0.5(Lr or S or R) (Equation 16-2)
• 1.2(D + F) + 1.6(Lr or S or R) + 1.6H + (f1L or 0.5W) (Equation 16-3)
• 1.2(D + F) + 1.0W + f1L + 1.6H + 0.5(Lr or S or R) (Equation 16-4)
• 1.2(D + F) + 1.0E + f1L + 1.6H + f2S (Equation 16-5)
• 0.9D+ 1.0W+ 1.6H (Equation 16-6)
• 0.9(D + F) + 1.0E+ 1.6H (Equation 16-7)

Special Inspections

• Special Inspections – Inspections of construction materials and components by qualified professionals for compliance with codes and construction documents
• Can be continuous (Full time) or periodic (Part time or intermittent)

Weld Symbols and Types

3D Statics

Statics in 3 dimensions introduces additional equations of equilibrium due to the third axis. Apply the same basic principles for the sum of the following forces: FX = 0 FY = 0 FZ = 0 MX = 0 MY = 0 MZ = 0

• First determine location of origin (0, 0, 0)

Moving Loads

• Moving Loads are most often from Live Load due to traffic
• Need to analyze position of load to cause the greatest stress
• Shear in general is greatest when loads are at the support
• Positive moment in general is greatest with the loads at midspan
• Negative Moment is greatest with the load cloase to the support

Hinges

Hinges are supports at which there is a zero moment and only an axial and vertical force can be transferred Hinges are best analyzed by taking free body diagrams to either side of the hinge

Cables

• Cables carry load only in tension
• Acts as axial two force tension members
• Can be analyzed similarly to trusses use the method of joints

Consider the example below: Determine support reactions by drawing free body diagram of entire system Then you can take free body diagrams of individual points to determine axial tensions:

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Eccentrically Loaded Bolts

The bolt which will see the largest resultant force in a bolt group is the upper most bolt on the side of which the force is applied Vp = vertical force per bolt = P/N P = applied force (kips) N = number of bolts Ve = Force due to eccentricity = Pexc/Io Xc = distance in X direction from centroid of bolt group to the subject bolt The moment of inertia the sum of the distances of all bolts in the x and y directions if all bolts have the same diameter. Sum the distances of each bolt to the appropriate neutral axis:

Elongation and Contraction due to Axial Loading

The elongation or contraction of a beam due to an applied force is determined from the following equation: D = PL/AE P = applied force (kips) L = length of beam (in) A = cross sectional area (in2) E = modulus of elasticity (ksi)

Elongation Due to Thermal Loading

The thermal elongation or contraction for steel is determined by the following equation: D = Loa(t1 - to) Lo = original length of beam (in) a = coefficient of thermal expansion t1 = new temperature (degrees Fahrenheit) to = original temperature (degrees Fahrenheit)

Composite Beams

For composite members, the stresses in the beams can only be determined by analysis of similar materials. To do this, the stronger material should be converted to an equivalent area of the weaker material. This is done using the ratio of the moduli of elasticity n = E1/E2 Then calculate the equivalent width of the weaker material bequiv = bn The member can then be analyzed as a single material.

Torsional Shear

Surcharge Load

Deflections

• Not all deflections are covered under beam chart equations

Horizontal Shear Stress

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)

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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.

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Mass Balance

Mass balance refers to the conservation of mass as it enters and exits a system. This concept is essential to the Water Resources and Environmental exam as it is a common method in solving for unknowns in many types of problems. This principle simply put is that mass is always conserved in fluid systems regardless of the properties of that system. Therefore what enters the system must also exit the system. The equation can be represented as mass: M1 = M2 M1 = Mass entering the system M2 = Mass exiting the system The equation can also be represented by equating flow rates. In this case the equation is commonly known as the continuity equation: Q1 = Q2 Q1 = Flow rate into system Q2 = Flow rate out of a system Given that the flow rate is equal to the area multiplied by the velocity, the equation can be used to equate these variables as well: A1V1 = A2V2

Hydraulic Loading

Hydraulic loading refers to the flows in MGD (Million Gallons per Day) or cu. Ft./day to a treatment plant or treatment process. The equation is as follows: HLR=QA HLR = Hydraulic loading rate Q = Flow rate A = Surface area of the wet basin Detention time is the amount of time it takes a given volume of wastewater to pass through the clarifier: td=VQ V = Volume of clarifier

Solids Loading

Solids loading similarly to hydraulic loading is the amount of suspended solids in a substance as it flows to the treatment facility. Solids loading is expressed as the following:

Hydraulic Flow Measurement

Many flow devices are available to measure either the flow rate or velocity of a given system. These methods are often used in conjunction with the laws of energy and mass conservation to be able to analyze a system. Here are a few of the more prevalent ones for the purposes of the PE exam: Pitot Static Tubes g = Force effect due to gravity (32.2 ft/s2) h = Difference in elevations of the fluid columns (ft) ρ = Density of water (62.4 lb/ft3) ρm = Density of manometer fluid (lb/ft3) v = Velocity (ft/s) 2. Orifice or Venturi Meter Cf = Flow coefficient Ao = Orifice area A1 = Pipe area p = Pressure ρ = Density g = Force due to gravity Cd = Discharge coefficient Cc = Coefficient of contraction Fva =Velocity of approach factor

Bernoulli Continuity 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 of a system and is conserved at any point in the system. Therefore:

Pressure Conduit

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 (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 geometric changes such as 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 a 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 can be determined: For Sudden Expansions: For Sudden Contractions: D1=Smaller diamter pipe D2=Larger diamter pipe Loss coefficients are then multiplied by the kinetic energy to determine the loss:

Pump Application and Analysis

A pump is a machine which adds energy to the flow of water or other fluids. A pump is often used to oppose the effects of gravity to transport a fluid to a position up grade. The head added by a pump can be determined from the following equation as a function of the total energy:

Pipe Network Analysis

A system of pipes can be arranged in different configurations to be able to appropriately transport water. There are a few types of common arrangements that can be used. Each has certain principles to follow when determining the flow through the system. It is important to remember the conservation of mass or flow principle when analyzing these systems: Series Pipe System: Pipes of different areas connected along the same line. In a series pipe, the total friction loss is the sum of the loss in all the individual pipes. Therefore, in a pipe such as the one shown above the total head loss can be determined as follows: Parallel Pipe Systems: As the name suggests, this is a pipe system with flow separating into parallel pipes. There are three concepts which are important to keep in mind during the analysis of parallel pipes:

1. The head loss in parallel pipes is equal
2. The head loss between the inlet and outlet is equal to that of each pipe individually
3. The flow rate at the outlet is equal to the sum of the flow rates from the parallel pipes

Pipe Networks: These are more complicated systems of pipes which have flow breaking off in multiple directions. Often pipe networks are very complicated and left to iterative analysis on computers. It is important to note the two concepts which govern the analysis however:

1. The flow entering the system is equal to the flow leaving the system (conservation of flow)
2. The sum of head losses in any closed loop is equal to zero

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Open Channel Flow

For open channel flow use the Chezy-Manning equation: Q = (1.49/n)AR2/3S1/2 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

Stormwater Collection and Drainage

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: K = Gutter flow constant = 0.56 ft3/(s*ft) z = Inverse of the cross slope of the gutter (Decimal) n = Roughness coefficient s = Slope of the gutter (Decimal) y = water depth at the curb (ft) Storm Sewer Pipes: Pipes installed under the road which carry the water from inlets to a suitable outlet.

Sub- and Supercritical Flow

Sub and super critical flows are relative to the critical flow depth. This depth is defined as that which minimizes the energy of the flow of water for a given channel cross section and slope. The critical flow depth is important because since the energy is minimized the flow rate is maximized. So when the flow depth is greater than the critical depth, the flow is subcritical and the velocity is less than the critical velocity. When the depth is less than the critical depth, the flow is supercritical and the velocity is faster than the critical. For a rectangular channel, the following equations can be used to determine the critical depth and critical velocity: dc = Critical depth of flow (ft) Q = Flow rate (ft3/s) w = Width (ft) The Froude number is used to qualify a flow channel and can be used to determine if it is sub or supercritical. The number is dimensionless: v = Velocity (ft/s) L = Characteristic length and is determined based on the channel geometry. For a rectangular section L = d For a circular section flowing half full L = πD/8 For trapezoidal and semi-circle sections L = the area of flow/top width of channel If the Froude number is less than 1, the flow is subcritical If the Froude number is greater than 1, the flow is supercritical A hydraulic jump is a rise in water elevation due to a supercritical flow abruptly meeting a subcritical flow. The following equations can determine the heights and velocities in a hydraulic jump for rectangular sections: d1=depth of supercritical flow (ft) d2=depth of subcritical flow (ft) Fr = Froude Number for associated depth v = Velocity at associated depth (ft/s) g = Force effect due to gravity (32.2 ft/s2)

Storm Characteristics

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.

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) 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.)

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:

Rainfall

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 and are covered below.

Time of Concetration

Stream Gauging

Stream gauging is the measurement of a stream channel to determine the discharge by obtaining the depth and velocity of the channel over time. The channel can be approximated by areas created by connected the dots of the measured depths. The discharge can be calculated by the following: w = Width of cross section (ft) y = Height of cross section (ft) v = Velocity at indicated cross section (ft/s)

Depletions

The change in storage for a body of water can be approximated from the following equation: ΔS=P+R+GI-GO-E-T-O S = Storage P = Precipitation R = Runoff GI = Groundwater inflow GO = Groundwater outflow E = Evaporation T = Transpiration O = Surface water release

Stormwater Management

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 control 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. Infiltration is the rate of which water seeps into the ground. The Horton equation can be used to approximate this rate. This assumes that the water supply is infinite and the ground is saturated:

Aquifers

Aquifers are bodies of saturated rock which contain and allow for the flow of water. Aquifers then by definition must be of a material that is porous and permeable. Some examples of material which are common for aquifers are sandstone, fractured limestone, and gravel but many others exist. Aquifers can be divided into 2 zones separated by the portion above and below the water table. The portion below is also saturated whereas that above may be fully, partially, or not saturated. Aquifers are often defined by certain characteristics which can be calculated using soil samples. These are the same as discussed in the soil properties section of the morning session but we define some of the most common characteristics here: The Hydraulic Gradient is also an important characteristic in defining an aquifer. This is defined as the change in hydraulic head over a particular distance: i = Hydraulic gradient H = Height (ft) L = Length (ft)

Groundwater Flow

Well Analysis

Wastewater Collection Systems

Wastewater is collected by a network of pipes known as sanitary sewer. Some residents may not be connected to the sewer line and may resort to septic tanks for their wastewater disposal. Wastewater in sewer networks is transported to the wastewater treatment plants to be treated. Lift stations are pump stations which can be used to facilitate the transportation of the waste water to the treatment plant. Smoke testing is a method of determining if there are leaks in a wastewater system. Smoke is pumped into a pipe and will seep through any cracks which can then be identified. Infiltration is water which enters the system due to imperfections in the system such as cracks in the line or improperly constructed portions. Inflow is water that enters the system from unanticipated or illegal means.

Wastewater Treatment Process

Wastewater treatment processes are the procedures for treating wastewater so that it may be used again. This process will remove sediments, sludge, taste, odors, and any other undesirable characteristics of the water. The process can be divided into preliminary, primary, and secondary treatment which will be discussed further below.

Wastewater Flow Rates

The quantity of wastewater from a municipal needs to be determined to properly design the treatment system. This is based on anticipated discharge from residential, commercial and other buildings. In addition, the system must account for infiltration and inflow as defined previously. Flow rate can be approximated as the average flow or the peak flow. The peak flow is the highest daily flow rate. The average and peak flow are related by the peaking factor: The peak factor can also be approximated by the population using the Harmon equation: P is the population in thousands of people

Preliminary Treatment

Preliminary treatment is the first step in the wastewater treatment process. This portion of the process is mostly the mechanical removal of debris and other large objects which may be caught in the flow. Heavy chemicals and large amounts of oil are also removed during this process. In general, anything that can be identified with the naked eye and easily screened will be removed during the preliminary treatment process. This process is often performed with large mechanical screens or filters. These large obstructions must also be removed so that they do not damage or impede the subsequent processes.

Primary Treatment

Primary treatment is the second level in wastewater treatment. In this portion the wastewater is allowed to settle to remove any remaining oils and any solids which are able to separate. Typically about half of the solids will be removed during this portion of the process. It is also expected that this level of the process will remove 25%-35% of the Biochemical Oxygen Demand (BOD) in the wastewater.

Nitrification and Dentrification

Nitrification is the use of oxygen by autotrophic bacteria. In this process the bacteria oxidizes ammonia to nitrites and nitrates. This process is important to understand as it relates to determining the Biochemical Oxygen Demand (BOD) of a particular sample and more specifically, the Ultimate Biochemical Oxygen Demand (BODu). To test for BOD, samples are diluted and dissolved oxygen is measured initially and typically after a 5-day period. The following equation is used to determine the Biochemical Oxygen Demand after that 5-day period (BOD5): DOi = Initial Dissolved Oxygen content DOf = Final Dissolved Oxygen content V = Volume The process of nitrification causes a deviation from the trajectory of the carbonaceous process of oxygen demand as it relates to time. This must be accounted for when determining the Ultimate BOD. The BOD at any time t is called the BOD exertion and is related to the ultimate by the following equation: It is important to note that at initially in a sample there is only a small amount of autotrophic bacteria present and the process of nitrification is delayed from having a significant effect on the BOD process. For reference the chemical equation for nitrification is: Denitrification is the removal or loss of nitrogen by the means of bacteria. The chemical equation is:

Phosphorous Removal

Phosphorous removal can be separated into two different types. A small percentage is insoluble and can be removed during primary settling. The remaining amount is soluble and must be chemically converted to an insoluble material for removal. Often aluminum sulfate, ferric sulfide, and lime is used to complete this process so that the phosphorous can precipitate and settle for removal. The most common is aluminum sulfate. The Chemical equations for removal are:

Solids Treatment

Mixed Liquor Suspended Solids (MLSS) is the concentration of bacteria, solids, and any other undesirable material in sludge. To remove sludge, the MLSS is considered food for the activated microorganisms in the aeration process. It is often important to determine the food to microorganism ratio from the equation below:

Digestion

Digestion is a process of treating sludge that is too thick or bulky to be easily worked with for disposal. In other words if the sludge is too thick it can be further broken down by digestion so that it can be moved more easily. There are 2 processes of digestion: aerobic and anerobic. Aerobic digestion is putting the sludge in a large open holding tank for a period of time. In this tank the sludge is stirred and left open to air. This allows bacteria to consume the sludge reducing the solids. Often, up to 70% of the solids can be removed through this process. Anaerobic digestion as the name suggests occurs without the use of oxygen. This process is more delicate in nature and proper care must be taken during as to not upset the desired result. However, it is often a more economical solution. Bacteria which does not require oxygen is introduced to the system. These bacteria, in a three-stage process, convert the sludge to gases which can then be released.

Disinfection

Disinfectants are chemicals which are used to kill bacteria that is present in water. In general when disinfectants are discussed, the chemical referred to is chlorine. Chlorine is easily the most widely used mainly because of the cost comparative to other types of disinfectants. Chlorine however is a toxic substance and can be extremely dangerous to public health. It must be handled safely and properly. In wastewater chlorine can be used to destroy common bacteria such as coliform. This is the presence of fecal matter in water supply.

Advanced Treatment

Advanced treatment also known as tertiary treatment and is a final level of the wastewater treatment process. This phase handles any remaining pollutants that are still above allowable levels that have not been removed during the previous stages. Here are some of the pollutants that may be removed during this level. Suspended Solids – At this point any solids remaining are very small in size and would need to be removed by more advanced techniques. This may involve microstrainers or filter beds which are able to remove very high gradation solids. Phosphorous – This stage may require the removal of phosphorous. This is done through the use of chemical precipitation. This process utilizes aluminum, iron, and lime coagulates. Ammonia – There are many processes for use of removal of ammonia to acceptable levels. These may include stripping, biological denitrification, breakpoint chlorination, anion exchange, and algae ponds.

Secondary Treatment

The most intensive of the levels of wastewater treatment is the secondary treatment. This may involve biological treatment in tickling filters and sludge treatment. The most amount of BOD will be removed in this stage.

Stream Degradation

Stream Degradation is the wearing away and lowering of a stream bed over time due to erosion from the flow of water within a stream. Often flow rates and velocities which are too high can cause this. The removal of the soil can affect the water quality by increasing the amount of sediment in the water and therefore decreasing clarity and oxygen in the stream.

Oxygen Dynamics

Oxygen dynamics is related to the amount of oxygen present in flowing water. More specifically this type of oxygen is referred to as Dissolved Oxygen (DO). Simply put dissolved oxygen is the amount of gaseous oxygen present in a moving volume of water. DO is also affected by the temperature and must be adjusted appropriately Dissolved Oxygen is one of the more relevant parameters when determining the quality of a mass of water so it is important to be able to understand and analyze its content. Typical concentrations of DO may vary greatly throughout the year for a given body of water. Concentrations may range anywhere from 1 mg/L to 20 mg/L. The level that is appropriate is based on the type of life that needs to be sustained. Certain organisms require a larger content of DO to survive than others. For example, larger marine animals such as trout or salmon may require 12-14 mg/L whereas others like pike may only need 3-4 mg/L. Re-aeration is a process used to increase the Dissolved Oxygen content of a specific water source. This is where oxygen from the air is dissolved into the water by causing turbulence in the water. Turbulence causes the water to move rapidly by forces such as a physical force, wind or currents. This causes a mixing of the water and air in which increased amounts of oxygen will begin to dissolve into the body of water. Turbulence can be used to mix bottom and top areas of water which may have uneven amounts of dissolved oxygen. Often the top portion of water will have higher concentrations. Mixing them will more evenly distribute the dissolved oxygen. To determine the final DO concentration resulting from the mixing of two sources, use the following: C = Concentration Q = Flow rate

Total Maximum Daily Load (TMDL)

Total Maximum Daily Load often referred to as TMDL, relates to the Clean Water Act of 1972 which set the standards for pollutants in water. TMDL in accordance with this legislation provides the maximum amount of a pollutant which a body of water can receive that will not violate the quality standards. Some of the pollutants which are of concern are nitrogen, phosphorous, and sediment among others. TMDL is the sum of all the pollutants entering a system and the inclusion of a factor of safety: TMDL=WLA+LA+MOS+SV WLA = Waste Land Allocation (Direct flow into the body such as pipes and ditches) LA = Land Allocation (Pollutants from land areas) MOS = Margin of Safety SV = Seasonal Variation

Biological Contaminants

Biological contaminants refers to the amount of organisms in the water. These organisms are also sometimes referred to as microbes. The microbes, because they are living, will reproduce if there is a sufficient supply of food. The food is called the substrate and may or may not be limited to facilitate the biological growth. The Monod equation is used to determine the rate at which substrate is converted into biomass which is simply the total mass of microorganisms in a given volume of water. The equation is as follows:

Chemical Contaminants

Chemical contaminants are a severe concern in water as they may impose health risks to the public. Water should be tested regularly for the presence of such chemicals and action taken immediately. Since chemicals pose a risk to human life, acceptable levels of risk need to be identified and associated with the concentrations of the chemical. The following equation can be used:

Drinking Water Distribution Systems

As the name suggests, systems are developed so that drinking water can be safely and efficiently distributed to the populations. These systems may consist of many components such as pipes, reservoirs, pumps, storage tanks and many others. These components carry water from a centralized distribution plant which maintains regulated levels of safe drinking water.

Drinking Water Treatment Process

There is a large number of processes which can be performed to get water meeting quality standards. The selection of which processes are performed depends heavily on the characteristics of the water specific to a certain plant. The procedure can be divided into 3 components: Pretreatment, Treatment, and Special Treatment. Here we will provide a breakdown of what may be involved in each portion depending on the type of water that needs to be treated. Pretreatment Screening: As the name suggests suspended solids which are large enough to be physically removed by allowing water to flow through fine screens is an initial process that is necessary to remove any debris. Microstraining: A second level of screening used to remove the more finer debris. This process is very effective in the removal of algae. Plain Settling: A removal of sediment by allowing the water to sit and the natural movement of sediments to fall to the bottom to occur. Aeration: The rapid moving of water to allow mixing or the infusion of oxygen into the water. Aeration can have many benefits depending on the desired result. It can increase dissolved oxygen, decrease dissolved gases, reduce iron and manganese, or decrease odor and taste compounds. Treatment Lime Softening: As the name suggests this is the process of adding lime water (calcium hydroxide) to soften water. This additive will react with the calcium and manganese to form precipitates. Coagulation and Sedimentation: This process is the addition of chemicals, called coagulates, to form together contaminants into solids which can then be removed. Coagulates form together precipitate which is called floc. This process is essential to the treatment of water and is covered in greater detail later on. Rapid Sand Filtration/Pressure Sand Filtration: See section on filtration.

Demands

Water demands need to be measured and analyzed so that distribution systems may be properly designed. Water demand is most often specified as gallons per capita per day (gpcd). It can also be expressed as Average Annual Daily Flow (AADF) which as the name suggests is the average daily use of water per person averaged over a year time period. A common value used for basic design purposes is often taken as 165 gpcd but should be adjusted based on the intended water use whether it be residential, commercial, or industrial. Besides the average flow demand throughout a day, there may be increased demands instantaneously which systems must have adequate capacity for. The average annual daily flow times a specified multiplier is often used to determine the instantaneous demand: Qinstant=M(AADF) It is also important to note that per capita demand needs to account for the entire population but it must often be specified at what time period. Because of growth, a distribution system should meet some future predicted growth of population.

Storage

Water supplies need to be stored for a variety of uses and as well as to ensure adequate supply in times of growth or emergency. Water can be distributed from storage either through gravity or pumping. Gravity is available when there is a sufficiently high point in elevation relative to the population. Otherwise pumping is necessary. Water is most often stored in surface or elevated tanks. Within these tanks the elevation of the surface water is monitored to determine the appropriate distribution pressure. These are often monitored by altitude valves.

Sedimentation

A plain sedimentation tank is used to allow water which includes suspended sediments to settle out. The time and velocity for the particles to settle is a function of the temperature of the water, the particle size and the specific gravity of the particles (however this is often taken as 2.65 for analysis). Assumed settling velocities can be taken as the following to calculate the actual settling velocities: Gravel: 3.28 ft/s Coarse Sand: 0.328 ft/s Fine Sand: 0.0328 ft/s Silt: 0.000328 ft/s Then the approach to determining the settlement time can be determined by first calculating the Reynolds number:

Taste and Odor Control

There are many processes which can aid in the elimination of undesirable taste and odor in water. Some include chlorination, aeration and micro straining. To identify the presence of taste or order, the threshold odor number (TON) is established and can be calculated as per below: TON= (V Raw Sample+V Dilution Water)/VRaw Sample Typically, a TON of less than 6 is desirable

Rapid Mixing

This process as mentioned above is the addition of chemicals, called coagulates, to form together contaminants into solids which can then be removed. Coagulates form together precipitate which is called floc. For this reason we have combined two of the NCEES syllabus items since it is most appropriate to discuss these topics together. The most common type of coagulates are aluminum sulfate commonly referred to simply as alum. Others include ferrous sulfate and chlorinated copperas. Alum is often provided in doses in the range of 5-50 mg/L. There are three requirements for Alum to be effective: A large enough quantity of Alum must be present to neutralize the negative particles present in the water Enough alkalinity must be present to facilitate the reaction of aluminum sulfate to aluminum hydroxide The PH must be within the acceptable range which is a function of the type on contaminant. Typically it is taken between 6-7 The amount of coagulate to successfully form floc must be determined. The equation for the feed rate is:

Filtration

Filtration is used to remove excess floc, precipitates from softening, algae, debris and any other suspended byproducts remaining in the treated water. The most common is rapid sand filtration. Rapid Sand Filtration is the filtering of water through a bed of sand and gravel as a medium for removing suspended particles. Water moves through a layer of sand in which the suspended particles will be held back by the sand. Depending on the type of filter, the loading rate can be anywhere from 2 – 10 gpm/ft2. The loading rate can be determined by the following equation: Load Rate= Flow Rate/Area Filters often need to be cleaned and therefore there is a high maintenance cost. The pores between the filters will become clogged and need to get washed out. To counteract this is a process called back washing. This is where water is pumped slowly in the reverse direction of the water to be filtered so that the pores in the sand can be expanded to release any trapped material. It is important during backwashing to monitor the rise rate of the water to ensure it does not exceed the settling velocity of the smallest particle intended to be left in the filter. These rates are often taken as about 1-3 ft/min. The amount of backwash needed can be determined by: V= Area Filter(Rise Rate)(t Backwash)

Disinfection

Disinfectants were defined earlier in the wastewater section. Here we will discuss by products. Chlorine in water produces the following chemical reaction depending on PH PH > 4: Cl2+ H2O →HCl+HOCl PH > 9: HOCl → H++ OCl- HCl and HOCL are hydrochloric and hypochlorous acids respectively. You can see that at PH greater than 9, the hypochlorous acid becomes hydrogen and hypochlorite ions.

Hardness and Softening

Hardness is a measure of the presence of calcium and magnesium ions expressed as calcium carbonate (CaCO3). Practically, hardness in water does not provide any health concerns but does have an effect on the usefulness of the water. One of the main concerns is often that hardness in water will greatly reduce the effectiveness of soap. It also has a detrimental effect on the pipes and storage facilities of a water distribution system. There are two types of hardness: Carbonate Hardness: Water containing Bicarbonate (HCO3-) Noncarbonate Hardness: Remaining hardness not carbonate due to sulfates, chlorides, and nitrates. Hardness can also be expressed as total hardness which is the sum of carbonate and noncarbonate hardness in mg/L as CaCO3. There is a clear connection between the alkalinity of water and the hardness. The following assumptions can be made:

• If Total Hardness = Alkalinity, all hardness is carbonate and there are no sulfates, chlorides, or nitrates present

Economic Analysis

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