Core Concepts for the Civil PE Exam:

Morning Breadth

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PROJECT PLANNING

Quantity Take Off Methods


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




Cost Estimating





Project Schedules


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




Activity Identification and Sequencing


The appropriate steps in the proper sequence need to be identified to complete a project. This involves understanding all the tasks involved in a specific project type and providing a timeline of events to properly facilitate the successful completion of the project. There are many types of projects and the specifics can vary. For the purposes of the PE Exam, it is important to have a general knowledge of common construction tasks and sequences. Below are some examples of design and construction tasks divided by when they occur in certain project phases:

Pre-Design/Design/Project Award

  • Owner initiates project
  • Owner hires Architect/Engineer or uses In-House Architect/Engineer
  • Contract documents and specifications are developed
  • Contractors bid on the project
  • Project is awarded

Pre-Construction

  • Contractor submittals are reviewed and approved
  • Sub-Contractors hired
  • Site survey, staking, and layout
  • Procurement of materials

Construction

  • Traffic Control, water handling, etc. installed if necessary
  • Crane set up and positioning
  • Temporary earth retaining systems installed if necessary
  • Excavation
  • Formwork or Erection
  • Testing of materials
  • Installation of rebar
  • Pouring of concrete
  • Concrete curing
  • Backfill

Post-Construction

  • Semi Final/Final Inspections
  • Open road to traffic
  • Punch-Lists
  • As-Built drawings





Means and Methods

Construction Loads


Construction loads are temporary loads, occurring within the duration of a project, imposed on a structure which may be partially or fully complete. This may include materials, personnel, equipment, or temporary structures. The concern for construction loads is to understand the different types of stresses they may impose on members as opposed to the final in-place condition of those members and ensure they are designed to handle these forces.

Materials: Storage of materials is an often overlooked aspect of a project. Rebar, excavated materials, or other building materials need to be stored in an accessible location and will often impose a large additional dead load on the structure.

Temporary Structures: Temporary structures may often be needed to either provide additional support to unstable members or access for personnel to continue the erection process. Temporary structures may also be for the housing of materials or personnel.

Equipment: Equipment is often needed for various construction activities such as welding or painting procedures. The weight and distribution of these loads should be accounted for.

Cranes: Cranes can also be considered equipment however special attention should be given to the sequencing of erection based on the cranes reach.

Members in Temporary Conditions: Along with additional dead load, construction can introduce stresses into members for which they are not designed. Some examples include the erection of a precast member such as a wall panel which may be designed for compression but will see some flexure about its weak axis while it is being picked and placed. Also, the first steel girder in a bridge before it is connected to the others through diaphragms will be unstable and must be temporarily supported. In these conditions, design measures need to be taken even though they are not required for the final condition.




Construction Methods


Steel: Strong and durable material. Steel has the capabilities to be used for long span bridges and high rise buildings. Steel members are manufactured using either the hot-rolled or cold-formed methods. Steel members are provided in predetermined shapes. Some examples include W-, S-, C, and HSS-shapes. Steel is connected and constructed by the use of bolted or welded connections. The advantages of steel are again the ability to span long distances and the weight of the members compared to the strength is relatively low. Some disadvantages include the high cost, lack of ability to form unique shapes, and tendency of the material to corrode. When steel is exposed to salts, a chemical reaction occurs causing the steel to rust and even loose section properties. To counteract corrosion some preventive measures are paint systems, coating systems such as galvanizing, or weathering steel.

Reinforced Concrete: Concrete is strong in compression but weak in tension. However it has the ability to bond to reinforcing steel to appropriately resist tension. Reinforced concrete is used in buildings and shorter span bridges or certain components of bridges. Some common applications are foundation elements, bridge decks and parapets, or retaining walls. The advantage of concrete is it can be formed to any shape or aesthetic look with proper formwork and is strong in compression. The disadvantages however are that concrete has a high self-weight, will likely crack, and has a limited span length. The reinforcing in concrete can also corrode and cause pop-outs or spalls.

Precast/Prestressed/Post-Tensioned Concrete: Precast concrete is concrete which is cast somewhere other than its final location, either at a plant or another area on the construction site, and is then stripped from its forming, transported to the site, and erected. Prestressed concrete is precast concrete which has been pre-compressed using steel strands with high elasticity. The strands are tensioned to a design force before the concrete is cast. Then the concrete mix is placed and cured. The strands are then cut at the ends. Since the strands have a high elasticity, they will try to return to their original state. However since the stands are now bonded to the concrete, there is a compressive force transferred to the concrete. This force will oppose the stresses caused by bending. Post-Tensioned concrete uses the same concept as prestressed concrete. However, the concrete member is cast first and the strands are tensioned through the member using plastic tubes embedded along the length of the member. The tube is then grouted and the strands are cut to transfer the force. Precast Concrete will have the lowest tensile capacity and therefore is used for the lowest spans. Precast is often used for compression members or bridge deck units. Prestressed Concrete is be able to span larger distances and is used for floor members. It is common in parking garages as double-tee shapes for floor members or for long span bridges with common shapes such as prestressed bulb tees. Post tensioned concrete is not as common and is used for much larger spans. Precast concrete advantages are the quality of concrete is often better under plant controlled conditions and the construction is much quicker. The disadvantages are there is a higher cost than reinforced concrete due to shipping and erection expenses and the tendons also are susceptible to corrosion.

Wood: Relatively low strength material. Wood is often used in residential applications or for very small span bridges. Wood is extremely cheap and lightweight for erection. In addition to the low strength, wood also will deteriorate due to rot and is highly sensitive to fire damage.

Masonry: Can be reinforced or unreinforced. Masonry is also strong in compression but weak in tension. Only used in small retaining wall applications and some older bridges still are composed of masonry components.




Temporary Structures


Structures which are built for a specific purpose, often to facilitate an aspect of a construction project, and are removed before the conclusion of the project are temporary structures. Some examples include:

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





Soil Mechanics

Lateral Earth Pressure





Soil Consolidation


Settlement is when the soil supporting the foundation consolidates which causes a decrease in volume and a drop in elevation. This causes the foundation to no longer be fully supported and will introduce additional stress. There are three phases of settlement:

  1. Immediate Settling or Elastic Settling: This settlement occurs immediately after the structure is built. The load from the structure causes instant consolidation of the soil. This is the main component of settlement in sandy soil conditions.

  1. Primary Consolidation: A more gradual consolidation which is due to water leaving the voids over time. This is mostly a factor only in clayey soils.

  1. Secondary Consolidation: Also occurs at a very gradual rate. This is due to the shifting and readjustment of soil grains. Most often this is the lowest magnitude of consolidation phases.




Effective Stress





Bearing Capacity


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




Slope Stability






Structural

Dead and Live Load


Dead Loads: Loads which are permanent in the final condition of the structure. Examples include self weight and additional permanent loads (such as pavement). Dead load factors are often lower than other types of loads. This is due to the higher level of reliability being able to predict the magnitude and character of these loads.

Live Loads: Loads which will or may change over time. In general live loads represent pedestrian or vehicle loads. The load factor for live loads is often much higher due to the unpredictability.

In LRFD different types of loads are factored to represent a safety factor based on the reliability of our ability to accurately predict certain loading conditions. If only Dead and Live loads are present, the likely load combination is:

1.2D + 1.6L




Trusses


Trusses are structural members used to span long distances. Trusses are built up by members which are only in axial tension or axial compression. They can be analyzed by the method of joints as illustrated below. Consider the example truss with nodes labeled. To design, the axial force in each member must be determined. If we wanted to find the force in member BD, first like a typical beam, the reactions at A and B can be found by summing forces. Then take a free body diagram of only the joint at A. This is shown below. In summing vertical reactions and since the reaction at A was found, the force in AC can be determined. Then there are only 2 horizontal forces and the force in AB can be found: Then take a free body diagram of Joint B as shown below. Since there are only two horizontal forces, the axial force in member BD can then be determined:

The remainder of the truss can be analyzed similarly.

Zero force members:

When determining how many 0-Force members a truss has, analyze each joint individually as a free body diagram and follow these guidelines:

  1. In a joint with 2 members and no external forces or supports, both members are 0-force
  2. In a joint with 2 members and external forces, If the force is parallel to one member and perpendicular to the other, then the member perpendicular to the force is a 0-force member.
  3. In a joint with 3 members and no external forces, if 2 members are parallel then the other is a 0-force member

All other members are non-zero.




Bending Stress


Bending Stress

Mc/I

M = Applied Moment

c = Distance from the Centroid of the Cross Section to the Desired Location of Stress

I = Moment of Inertia of the Cross Section




Shear Stress


Shear stress at any point along a beam is the shear at that point over the area.

t = V/A

V = Shear at the point of interest

A = Cross sectional area

There is also horizontal shear stress due to bending

Horizontal shear stress t = VQ/Ib

V = Applied Shear Force (kips)

Q = First Moment of the Desired Area = ay.

a = Cross Sectional Area from Point of Desired Shear Stress to Extreme Fiber (in2)

y = Distance from Centroid of Beam to Centroid of Area “a” (in)

I = Moment of Inertia of Beam (in3)

b = Width of Member (in)




Axial Stress


Axial Stress:

P/A

P = Applied Force

A = Cross Sectional Area




Deflection


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




Beams


The chart below shows reactions, moments, and max deflections for common beam types:

Shear and Moment Diagrams

Shear and moment diagrams are a graphical representation of the forces applied along the length of a beam. The following rules are used to develop shear diagrams:

-A concentrated force causes a jump In the shear diagram of equal magnitude

-A distributed load causes a line in the diagram with slope equal to the distributed load

-Forces up are positive and down is negative

This is depicted graphically below:

The following are rules for construction of a moment diagram:

-The moment at any point on the graph is equal to the area under the shear diagram up to this point

-An isolated moment causes a jump in the diagram of equal magnitude

-The shear at any point in the beam is equal to the slope of the same point on the moment diagram

-A distributed load will cause a parabolic moment diagram curve




Columns





Slabs


One way slabs:

Slabs are structural elements whose length and widths are large compared to the thickness. Slabs are often used as floors or as foundation elements.

Flexure:

Slabs must be analyzed by simplified methods due to the indeterminacy of a full analysis. The most common of which is to analyze as a 1- foot wide strip and treat the span length as a beam. Transverse reinforcement is necessary to control temperature and shrinkage.

Shear:

Shear in slabs is also determined by taking one foot wide sections to analyze as a beam. However often shear will not control.




Footings





Retaining Walls


Retaining walls are built to facilitate an immediate change in elevation. Some uses are to support roadways or a need for a wide, level area to be formed from a sloping existing grade. Retaining walls are designed to resist lateral loads from active earth pressure (see geotechnical section for computation of these loads) and surcharge loads which is any additional load imposed on the soil above, which when close enough will cause an additional pressure on the load due to the distribution of this load through soil. The stem of retaining walls can be analyzed as a cantilever beam extending vertically from the footing. The footing is composed of the toe which is the portion on the side of the lower elevation of soil and the heel which is portion on the side of the higher elevation of soil. Retaining walls are analyzed on a per foot width:

Moment at base of stem= Mstem=Rahya

Rah = Horizontal Active Earth Pressure per ft Width

ya = Eccentricity of Horizontal Active Earth Pressure

For shear, the critical section is a distance, d, from the base of the stem where d is the distance from the main flexural reinforcement (Heel side) to the extreme compression face (Toe side):

Vstem=Rah





Hydraulics and Environmental

Open Channel Flow


For open channel flow use the Chezy-Manning equation:

Q = Flow Rate (cfs)

n = Roughness Coefficient

A = Area of Water

R = Hydraulic Radius

S = Slope (decimal form)

The hydraulic radius is the area of water divided by the wetted perimeter which is the perimeter of the sides of the channel which are in contact with water.




Stormwater Collection


There are many components used in the collection of stormwater some examples include:

Culverts: A pipe carrying water under or through a feature. Culverts often carry brooks or creeks under roadways. Culverts must be designed for large intensity storm events.

Stormwater Inlets: Roadside storm drains which collect water from gutter flow or roadside swales.

Gutter/Street flow: Flow which travels along the length of the street or gutter.

Storm Sewer Pipes: Pipes installed under the road which carry the water from inlets to a suitable outlet.

The principle of Conservation of Flow is often applicable when analyzing drainage. It states that the flow in must equal a flow out and therefore:

Q1 + Q2 = Q3




Storm Characteristics


Storm characteristics include duration, total volume, and intensity

Duration: The length of time of a storm. Often measured in days and hours.

Total Volume: The entire amount of precipitation throughout the duration of the storm in a defined area.

Storm Intensity: Total volume of the storm divided by the duration of the storm event. Intensities can be averaged over the entire storm or at shorter intervals to provide instantaneous high intensity portions of the storm. Hyetographs are bar graphs used to measure instantaneous rainfall intensities over time.

A design storm must be specified when performing any calculations. The design storm is defined by its recurrence interval which is the given amount of time it is likely to see a storm of a certain intensity. Design storms are often 10, 20, 50, or 100-year storms meaning a storm of a certain intensity would only occur once within the given duration.

Hyetographs – Graphical representation of rainfall distribution over time

Hydrograph – Graphical representation of rate of flow vs time past a given point often in a river, channel or conduit

Parts of a Hydrograph are shown graphically:




Runoff Analysis


The rational method can be used to determine the flow rate from runoff of a drainage area. The equation is:

Q = ACi

Q = Flow Rate (cfs)

A = Drainage Area (Acres)

C = Runoff Coefficient

i = Rainfall Intensity (in/hr)

For total flow from multiple areas to a single outlet the conservation of flow principle is applied and the total is the sum of all flow into the outlet.

Time of Concentration, tc: The time of travel for water to move from the hydraulically most remote point in a watershed to the outlet. The time of concentration is the sum of three components:

tc=tsheet+tshallow+tchannel

For approximately the first 300 ft, water moves as sheet flow:




NRCS/SCS Runoff Method


This is an alternative method for determining runoff:

S = Storage Capacity of Soil (in.)

CN = NRCS Curve Number

Q = Runoff (in.)

Pg = Gross Rain Fall (in.)




Detention and Retention Ponds


Detention and retention ponds are often used to collect water for flood control and stormwater runoff treatment.

Detention Ponds: Also known as dry ponds. These are ponds which are often kept dry except during flood events. The pond will fill up during increased precipitation to control the flow intensity. This is common in dry, arid or urban areas to prevent excessive flooding. The ponds typically will be designed to hold water for about 24 hours. Detention ponds also controls the amount of sediment since it is captured in the pond and then typically becomes accessible after the pond has dried.

Retention Ponds: Also called wet ponds since they contain a volume of water at all times. The elevation of the water will vary depending on precipitation but will always maintain a permanent amount of water based on low flow conditions. This allows sediment control since the deposits will settle to the bottom and allow for collection.




Pressure Conduits


The Darcy Equation is used for fully turbulent flow to find the head loss due to friction. The equation is:

hf = Head Loss Due to Friction (ft)

f = Darcy Friction Factor

L = Length of Pipe (ft)

v = Velocity of Flow (ft/sec)

D = Diameter of Pipe (ft)

g = Acceleration Due to Gravity, Use 32.2 ft/sec2

The Hazen-Williams equation is also used to determine head loss due to friction. Be aware of units as this equation may be presented in different forms. The most common is the following:

hf = Head Loss due to Friction (ft)

L = Length (ft)

V = Velocity (gallons per minute)

C = Roughness Coefficient

d = Diameter (ft)

In addition to these losses, there is also what is called minor losses of energy due to friction

Minor Losses – Friction losses due to fittings in the line, changes in the dimensions of the pipe, or changes in direction

  • Minor losses can be calculated as per the Method of Loss coefficients.
  • Each change in the flow of pipe is assigned a loss coefficient, K
  • Loss coefficients for fittings are most often determined and provided by the manufacturer
  • Loss coefficients for sudden changes in area must be determined:

For Sudden Expansions:

For Sudden Contractions:
  • D1=Smaller diamter pipe

Loss coefficients are then multiplied by the kinetic energy to determine the loss.




Bernoulli Energy Equation


The Bernoulli equation for the conservation of energy states that the total energy is equal to the sum of the pressure + kinetic energy + potential energy and is conserved at any point in the system. Therefore:

Epr = Pressure = p

Ev = Kinetic Energy = v2/2g

v = Velocity (ft/s)

g = Acceleration Due to Gravity (32.2 ft/s2)

Ep = Potential Energy = z = Height above point of interest to surface of water (ft)





Transportation

Dead and Live Load


Dead Loads: Loads which are permanent in the final condition of the structure. Examples include self weight and additional permanent loads (such as pavement). Dead load factors are often lower than other types of loads. This is due to the higher level of reliability being able to predict the magnitude and character of these loads.

Live Loads: Loads which will or may change over time. In general live loads represent pedestrian or vehicle loads. The load factor for live loads is often much higher due to the unpredictability.

In LRFD different types of loads are factored to represent a safety factor based on the reliability of our ability to accurately predict certain loading conditions. If only Dead and Live loads are present, the likely load combination is:

1.2D + 1.6L




Trusses


Trusses are structural members used to span long distances. Trusses are built up by members which are only in axial tension or axial compression. They can be analyzed by the method of joints as illustrated below. Consider the example truss with nodes labeled. To design, the axial force in each member must be determined. If we wanted to find the force in member BD, first like a typical beam, the reactions at A and B can be found by summing forces. Then take a free body diagram of only the joint at A. This is shown below. In summing vertical reactions and since the reaction at A was found, the force in AC can be determined. Then there are only 2 horizontal forces and the force in AB can be found: Then take a free body diagram of Joint B as shown below. Since there are only two horizontal forces, the axial force in member BD can then be determined:

The remainder of the truss can be analyzed similarly.

Zero force members:

When determining how many 0-Force members a truss has, analyze each joint individually as a free body diagram and follow these guidelines:

  1. In a joint with 2 members and no external forces or supports, both members are 0-force
  2. In a joint with 2 members and external forces, If the force is parallel to one member and perpendicular to the other, then the member perpendicular to the force is a 0-force member.
  3. In a joint with 3 members and no external forces, if 2 members are parallel then the other is a 0-force member

All other members are non-zero.




Bending Stress


Bending Stress

Mc/I

M = Applied Moment

c = Distance from the Centroid of the Cross Section to the Desired Location of Stress

I = Moment of Inertia of the Cross Section




Shear Stress


Shear stress at any point along a beam is the shear at that point over the area.

t = V/A

V = Shear at the point of interest

A = Cross sectional area

There is also horizontal shear stress due to bending

Horizontal shear stress t = VQ/Ib

V = Applied Shear Force (kips)

Q = First Moment of the Desired Area = ay.

a = Cross Sectional Area from Point of Desired Shear Stress to Extreme Fiber (in2)

y = Distance from Centroid of Beam to Centroid of Area “a” (in)

I = Moment of Inertia of Beam (in3)

b = Width of Member (in)




Axial Stress


Axial Stress:

P/A

P = Applied Force

A = Cross Sectional Area




Deflection


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




Beams


The chart below shows reactions, moments, and max deflections for common beam types:

Shear and Moment Diagrams

Shear and moment diagrams are a graphical representation of the forces applied along the length of a beam. The following rules are used to develop shear diagrams:

-A concentrated force causes a jump In the shear diagram of equal magnitude

-A distributed load causes a line in the diagram with slope equal to the distributed load

-Forces up are positive and down is negative

This is depicted graphically below:

The following are rules for construction of a moment diagram:

-The moment at any point on the graph is equal to the area under the shear diagram up to this point

-An isolated moment causes a jump in the diagram of equal magnitude

-The shear at any point in the beam is equal to the slope of the same point on the moment diagram

-A distributed load will cause a parabolic moment diagram curve




Columns





Slabs


One way slabs:

Slabs are structural elements whose length and widths are large compared to the thickness. Slabs are often used as floors or as foundation elements.

Flexure:

Slabs must be analyzed by simplified methods due to the indeterminacy of a full analysis. The most common of which is to analyze as a 1- foot wide strip and treat the span length as a beam. Transverse reinforcement is necessary to control temperature and shrinkage.

Shear:

Shear in slabs is also determined by taking one foot wide sections to analyze as a beam. However often shear will not control.




Footings





Retaining Walls


Retaining walls are built to facilitate an immediate change in elevation. Some uses are to support roadways or a need for a wide, level area to be formed from a sloping existing grade. Retaining walls are designed to resist lateral loads from active earth pressure (see geotechnical section for computation of these loads) and surcharge loads which is any additional load imposed on the soil above, which when close enough will cause an additional pressure on the load due to the distribution of this load through soil. The stem of retaining walls can be analyzed as a cantilever beam extending vertically from the footing. The footing is composed of the toe which is the portion on the side of the lower elevation of soil and the heel which is portion on the side of the higher elevation of soil. Retaining walls are analyzed on a per foot width:

Moment at base of stem= Mstem=Rahya

Rah = Horizontal Active Earth Pressure per ft Width

ya = Eccentricity of Horizontal Active Earth Pressure

For shear, the critical section is a distance, d, from the base of the stem where d is the distance from the main flexural reinforcement (Heel side) to the extreme compression face (Toe side):

Vstem=Rah





Materials

Dead and Live Load


Dead Loads: Loads which are permanent in the final condition of the structure. Examples include self weight and additional permanent loads (such as pavement). Dead load factors are often lower than other types of loads. This is due to the higher level of reliability being able to predict the magnitude and character of these loads.

Live Loads: Loads which will or may change over time. In general live loads represent pedestrian or vehicle loads. The load factor for live loads is often much higher due to the unpredictability.

In LRFD different types of loads are factored to represent a safety factor based on the reliability of our ability to accurately predict certain loading conditions. If only Dead and Live loads are present, the likely load combination is:

1.2D + 1.6L




Trusses


Trusses are structural members used to span long distances. Trusses are built up by members which are only in axial tension or axial compression. They can be analyzed by the method of joints as illustrated below. Consider the example truss with nodes labeled. To design, the axial force in each member must be determined. If we wanted to find the force in member BD, first like a typical beam, the reactions at A and B can be found by summing forces. Then take a free body diagram of only the joint at A. This is shown below. In summing vertical reactions and since the reaction at A was found, the force in AC can be determined. Then there are only 2 horizontal forces and the force in AB can be found: Then take a free body diagram of Joint B as shown below. Since there are only two horizontal forces, the axial force in member BD can then be determined:

The remainder of the truss can be analyzed similarly.

Zero force members:

When determining how many 0-Force members a truss has, analyze each joint individually as a free body diagram and follow these guidelines:

  1. In a joint with 2 members and no external forces or supports, both members are 0-force
  2. In a joint with 2 members and external forces, If the force is parallel to one member and perpendicular to the other, then the member perpendicular to the force is a 0-force member.
  3. In a joint with 3 members and no external forces, if 2 members are parallel then the other is a 0-force member

All other members are non-zero.




Bending Stress


Bending Stress

Mc/I

M = Applied Moment

c = Distance from the Centroid of the Cross Section to the Desired Location of Stress

I = Moment of Inertia of the Cross Section




Shear Stress


Shear stress at any point along a beam is the shear at that point over the area.

t = V/A

V = Shear at the point of interest

A = Cross sectional area

There is also horizontal shear stress due to bending

Horizontal shear stress t = VQ/Ib

V = Applied Shear Force (kips)

Q = First Moment of the Desired Area = ay.

a = Cross Sectional Area from Point of Desired Shear Stress to Extreme Fiber (in2)

y = Distance from Centroid of Beam to Centroid of Area “a” (in)

I = Moment of Inertia of Beam (in3)

b = Width of Member (in)




Axial Stress


Axial Stress:

P/A

P = Applied Force

A = Cross Sectional Area




Deflection


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




Beams


The chart below shows reactions, moments, and max deflections for common beam types:

Shear and Moment Diagrams

Shear and moment diagrams are a graphical representation of the forces applied along the length of a beam. The following rules are used to develop shear diagrams:

-A concentrated force causes a jump In the shear diagram of equal magnitude

-A distributed load causes a line in the diagram with slope equal to the distributed load

-Forces up are positive and down is negative

This is depicted graphically below:

The following are rules for construction of a moment diagram:

-The moment at any point on the graph is equal to the area under the shear diagram up to this point

-An isolated moment causes a jump in the diagram of equal magnitude

-The shear at any point in the beam is equal to the slope of the same point on the moment diagram

-A distributed load will cause a parabolic moment diagram curve




Columns





Slabs


One way slabs:

Slabs are structural elements whose length and widths are large compared to the thickness. Slabs are often used as floors or as foundation elements.

Flexure:

Slabs must be analyzed by simplified methods due to the indeterminacy of a full analysis. The most common of which is to analyze as a 1- foot wide strip and treat the span length as a beam. Transverse reinforcement is necessary to control temperature and shrinkage.

Shear:

Shear in slabs is also determined by taking one foot wide sections to analyze as a beam. However often shear will not control.




Footings





Retaining Walls


Retaining walls are built to facilitate an immediate change in elevation. Some uses are to support roadways or a need for a wide, level area to be formed from a sloping existing grade. Retaining walls are designed to resist lateral loads from active earth pressure (see geotechnical section for computation of these loads) and surcharge loads which is any additional load imposed on the soil above, which when close enough will cause an additional pressure on the load due to the distribution of this load through soil. The stem of retaining walls can be analyzed as a cantilever beam extending vertically from the footing. The footing is composed of the toe which is the portion on the side of the lower elevation of soil and the heel which is portion on the side of the higher elevation of soil. Retaining walls are analyzed on a per foot width:

Moment at base of stem= Mstem=Rahya

Rah = Horizontal Active Earth Pressure per ft Width

ya = Eccentricity of Horizontal Active Earth Pressure

For shear, the critical section is a distance, d, from the base of the stem where d is the distance from the main flexural reinforcement (Heel side) to the extreme compression face (Toe side):

Vstem=Rah





Site Development

Excavation


The most common method for determining the volume of excavation for cut and fill is the average end area method:

V = L(A1+A2)/2

L = Distance Between Area 1 and 2 (ft)

A1 and A2 = Respective Cross-Sectional Areas (ft2)




Construction Site Layout


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




Soil Erosion and Sediment Control


During construction activities involving excavation, there can be a significant amount of soil erosion leading to a dispersion of sediment. This needs to be controlled to prevent a negative impact to the surrounding areas. There are a number of options for sediment control:

Silt Fences: Fences consisting of a geotextile fabric and posts which allow the passing of runoff water but will catch the suspended sediment. They will be placed at the bottom of slopes and/or at the perimeter of the job sites at low points.

Hay Bales: Placed at the toe of slopes to help control runoff. Bales should be embedded in the ground and anchored securely with wooden posts.

Erosion Control Fabric: Geotextile fabric used for the control of erosion on steep slopes. Often these are used on piles of excavated material.

Temporary Seeding and Mulch: This involves seeding and mulching slopes to create growth that can control erosion due to the roots holding together soil. This is often used as a permanent measure for cut slopes.

Slope drain: A drain constructed to direct water to a specified area. The drain can be constructed with numerous materials such as plastic or metal pipes and concrete or asphalt. Drains must be properly anchored to resist forces from the flow of water. The outlet often is required to slow the flow of water by using energy dissipaters such as riprap.

Sediment Structure: An energy dissipating structure often made of rocks used to slow the flow of water and catch sediment.

Temporary Berm: A hill constructed of compacted soil to prevent runoff flowing in a specific direction. Berms are placed either at the top or bottom of slopes.

Impact of Construction on Adjacent Facilities

Construction can have a negative effect on surrounding properties and areas. These issues need to be anticipated and mitigated as possible. Some of the concerns include:

Construction Noise: OHSA sets maximum decibel limits on daily sound exposure. In the United States, this is typically 90 dBA for the eight hour noise level

Runoff and Sediment: Construction sites, especially those involving excavation, can change the dynamics of runoff and drainage. See the section on Soil Erosion and Sediment Control for more details.

View: Construction projects often change the landscape of the affected area. This may have an impact on the look and feel of an area. The needs of adjacent properties may need to be considered for these changes.

Rights of Way: Often, land which is not owned by the owner of the project is necessary for the final or temporary conditions. In these cases land needs to be acquired temporarily or permanently to complete the work. The owner of the project and of the land must come to an agreement to allow use of the property

Economic or social impact: Construction during and after may impact the access or desirability of a business or residential area. Consideration should be taken to limit the impacts to businesses or residents. For example, a bridge detour may cut off access to a restaurant which collects patrons mostly from tourists passing the effected route. The owner would then be compensated for the loss of business.




Safety


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

  • Excavation Safety: Except for excavations in rock, anything deeper than 5 ft must be stabilized to prevent cave-in. This may be achieved by providing appropriate earth retention systems or sloping at appropriate rates. This is determined by the depth of excavation, soil type, and other requirements.
  • Fall protection: Drop-offs must be protected from fall based on the height of the drop. Some examples of protection include temporary fences, nets, or lifelines.
  • Roadside Safety: Construction sites adjacent to traffic must be sufficiently protected from impact. At higher speeds concrete barriers may be needed also known as temporary precast concrete barrier curbs (TPCBC). At lower speeds it may be acceptable to provide barrels or cones to delineate the work area.
  • Power line Hazards: For power lines which are electrified, all construction activities must be a minimum distance from the lines. This is based on the voltage of the lines. Typically the safe operational distance is 10 ft. for lines less than 50 kV and typically 35 ft. for lines greater than 50 kV.
  • Confined Spaces: Anyone required to enter confined spaces must be appropriately trained and equipped. Oxygen must be monitored and kept at an acceptable level.
  • Personal Protective Equipment (PPE): Equipment required by any personnel present on a job site. The main aspects are acceptable head protection and steel toed shoes.





 
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