Skip to content

Construction

Construction Engineering · FE Reference Handbook section

Construction Engineering
0 formulas
10 exam-style examples
~45 min
All Construction Engineering lectures

Learning objectives

What you must be able to do before leaving this section.

This chapter section covers Construction within Construction Engineering. Read it the way you would read a textbook chapter: the theory first so the relations mean something, then every equation with its use and its trap, then 10 fully worked examples with the arithmetic shown line by line, and finally a self-check you should be able to answer without notes.

  • Explain, in your own words, what construction describes physically and when it applies.
  • State every one of the 0 relations the handbook lists here and name each symbol with its unit.
  • Select the correct relation from the wording of an exam stem within 20 seconds.
  • Carry a complete solution from givens to a "most nearly" answer with the correct unit.
  • Recognise the distractors generated by the unit trap: crew-hours, cubic yards and dollars per unit.

Lecture

Why this section exists. Construction is the part of Construction Engineering that lets you connect an activity network or production operation to a number you can defend. Before any equation is useful you must be able to picture the physical situation it describes; the schematic below is that picture.

How the theory is built. The handbook prints results, not derivations. Each relation in this section comes from one governing principle applied to the idealised system: state the principle, impose the stated assumptions, and the printed equation follows. Knowing which assumption each relation rests on is what lets you reject a wrong answer choice in seconds.

How it is examined. Items from this page are written as a schedule, productivity or earned-value computation. Roughly two thirds are direct substitution, one third require one intermediate quantity from a neighbouring relation, and a small number are conceptual — testing whether you know the assumption, not the arithmetic.

The habit that earns the points. Unit discipline. crew-hours, cubic yards and dollars per unit. Every relation below is dimensionally consistent only when that rule is honoured, and the distractor set is deliberately built from candidates who ignored it. Write the unit next to every number you substitute, every time.

How to study this page. Read the theory, then cover the formula cards and try to reproduce each relation from its description. Then work the examples with the solution hidden, revealing one line at a time. Finish with the self-check questions; if you cannot answer one, return to the matching formula card.

Three engineers in hard hats and safety vests reviewing drawings on a truck tailgate.

Photo 1. Where this shows up in practice: construction.

Capstone Studio instructional photograph

timecostEarned valuePV, EV and AC curves

Construction Engineering — Construction: reference schematic for orienting the symbols used in this section.

Theory, developed

Read this before the equations — it is what makes them memorable.

The physical situation

Every item from this section describes an activity network or production operation. Sketch it before you compute — a labelled sketch with the givens on it converts a wordy stem into a solvable problem and exposes the quantity the examiner left out on purpose.

The governing principle

The 0 relations on this page are consequences of one principle applied to that idealised system. Identify which quantity is conserved, balanced, or defined, and the correct equation follows without memorisation.

Assumptions and limits of validity

Each printed relation carries silent assumptions — linearity, steady state, uniformity, small deformation, or standard conditions, depending on the subject. Conceptual exam items are written by violating exactly one of these, so read the sentence above the equation as carefully as the equation itself.

Solution procedure you should automate

1) Read the last sentence of the stem to identify the requested quantity. 2) Locate the relation on this page whose left-hand side is that quantity. 3) Tabulate the givens with units and mark the missing symbol. 4) If a symbol is missing, find the one relation that produces it. 5) Rearrange symbolically, substitute once, evaluate, and round only at the end.

Three engineers in hard hats and safety vests reviewing drawings on a truck tailgate.

Photo 2. Construction Engineering: the physical system the theory above idealises.

Capstone Studio instructional photograph

Handbook notes for this section

Definitions and conditions exactly as the handbook states them.

  • Construction project scheduling and analysis questions may be based on either the activity-on-node method or the activity-on-
  • arrow method.
  • CPM Precedence Relationships
  • ACTIVITY-ON-NODE
  • A A
  • A B
  • B B
  • START-TO-START: START OF B FINISH-TO-FINISH: FINISH OF B FINISH-TO-START: START OF B
  • DEPENDS ON THE START OF A DEPENDS ON THE FINISH OF A DEPENDS ON THE FINISH OF A
  • ACTIVITY-ON-ARROW ANNOTATION ACTIVITY-ON-NODE ANNOTATION
  • EARLY START/LATE START EARLY FINISH/LATE FINISH EARLY EARLY
  • START FINISH
  • ACTIVITY
  • i j
  • DURATION ACTIVITY DESCRIPTION
  • DURATION FLOAT
  • LATE LATE
  • START FINISH

Core formulas for this FE topic

Definitions, applicability, units, assumptions and worked examples for each relation.

This section is conceptual; there are no equations to memorise.

Worked exam-style examples

The four ways this section is written on the real exam — thoughts first, then equations, then substitution.

Example 1
Earned-value analysis: performance indices and forecast at completion — Construction

A $6.0M project reports planned value $3,900,000, earned value $4,320,000 and actual cost $5,356,800 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $6,000,000
  • PV = $3,900,000
  • EV = $4,320,000
  • AC = $5,356,800

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

  2. Substituting — CV = 4,320,000 − 5,356,800 = $-1,036,800

  3. Formula

  4. Substituting — SV = 4,320,000 − 3,900,000 = $420,000

  5. Indices

  6. Formula

  7. Substituting — EAC = 6,000,000/0.806 = $7,440,000

Answer: CPI = 0.81, SPI = 1.11, EAC ≈ $7,440,000

Why the other options are there

  • EAC = $4,838,710 (multiplied by the index)
  • CPI = 1.240 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Example 2
Earned-value analysis: performance indices and forecast at completion — Construction (2)

A $6.0M project reports planned value $2,100,000, earned value $1,980,000 and actual cost $1,920,600 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $6,000,000
  • PV = $2,100,000
  • EV = $1,980,000
  • AC = $1,920,600

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

  2. Substituting — CV = 1,980,000 − 1,920,600 = $59,400

  3. Formula

  4. Substituting — SV = 1,980,000 − 2,100,000 = $-120,000

  5. Indices

  6. Formula

  7. Substituting — EAC = 6,000,000/1.031 = $5,820,000

Answer: CPI = 1.03, SPI = 0.94, EAC ≈ $5,820,000

Why the other options are there

  • EAC = $6,185,567 (multiplied by the index)
  • CPI = 0.970 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Example 3
Earned-value analysis: performance indices and forecast at completion — Construction (3)

A $5.0M project reports planned value $1,500,000, earned value $1,650,000 and actual cost $1,815,000 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $5,000,000
  • PV = $1,500,000
  • EV = $1,650,000
  • AC = $1,815,000

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

  2. Substituting — CV = 1,650,000 − 1,815,000 = $-165,000

  3. Formula

  4. Substituting — SV = 1,650,000 − 1,500,000 = $150,000

  5. Indices

  6. Formula

  7. Substituting — EAC = 5,000,000/0.909 = $5,500,000

Answer: CPI = 0.91, SPI = 1.10, EAC ≈ $5,500,000

Why the other options are there

  • EAC = $4,545,455 (multiplied by the index)
  • CPI = 1.100 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Example 4
Earned-value analysis: performance indices and forecast at completion — Construction (4)

A $12.0M project reports planned value $4,200,000, earned value $4,440,000 and actual cost $4,884,000 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $12,000,000
  • PV = $4,200,000
  • EV = $4,440,000
  • AC = $4,884,000

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

  2. Substituting — CV = 4,440,000 − 4,884,000 = $-444,000

  3. Formula

  4. Substituting — SV = 4,440,000 − 4,200,000 = $240,000

  5. Indices

  6. Formula

  7. Substituting — EAC = 12,000,000/0.909 = $13,200,000

Answer: CPI = 0.91, SPI = 1.06, EAC ≈ $13,200,000

Why the other options are there

  • EAC = $10,909,091 (multiplied by the index)
  • CPI = 1.100 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Example 5
Earned-value analysis: performance indices and forecast at completion — Construction (5)

A $4.0M project reports planned value $2,400,000, earned value $2,280,000 and actual cost $2,143,200 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $4,000,000
  • PV = $2,400,000
  • EV = $2,280,000
  • AC = $2,143,200

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

  2. Substituting — CV = 2,280,000 − 2,143,200 = $136,800

  3. Formula

  4. Substituting — SV = 2,280,000 − 2,400,000 = $-120,000

  5. Indices

  6. Formula

  7. Substituting — EAC = 4,000,000/1.064 = $3,760,000

Answer: CPI = 1.06, SPI = 0.95, EAC ≈ $3,760,000

Why the other options are there

  • EAC = $4,255,319 (multiplied by the index)
  • CPI = 0.940 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Example 6
Earned-value analysis: performance indices and forecast at completion — Construction (6)

A $4.0M project reports planned value $1,800,000, earned value $1,320,000 and actual cost $1,372,800 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $4,000,000
  • PV = $1,800,000
  • EV = $1,320,000
  • AC = $1,372,800

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

  2. Substituting — CV = 1,320,000 − 1,372,800 = $-52,800

  3. Formula

  4. Substituting — SV = 1,320,000 − 1,800,000 = $-480,000

  5. Indices

  6. Formula

  7. Substituting — EAC = 4,000,000/0.962 = $4,160,000

Answer: CPI = 0.96, SPI = 0.73, EAC ≈ $4,160,000

Why the other options are there

  • EAC = $3,846,154 (multiplied by the index)
  • CPI = 1.040 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Example 7
Earned-value analysis: performance indices and forecast at completion — Construction (7)

A $8.0M project reports planned value $4,400,000, earned value $3,600,000 and actual cost $3,276,000 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $8,000,000
  • PV = $4,400,000
  • EV = $3,600,000
  • AC = $3,276,000

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

  2. Substituting — CV = 3,600,000 − 3,276,000 = $324,000

  3. Formula

  4. Substituting — SV = 3,600,000 − 4,400,000 = $-800,000

  5. Indices

  6. Formula

  7. Substituting — EAC = 8,000,000/1.099 = $7,280,000

Answer: CPI = 1.10, SPI = 0.82, EAC ≈ $7,280,000

Why the other options are there

  • EAC = $8,791,209 (multiplied by the index)
  • CPI = 0.910 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Example 8
Earned-value analysis: performance indices and forecast at completion — Construction (8)

A $12.0M project reports planned value $5,400,000, earned value $6,240,000 and actual cost $7,488,000 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $12,000,000
  • PV = $5,400,000
  • EV = $6,240,000
  • AC = $7,488,000

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

  2. Substituting — CV = 6,240,000 − 7,488,000 = $-1,248,000

  3. Formula

  4. Substituting — SV = 6,240,000 − 5,400,000 = $840,000

  5. Indices

  6. Formula

  7. Substituting — EAC = 12,000,000/0.833 = $14,400,000

Answer: CPI = 0.83, SPI = 1.16, EAC ≈ $14,400,000

Why the other options are there

  • EAC = $10,000,000 (multiplied by the index)
  • CPI = 1.200 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Example 9
Earned-value analysis: performance indices and forecast at completion — Construction (9)

A $10.0M project reports planned value $3,500,000, earned value $2,300,000 and actual cost $2,208,000 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $10,000,000
  • PV = $3,500,000
  • EV = $2,300,000
  • AC = $2,208,000

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

  2. Substituting — CV = 2,300,000 − 2,208,000 = $92,000

  3. Formula

  4. Substituting — SV = 2,300,000 − 3,500,000 = $-1,200,000

  5. Indices

  6. Formula

  7. Substituting — EAC = 10,000,000/1.042 = $9,600,000

Answer: CPI = 1.04, SPI = 0.66, EAC ≈ $9,600,000

Why the other options are there

  • EAC = $10,416,667 (multiplied by the index)
  • CPI = 0.960 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Example 10
Earned-value analysis: performance indices and forecast at completion — Construction (10)

A $8.0M project reports planned value $4,400,000, earned value $3,600,000 and actual cost $4,392,000 at the reporting date. Compute the cost and schedule variances, both performance indices, and forecast the estimate at completion.

Given

  • BAC = $8,000,000
  • PV = $4,400,000
  • EV = $3,600,000
  • AC = $4,392,000

Find

CV, SV, CPI, SPI and EAC

Start with the thinking

  • Earned-value analysis compares what was accomplished (EV) with what was spent (AC) and what was scheduled (PV).
  • An index below 1.00 signals an overrun; the forecast divides the budget by the cost index.

Step-by-step solution

  1. Formula

  2. Substituting — CV = 3,600,000 − 4,392,000 = $-792,000

  3. Formula

  4. Substituting — SV = 3,600,000 − 4,400,000 = $-800,000

  5. Indices

  6. Formula

  7. Substituting — EAC = 8,000,000/0.820 = $9,760,000

Answer: CPI = 0.82, SPI = 0.82, EAC ≈ $9,760,000

Why the other options are there

  • EAC = $6,557,377 (multiplied by the index)
  • CPI = 1.220 (inverted)

Reference: FE Reference Handbook — Construction Engineering → Construction

Self-check

Answer these without notes before moving on.

  1. Without looking, state the relation on this page whose left-hand side is the quantity most often requested, and name every symbol in it.
  2. Which assumption, if violated, makes the main relation of this section invalid?
  3. Given an activity network or production operation, what is the first quantity you would compute, and why that one first?
  4. Which unit conversion in this subject most often produces a wrong answer choice, and what is its numerical factor?
  5. Rework Example 1 above from the givens alone, without reading the solution lines.

Chapter summary

  • Construction contains 0 relations; you must be able to find this page in under 15 seconds.
  • Exam style: a schedule, productivity or earned-value computation.
  • Unit rule: crew-hours, cubic yards and dollars per unit.
  • Work the 10 examples until the solution path, not the answer, is automatic.

Common traps in this section

  • crew-hours, cubic yards and dollars per unit
  • Answering the intermediate quantity instead of the quantity requested.
  • Rounding intermediate values before the final step.
  • Using a relation from an adjacent handbook section that shares a symbol.
  • Skipping the sketch — most lost points on this page start with a misread geometry.
© 2026 Civil Engineering Capstone Studio. All rights reserved.