Construction Engineering and Management
Construction engineering turns a design into a built project on time and on budget. The PE tests CPM scheduling, earned-value cost control, earthwork and quantity take-offs, equipment production, temporary works, and jobsite safety. Many questions are short arithmetic once you know the right definition, so precise vocabulary — float, swell, EV, CPI — is half the battle.
CPM Scheduling and Float
The Critical Path Method models a project as a network of activities. A forward pass computes early start (ES) and early finish (EF = ES + duration); a backward pass computes late finish (LF) and late start (LS). Total float — the delay an activity can absorb without pushing the project end — is LF - EF (equivalently LS - ES). Free float is the delay that does not push any successor's early start (successor ES - activity EF). The critical path is the longest path through the network, and its activities have zero total float; it sets the shortest possible project duration, so shortening the project means shortening critical activities. In precedence (activity-on-node) diagrams the default relationship is finish-to-start, and milestones carry zero duration. Crashing means buying time by adding resources; the crash cost slope, ($_crash - $_normal)/(days saved), tells you which activity is cheapest to accelerate.
Earned Value and Cost Control
Earned-value management compares three dollar figures at a point in time: planned value (PV, budgeted cost of scheduled work), earned value (EV, budgeted cost of work actually done), and actual cost (AC, real spend). Two indices flag trouble, both dividing EV by a baseline: the Cost Performance Index CPI = EV/AC and the Schedule Performance Index SPI = EV/PV. Below 1.0 means over budget or behind schedule respectively; above 1.0 is favorable. Variances are the differences: cost variance CV = EV - AC and schedule variance SV = EV - PV, where a negative SV means behind schedule. Forecasting uses the CPI: estimate at completion EAC = BAC/CPI, so a CPI of 0.80 on a $100,000 budget forecasts $125,000. An S-curve plots cumulative cost or progress over time and typically lags then accelerates then flattens.
Earthwork: Swell, Shrinkage, and Volumes
Soil changes volume as it is handled, and the exam keys on three states: bank (in-place), loose (excavated/hauled), and compacted (in the fill). Excavation loosens soil so it swells: loose volume = bank × (1 + swell), and the load factor = 1/(1 + swell) converts loose back to bank for hauling calculations. Placed fill is compacted denser than bank, so it shrinks: compacted volume = bank × (1 - shrinkage), meaning you must excavate MORE bank than the neat fill volume. Roadway earthwork volumes between cross-sections use the average-end-area method, V = (A_1 + A_2)/2 × L / 27 (to yards); it slightly overestimates versus the more exact prismoidal formula. A mass (haul) diagram plots cumulative cut-minus-fill along the alignment to balance earthwork and identify haul direction and overhaul (haul beyond the free-haul distance).
Concrete and Material Quantities
Quantity take-offs are unit-conversion discipline. The essential fact: 1 cubic yard = 27 cubic feet, so any concrete volume in cubic feet divides by 27 to get yards. For a slab, volume = length × width × thickness; for a round column, volume = (π/4)·D^2·H. Compute self-weight or tonnage from unit weight (concrete ≈ 150 pcf, asphalt ≈ 145 pcf): a road layer's weight is area × thickness × unit weight, converted to tons by dividing by 2,000. These feed material ordering, truck counts, and cost. A frequent multi-step question: find a placement volume in cubic feet, convert to cubic yards, then to truckloads or dollars — keep the chain of units explicit and the arithmetic is straightforward.
Equipment Production and Compaction
Equipment output is cycles per hour times payload per cycle, adjusted for real conditions. Production = (bucket or truck volume) × (60/cycle time in minutes) × efficiency, where a common efficiency is the 50-minute working hour (factor 50/60 ≈ 0.83) that accounts for delays, operator breaks, and jobsite friction. Balancing a fleet, the number of trucks a loader keeps busy equals truck cycle time divided by loading time. Field compaction is checked against the lab Proctor: relative compaction = field dry density / maximum Proctor dry density × 100%, with specs commonly requiring 95%. Roller choice matches the soil — a sheepsfoot (padfoot) roller kneads cohesive clay, while vibratory smooth-drum rollers suit granular soils — and thinner lifts compact more uniformly than thick ones.
Temporary Works, Estimating, and Safety
Formwork must resist fresh concrete's lateral pressure, which at the full-liquid-head limit is p = γ·h (about 150·h psf); a faster placement rate raises the pressure because concrete stays fluid deeper before it sets, and form ties carry that pressure. Rigging follows statics: a two-leg sling's leg tension is (load/2)/sin θ where θ is the angle from horizontal, so as the sling flattens the tension climbs steeply toward infinity. On bidding, know the two markup conventions: markup on cost gives price = cost × (1 + m), whereas a target margin on the selling price gives price = cost/(1 - m) — these differ and the exam exploits the confusion. Contingency covers identified-but-unquantified risk, and a change order formally modifies scope, price, or time. Safety is largely OSHA: excavations 5 ft or deeper generally require a protective system (sloping, shoring, or shielding), Type C soil is sloped no steeper than 1.5H:1V, and a 'competent person' is one able to identify hazards and authorized to correct them.
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