Junior Engineer cheat sheet

Unit conversions: 1 kip = 4.448 kN; 1 ksi = 6.895 MPa; 1 ft = 0.3048 m; 1 in = 25.4 mm; 1 psi = 6.895 kPa.

Quadratic formula for ax² + bx + c = 0: x = [-b ± √(b² − 4ac)] / (2a); discriminant b² − 4ac < 0 means no real root.

Right-triangle relations: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent; law of cosines c² = a² + b² − 2ab·cos C.

Statics equilibrium for a planar body: ΣFx = 0, ΣFy = 0, ΣM = 0; a three-force body in equilibrium has concurrent or parallel lines of action.

Resultant of two perpendicular vectors: R = √(Fx² + Fy²), direction θ = arctan(Fy/Fx) measured from the x-axis.

Centroid of a rectangle is at mid-height and mid-width; for a triangle it lies one-third of the height above the base.

Moment of inertia of a rectangle about its centroidal axis: I = b·h³/12; parallel-axis theorem I = I_c + A·d².

Flow continuity: Q = A·v; for incompressible flow through a pipe, A₁v₁ = A₂v₂, so halving area doubles velocity.

Slope and area relationships: the integral of a load diagram gives shear, and the integral of shear gives moment; slope of the moment diagram equals shear.

Axial stress σ = P/A; axial strain ε = ΔL/L; Hooke's law σ = E·ε applies below the proportional limit.

Elastic elongation of a bar: ΔL = P·L/(A·E); stiffness rises with area and modulus and falls with length.

Poisson's ratio ν = −lateral strain / axial strain, typically 0.25–0.35 for metals and about 0.15–0.20 for concrete.

Bending stress σ = M·c/I, where c is distance from the neutral axis to the extreme fiber; section modulus S = I/c gives σ = M/S.

Shear stress in a beam: τ = V·Q/(I·t), maximum at the neutral axis for a rectangular section and zero at the extreme fibers.

Deflection limits are serviceability criteria, commonly L/360 for floors under live load and L/240 or L/180 for roofs, set by the governing code.

Concrete compressive strength is specified by 28-day cylinder strength f'c; tensile strength is roughly 8–12% of f'c, so steel reinforcement carries tension.

Thermal strain ε = α·ΔT; restrained thermal movement generates stress σ = E·α·ΔT, so expansion joints prevent cracking.

Ductility is measured by elongation at rupture; a ductile failure gives warning deformation, whereas a brittle failure occurs with little strain.

Drawing set order of precedence is normally stated in the contract: typically specifications govern over drawings, and large-scale detail drawings govern over small-scale plans.

A scale of 1:100 means one drawing unit equals 100 real units; a 25 mm dimension on a 1:100 plan represents 2,500 mm on site.

Line conventions: continuous thick lines for visible edges, dashed lines for hidden edges, chain lines for centerlines and section cut lines.

A section view is identified by a cutting-plane line with arrows showing the direction of view and letters matching the section title.

Quantity takeoff measures net dimensions from the drawings, then applies waste or overlap allowances separately; concrete is measured in cubic meters, formwork in square meters of contact area.

Rebar weight: mass = length × area × density; for a round bar, kg/m = d²/162 with d in mm (e.g., 16 mm bar ≈ 1.58 kg/m).

Specification divisions follow a master format grouping (e.g., concrete, masonry, metals, thermal and moisture protection); the specification governs quality, the drawing governs geometry.

A bill of quantities is a measured schedule of work items with units and quantities; a schedule of values allocates the contract sum to work items for progress payment.

Concrete placement: free fall should not exceed about 1.5 m without a tremie or drop pipe to avoid segregation; vibration is by poker vibrator at regular spacing.

Formwork stripping: sides of beams and columns may be removed after concrete hardens enough to resist damage; soffits of slabs and beams require the concrete to reach a specified strength, commonly 70% of f'c.

Excavation support: sloping, benching, shoring, or shielding is selected by soil type and depth; spoil and equipment must be kept back from the crest.

Compaction equipment matches soil: smooth drum rollers for granular subgrade, sheepsfoot rollers for cohesive soils, plate compactors for trenches and confined areas.

Crane capacity falls as radius and boom length increase; the load chart must be checked for the actual radius, and capacity deductions apply for jib, hook block, and rigging.

Earthwork volume by the average end area method: V = L·(A₁ + A₂)/2; the prismoidal formula adds mid-section correction V = L·(A₁ + 4A_m + A₂)/6.

Asphalt compaction must begin while the mix is within the rolling temperature range; breakdown rolling follows the paver closely, then intermediate and finish rolling.

Dewatering by sump pumps suits shallow granular excavation; wellpoints lower the water table by roughly 4–6 m per stage.

Leveling: elevation difference = backsight − foresight; height of instrument = known elevation + backsight; new elevation = HI − foresight.

Arithmetic check of a level run: Σ backsight − Σ foresight = last elevation − first elevation.

A closed traverse should satisfy Σ interior angles = (n − 2) × 180°; the misclosure is distributed equally among the angles.

Latitude = distance × cos(bearing), departure = distance × sin(bearing); a closed traverse requires Σ latitude = 0 and Σ departure = 0.

Slope correction to a measured distance: C = −h²/(2L), where h is the elevation difference and L the measured slope distance.

Temperature correction for a steel tape: C = L·α·(T − T₀), with α ≈ 1.16 × 10⁻⁵ per °C for steel.

Total station coordinates: ΔN = d·cos(azimuth), ΔE = d·sin(azimuth); azimuth is measured clockwise from north, bearings are measured from north or south within a quadrant.

A 3-4-5 triangle (or multiples) sets a right angle in the field; the diagonal check confirms a rectangular layout before setting out.

Hierarchy of controls, most to least effective: elimination, substitution, engineering controls, administrative controls, personal protective equipment.

Fall protection is generally required at heights of 1.8 m (6 ft) or more in general industry practice; guardrails, nets, or personal fall-arrest systems are acceptable controls.

Excavations 1.5 m (5 ft) or deeper require a protective system unless the excavation is entirely in stable rock; a competent person must inspect daily and after rain.

Ladder use: the 4:1 rule sets the base one unit out for every four units of height; ladders must extend about 1 m above the landing.

Scaffold guardrails are typically at 1.0 m and 0.5 m above the platform with toe boards; the scaffold must be designed and erected by qualified persons.

Electrical safety: ground-fault circuit interrupter protection is required for temporary receptacles; lockout/tagout isolates energy before maintenance.

Hazardous noise exposure commonly triggers a hearing conservation program at an 8-hour average of 85 dBA; controls follow the hierarchy.

Environmental controls: silt fences and sediment basins intercept runoff, and concrete washout must be contained away from drains and watercourses.

Incident rate = (number of recordable incidents × 200,000) / total hours worked; 200,000 equals 100 workers at 40 hours for 50 weeks.

Critical path is the longest-duration path through the network; it determines project duration and has zero total float.

Total float = late start − early start = late finish − early finish; free float is the delay possible without delaying any successor.

Forward pass computes early start and finish (ES + duration = EF); backward pass computes late finish and start (LF − duration = LS).

Crashing shortens duration by adding resources to critical activities; it is effective only on the critical path and raises direct cost.

Earned value: CV = EV − AC, SV = EV − PV, CPI = EV/AC, SPI = EV/PV; CPI below 1.0 means cost overrun.

Estimate at completion: EAC = BAC/CPI when the current cost performance is expected to continue; EAC = AC + (BAC − EV) when remaining work proceeds at budgeted rate.

Percent complete by cost = earned value / budget at completion; physical percent complete should be measured by installed quantities, not elapsed time.

A Gantt bar chart shows timing but not logic dependencies; a network diagram (CPM) shows dependencies and float.

S-curve plots cumulative cost or progress against time; the gap between planned and actual curves shows schedule variance.

A valid contract requires offer, acceptance, consideration, capacity, and legality; a counteroffer rejects the original offer.

Design-bid-build separates design and construction; design-build gives one entity responsibility for both; construction management is a delivery method, not a contract type.

Standard contract documents include the agreement, general and supplementary conditions, specifications, drawings, and addenda; addenda issued before bid opening become part of the contract.

Liquidated damages must be a genuine pre-estimate of loss, not a penalty; they are stated per day of delay in the contract.

A change order is a written, signed modification to scope, price, or time; a field instruction or construction change directive may precede it.

Retainage is a percentage held from progress payments until acceptance; it is released per the contract, often partly at substantial completion.

Professional ethics: engineers sign and seal only work they prepared or directly supervised, disclose conflicts of interest, and report unsafe conditions to the responsible authority.

Substantial completion is the stage when the work is usable for its intended purpose, triggering warranty start and release of part of retainage; final completion follows punch-list closeout.

Bid protest and dispute paths usually run through the contract's dispute clause: negotiation, then mediation or arbitration, then litigation, as specified.

Concrete slump test (ASTM C143) measures workability; slump is measured as the drop of the cone-shaped sample after removal of the mold.

Concrete compressive strength is tested on cylinders (ASTM C39); standard 150 × 300 mm cylinders are cured and tested at 7 and 28 days.

Acceptance of concrete strength commonly requires the average of three consecutive tests to equal or exceed f'c, with no single test below f'c − 3.5 MPa.

Soil compaction is verified by field density (sand cone, nuclear gauge) compared with laboratory maximum dry density from a Proctor test; the ratio is relative compaction.

Standard Proctor uses lower energy than Modified Proctor; Modified Proctor yields a higher maximum dry density at a lower optimum moisture content.

Asphalt density acceptance compares field density to laboratory Marshall or gyratory density; typical required relative density is 92–96% of the laboratory value.

Steel weld inspection: visual inspection first, then nondestructive methods such as ultrasonic, radiographic, magnetic particle, or dye penetrant depending on joint type.

Rebar placement is checked against cover and spacing tolerances before concrete placement; a pre-pour inspection checklist is signed off before release.

Test reports must record sample location, date, specimen identification, test method, and result; nonconformance triggers a documented corrective action.