FE Exam-Civil Eng. Full Test with Detailed Solutions-Set #1

Analyze a six-data sample to practice standard deviation, distinguishing sample from population, computing the mean and squared deviations to obtain the sample standard deviation of about 59.16.

construct a 95 percent confidence interval for the population mean using the known sigma, with n=16 and x-bar=160 cm, yielding about 151 to 164.9 cm.

Explore engineering ethics as a licensed professional evaluates online ready-to-use drawings, checks foundation and soil considerations, updates as needed, and verifies all documents before signing.

A senior civil engineer should first contact related agencies to gather information about a proposed roadway affecting a freshwater resource, rather than speaking to the media or taking immediate action.

This lecture solves a net present value problem in engineering economics by converting annual costs and a future sale into value using annuity and value factors, yielding a positive npv.

Calculate a monthly payment for a $300,000 mortgage using a 0.5% monthly rate over 60 months; apply the annuity factor to find about $4,825 per month.

Explain how inflation affects the nominal interest rate to form the effective interest rate, then use P/F with that rate to derive present value from a future value.

Apply break-even analysis to compare manual and machine production costs, solve for the break-even quantity (1500 shoes), and determine it takes 50 days at 30 shoes per day.

Calculate depreciation and book value for a fleet over five years, showing annual depreciation of 240,000 and a four-year book value of 1,040,000 from a 2,000,000 cost with 800,000 salvage.

Resolve multiple forces into x and y components using cosine and sine with a consistent sign convention, then compute the resultant magnitude with the Pythagorean theorem.

Analyze a simple supported beam using force and moment equilibrium to determine the reaction at support B, converting a triangular load to a point load and solving for BY.

Apply force and moment equilibrium about a hinge using moment arms and sign conventions; conclude a 500 N force at 21 cm from the hinge (point B).

Apply the method of joints to a truss, determine reactions, analyze joint A, and deduce member forces AB and AC, with AB and AC in compression.

Assess beam determinacy by counting pin, roller, and fixed reactions to five unknowns, then apply equilibrium to obtain three equations, yielding a degree of indeterminacy of two.

Solve a frame analysis to determine the pin B reactions (Bx, By) and the roller reaction ay, converting the uniform load to a midspan point load and applying moment equilibrium.

Calculate the centroid of a composite shape by combining individual centroids of rectangles, triangles, and circles, using area-weighted coordinates from a 0,0 reference after converting units to centimeters.

Compute the area moment of inertia for combined shapes by locating individual centroids, applying the centroidal axis and parallel axis theorem, and summing I_x components to obtain the overall I.

Solve a static-equilibrium problem for a box on an inclined surface with friction mu = 0.25. Use mg sin theta and mg cos theta to find the holding force.

Compute the push force for a 100 kg block on a 40-degree incline in motion to reach 6 m/s in 2 s, with no friction, about 930 N.

Explore linear motion by analyzing constant acceleration from rest to 60 mph, a 30-second constant-velocity interval, and negative-acceleration deceleration, with distance expressed in yards.

Explore projectile motion with a vertical launch, compute h max from v_y^2/(2g) using 36 m/s and 9.8 m/s^2, showing kinetic to potential energy conversion.

Compute ax and ay by differentiating velocity components in x and y, then determine the resultant using the hypotenuse at t = 5 s, about 585 m/s^2.

Visualize the cylinder load and compute stress by dividing the 500‑pound force by the cross‑section area. Convert 4.42 psi to about 0.32 tsf to select the correct answer.

Apply delta L = alpha * L0 * delta T to steel, and compute the 50 m member’s 18 mm elongation from 5° to 35°C.

Compute the original wood column length under axial load using L = (delta l · A · E) / P, then convert the result to yards.

Use torsional strain: L = phi G J / T; convert phi to radians, apply G = 45e9 Pa and T = 2e6 N m to find about 0.64 m.

Determine the reactions Ay and By for a simply supported beam with a point and uniform load, then sketch the shear diagram to identify the maximum shear of 62.5 caps.

Explain hoop stress for cylindrical pressure vessels using the p r / t formula, converting internal pressure and dimensions to calculate about 31 gigapascals.

analyze the deflection of a beam under a midspan point load, computing downward deflection at 10 feet with careful unit handling, yielding about 1 inch.

Calculate the maximum bending stress for a 0.5 m by 1 m rectangle under 15 kN·m using I = b h^3 / 12, c = 0.5 m, yielding 180 kPa.

Calculate the ultimate compressive strength of concrete from three cylinder tests by averaging the three stress values, then determine the corresponding load using uniaxial loading and the cylinder's cross‑sectional area.

Apply a water-cement ratio of 0.4 to determine cement needed: 1 yd³ contains 1,215 lb of cement, so 11 yd³ in the truck equals 13,365 lb.

Explore the saturated surface dry concept via absorption tests and compute water content from the water-cement ratio, accounting for aggregate absorption to determine the required mix.

Analyze the stress–strain curve from the elastic region through yielding to permanent deformation. Learn about ultimate stress, strain hardening, necking, and rupture with steel examples.

Apply the structural number formula to determine asphalt thickness from the SN target, sketch the layers, and design for 7 inches.

Explore how to solve capillary rise problems by rearranging the formula to solve for diameter, using sigma, beta, gamma, and unit conversions, with attention to temperature and units.

Calculate the force on a tank base using pressure difference (gamma h) with gamma at 25 °C and a 5 by 8 m base to yield about 3.9 million newtons.

Apply Archimedes principle to relate buoyant force to sea water displaced, compute submerged volume from ship's 200 meter square area and dimensions, and determine the height above sea level.

Apply the continuity equation q equals v a to analyze a 600 gal per minute flow splitting into two pipes of 6 and 5 inches, computing q1, q2, and v2.

Apply the Darcy-Weisbach equation to compute head loss using velocity from Q and D, determine friction factor from Moody's diagram via Reynolds number and relative roughness.

Analyze flow measurement with an orifice using the discharge formula, considering height difference, area A0, diameter, and discharge coefficient C to determine fill time from volume over Q, 17 seconds.

Explore navigation by azimuth in a surveying problem, using the hypotenuse and cosine to determine the vertical (Y) distance, and noting significant digits to identify the correct answer (C).

Compute the total area of a garden with a half circle, a 65 by 50 ft rectangle, and a 35 by 50 ft triangle, 19,980 square feet (≈2,220 square yards).

Compute earthwork quantities by adjusting bank volumes for swell and compaction, convert 2 million cubic feet to 92,592.6 cubic yards, and estimate trucks needed with 19 cubic yards per truck.

the lecture demonstrates using the pyramid method and the average end area method to compute volumes from end areas and distances, concluding that the closest value is A.

Calculate northing and easting by rotating a south bearing 35 degrees toward west, using 1800.52 m with sine and cosine to update coordinates.

Perform differential leveling using a benchmark and total station readings, then compute unknown elevations by back sight and fore sight measurements with successive additions and subtractions.