5 Engineers Every FE Civil Student Should Know (and Why It Matters on the Exam)

When you sit down for the FE Civil exam, you will spend five hours solving problems that span statics, geotechnical engineering, fluid mechanics, structural analysis, and more. Most of those problems rely on equations and methods that carry someone’s name—Darcy’s law, Euler’s formula, Mohr’s circle. You have probably used these tools hundreds of times without thinking much about the people behind them.

That is worth changing. Understanding why a formula was developed—what problem its inventor was actually trying to solve—gives you an intuitive sense of when to apply it and, just as importantly, when not to. On an exam where time is your scarcest resource, that intuition can be the difference between confidently selecting the right answer and second-guessing yourself for three minutes.

Here are five engineers whose contributions you will almost certainly encounter on the FE Civil exam. For each one, we will cover who they were, what they built or discovered, and exactly where their work shows up on test day.

---

1. Karl Terzaghi (1883–1963) — The Father of Soil Mechanics

Before Karl Terzaghi, designing foundations was largely guesswork. Engineers knew that some soils held up buildings and others did not, but there was no rigorous framework for predicting how soil would behave under load. Terzaghi changed that single-handedly.

Born in Prague (then part of the Austro-Hungarian Empire), Terzaghi trained as a mechanical engineer before turning his attention to the ground beneath structures. His landmark 1925 book, Erdbaumechanik (“Soil Mechanics”), established the field as a distinct engineering discipline. He went on to teach at MIT and Harvard, consulting on major projects including the Aswan Dam in Egypt and numerous highway and bridge foundations across the United States.

Terzaghi’s greatest contribution was his principle of effective stress: the idea that soil behavior is governed not by the total stress applied, but by the stress carried by the soil skeleton after accounting for pore water pressure. This single insight underpins virtually everything in modern geotechnical engineering—consolidation theory, shear strength analysis, earth pressure calculations, and bearing capacity design.

He also developed the Terzaghi bearing capacity equation, which gives the ultimate load a shallow foundation can support based on soil cohesion, overburden pressure, foundation width, and a set of bearing capacity factors (N_c, N_q, N_γ).

---

2. Henri Darcy (1803–1858) — The Man Who Mapped How Water Moves Underground

Henri Darcy was a French hydraulic engineer who spent most of his career working on the public water supply for the city of Dijon, France. In an era when waterborne diseases killed thousands, Darcy designed a pressurized distribution system that brought clean water to every household in the city—one of the first of its kind in Europe.

But his most enduring legacy came from a series of experiments he ran in 1856 on water flowing through sand columns. Darcy demonstrated that the flow rate of water through a porous medium is proportional to the hydraulic gradient and the cross-sectional area, and inversely related to the length of flow. This relationship, published in Les Fontaines Publiques de la Ville de Dijon, became known as Darcy’s Law:

Q = −kA(dh/dL)

where Q is the volumetric flow rate, k is the hydraulic conductivity of the soil, A is the cross-sectional area, and dh/dL is the hydraulic gradient. The negative sign indicates flow moves from high hydraulic head to low—downhill, in the simplest case.

Darcy’s Law is fundamental to groundwater hydrology, geotechnical seepage analysis, contaminant transport modeling, and the design of wells, dams, and drainage systems. It is, quite literally, the equation that makes modern water resources engineering possible.

---

3. Hardy Cross (1885–1959) — The Engineer Who Made Complex Structures Solvable by Hand

Before computers, analyzing a multi-story building frame or a continuous beam was an enormously tedious task. The equations of static equilibrium alone were not enough—you needed to account for how members deformed, how moments redistributed, and how joints rotated. Solving these problems required setting up and solving large systems of simultaneous equations, which was impractical for everyday design work.

Hardy Cross, a professor at the University of Illinois, solved this problem in 1930 with the moment distribution method. His approach was elegant: instead of solving all the equations at once, you start by assuming all joints are locked (fixed), calculate the fixed-end moments, then “unlock” one joint at a time, distributing and carrying over moments iteratively until the system converges. Each cycle brings you closer to the exact answer, and for most practical structures, two or three cycles are enough.

The moment distribution method was revolutionary. It turned structural analysis from a research-level mathematics problem into something a practicing engineer could do with pencil and paper during a lunch break. It remained the dominant method for analyzing indeterminate structures for over 30 years—until matrix methods and computers took over in the 1960s.

Cross also developed a similar iterative technique for analyzing pipe networks (the Hardy Cross method for pipe flow), which is still used for water distribution system design.

---

4. Leonhard Euler (1707–1783) — The Mathematician Who Explained Why Columns Fail

Leonhard Euler was not a civil engineer—he was a Swiss mathematician and physicist who is widely considered one of the most prolific scientists in history. He made foundational contributions to calculus, graph theory, mechanics, optics, and number theory, publishing over 800 papers across his career. (He continued publishing even after going nearly blind in both eyes, dictating his work to assistants.)

Euler’s contribution to structural engineering came from his study of elastic stability. In 1744, he derived the critical load at which a slender column will buckle—that is, suddenly bend sideways under axial compression, even if the material itself has not yielded. The result is Euler’s buckling formula:

P_cr = π²EI / (KL)²

where E is the modulus of elasticity, I is the minimum moment of inertia of the cross section, L is the column length, and K is the effective length factor that accounts for end conditions (K = 1.0 for pinned-pinned, K = 0.5 for fixed-fixed, K = 0.7 for fixed-pinned, and K = 2.0 for fixed-free).

This equation explains something that had puzzled builders for centuries: why tall, slender columns sometimes fail catastrophically at loads far below what the material can handle in pure compression. The answer is geometry—a long, thin column is vulnerable to buckling, and Euler’s formula tells you exactly when that will happen.

---

5. Christian Otto Mohr (1835–1918) — The Man Who Made Stress Visual

Christian Otto Mohr was a German civil engineer who spent his career designing bridges and teaching structural mechanics at the University of Stuttgart and later the Dresden Polytechnic. He made several contributions to structural analysis, including work on influence lines and the virtual work method, but he is best remembered for a graphical tool that every engineering student learns to draw: Mohr’s Circle.

Introduced in 1882, Mohr’s Circle is a geometric representation of the state of stress at a point. It transforms an abstract set of equations—the stress transformation formulas—into a circle on a graph, where the horizontal axis represents normal stress and the vertical axis represents shear stress. By reading the circle, you can instantly find the principal stresses (maximum and minimum normal stresses), the maximum shear stress, and the orientation of the planes on which they act.

What made Mohr’s Circle so powerful was not that it could solve problems that were previously unsolvable. The stress transformation equations already existed. What Mohr did was make the solution visible. An engineer sketching the circle could see, at a glance, how stress components change with orientation—and catch sign errors or conceptual mistakes that would be invisible in a page of algebra.

More than 140 years later, Mohr’s Circle remains one of the most commonly taught topics in undergraduate mechanics of materials courses, and it is firmly embedded in the FE exam.

---

What These Five Engineers Have in Common

Terzaghi, Darcy, Cross, Euler, and Mohr worked across three different centuries, in five different countries, on problems ranging from soil mechanics to pure mathematics. But they share something important: each of them took a real engineering problem that practitioners were struggling with and gave the profession a usable tool to solve it.

Terzaghi did not just study soil—he gave engineers a way to predict foundation capacity. Darcy did not just observe groundwater—he gave engineers an equation they could use to design wells and dams. Cross did not just analyze frames—he gave engineers a method they could actually execute by hand. That is what makes their work endure.

As you prepare for the FE Civil exam, remember that the formulas in the reference handbook are not arbitrary. Each one was developed to solve a specific problem. When you understand the problem, the formula makes sense—and you are far less likely to misapply it under exam pressure.

How to Study These Topics Effectively

Knowing the history is motivating, but passing the exam requires practice. Here is how to turn this knowledge into exam performance:

• Practice under timed conditions. You have about 3 minutes per question on the FE exam. Set a timer and work problems in each of these topic areas until you can solve them within that window.
• Use the FE Reference Handbook during practice. The bearing capacity factors, Mohr’s Circle equations, Euler’s formula, and Darcy’s Law are all in the handbook. Practice finding them quickly so you do not waste exam time flipping through pages.
• Focus on the high-weight topics. Geotechnical Engineering and Mechanics of Materials each carry 7–11% of the exam. Fluid Mechanics and Structural Analysis each carry 4–6%. Together, these topics account for roughly one-third of all exam questions.
• Work problems that combine concepts. The exam often combines topics—for example, a geotechnical problem that requires both effective stress (Terzaghi) and seepage flow (Darcy). Practice these crossover problems.
• Review your mistakes. When you get a problem wrong, identify whether the error was conceptual (used the wrong formula), computational (arithmetic mistake), or procedural (forgot a step like converting units). Each type requires a different fix.

Frequently Asked Questions

Disclaimer: This content is for educational purposes only and is not affiliated with, endorsed by, or sponsored by NCEES. “FE” and “Fundamentals of Engineering” are trademarks of NCEES. Always refer to the official NCEES website for the most current exam specifications and policies.