Statics is 9-14 questions on the FE Mechanical exam, making it one of the largest knowledge areas on the paper. It is also load-bearing in a second sense: mechanics of materials and mechanical design both start from a free-body diagram, so weakness here spreads.
The good news is that statics questions are the most predictable on the exam. Sum forces, sum moments, solve. The failures are almost never conceptual.
Exam weight: NCEES lists Statics at 9-14 questions (8-13%) of the 110-question FE Mechanical exam. Work each problem below on paper first, then reveal the worked solution — reading a solution you have not attempted builds recognition, not recall.
What NCEES Tests in Statics
The specification covers resultants of force systems, concurrent and non-concurrent systems, equilibrium of rigid bodies, frames and trusses, centroids and moments of inertia, and friction. Expect a truss member force by joints or sections, a reaction at a pin or roller, a frame with an internal hinge, and a block on the verge of sliding.
Moment of inertia items are usually composite sections requiring the parallel axis theorem. These feed directly into the beam bending and column buckling questions in Mechanics of Materials, so the same table lookup earns points twice.
5 Free Statics Practice Problems
Each problem below comes from the PECivilClick FE Mechanical question bank and matches the style, difficulty and format of the real exam. Attempt each one under a three-minute limit — roughly the pace the exam demands.
Problem 1 — A. Resultants of force systems
Three forces act at a point: F\(_{1}\) = 100 N at 0°, F\(_{2}\) = 80 N at 90°, and F\(_{3}\) = 60 N at 180°. What is the magnitude of the resultant force?
A) 100 N
B) 40 N
C) 240 N
D) 89.4 N
Answer: D) 89.4 N
Resolve forces into components:
\(\Sigma F_x = 100\cos(0^{\circ}) + 80\cos(90^{\circ}) + 60\cos(180^{\circ}) = 100 + 0 - 60 = 40\) N
\(\Sigma F_y = 100\sin(0^{\circ}) + 80\sin(90^{\circ}) + 60\sin(180^{\circ}) = 0 + 80 + 0 = 80\) N
Resultant magnitude:
\(F_R = \sqrt{(\Sigma F_x)^2 + (\Sigma F_y)^2} = \sqrt{40^2 + 80^2} = \sqrt{8000}\)
\(\boxed{F_R = 89.4\ \text{N}}\)
Problem 2 — A. Resultants of force systems
A force of 500 N acts along a line from point A(1, 2, 3) to point B(4, 6, 3). What is the x-component of this force?
A) 250 N
B) 400 N
C) 200 N
D) 300 N
Answer: D) 300 N
Direction vector from A to B:
\(\vec{d} = (4-1, 6-2, 3-3) = (3, 4, 0)\)
Magnitude: \(|\vec{d}| = \sqrt{3^2 + 4^2 + 0^2} = 5\)
Unit vector: \(\hat{u} = \frac{1}{5}(3, 4, 0) = (0.6, 0.8, 0)\)
Force component:
\(F_x = F \cdot u_x = 500 \times 0.6\)
\(\boxed{F_x = 300 \text{ N}}\)
Problem 3 — A. Resultants of force systems
A force system consists of F\(_{1}\) = 40i + 30j N acting at point (2, 0) m and F\(_{2}\) = -20i + 50j N acting at point (0, 3) m. What is the moment of this system about the origin?
A) 120 N·m (counterclockwise)
B) 260 N·m (clockwise)
C) 60 N·m (counterclockwise)
D) 100 N·m (clockwise)
Answer: A) 120 N·m (counterclockwise)
Moment = \(\vec{r} \times \vec{F}\) (using \(M_z = xF_y - yF_x\))
For \(F_1\) at (2, 0):
\(M_1 = (2)(30) - (0)(40) = 60\) N·m
For \(F_2\) at (0, 3):
\(M_2 = (0)(50) - (3)(-20) = 60\) N·m
Total moment:
\(M_{total} = 60 + 60\)
\(\boxed{M_{total} = 120 \text{ N·m (counterclockwise)}}\)
Problem 4 — A. Resultants of force systems
Two forces F\(_{1}\) = 200 N and F\(_{2}\) = 150 N act at a point with an angle of 60° between them. What is the magnitude of the resultant?
A) 350 N
B) 175 N
C) 250 N
D) 304 N
Answer: D) 304 N
Using the law of cosines (parallelogram law):
\(R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2\cos\theta}\)
\(R = \sqrt{200^2 + 150^2 + 2(200)(150)\cos(60^{\circ})}\)
\(R = \sqrt{40000 + 22500 + 30000} = \sqrt{92500}\)
\(\boxed{R = 304 \text{ N}}\)
Problem 5 — B. Concurrent force systems
For a concurrent force system to be in equilibrium, which condition must be satisfied?
A) ΣM = 0 only
B) ΣF = 0
C) ΣF = 0 and ΣM ≠ 0
D) The forces must be equal in magnitude
Answer: B) ΣF = 0
For a concurrent force system (all forces pass through a single point), equilibrium requires:
\(\Sigma \vec{F} = 0\)
or in component form:
\(\Sigma F_x = 0\) and \(\Sigma F_y = 0\)
Since all forces pass through the same point, the moment about that point is automatically zero for all forces.
Using the FE Reference Handbook for Statics
The Statics section holds the centroid and moment-of-inertia tables for standard shapes, and those are the pages you will open most. The parallel axis theorem is stated there too. Practise pulling up a composite-area problem and finding the right table in under twenty seconds, because on a two-shape section that lookup is most of the work.
Four Mistakes That Cost Points
- Assuming a two-force member carries a moment. A member pinned at both ends with no load in between carries only axial force along its line. Recognising two-force members collapses a frame problem to a few equations, and missing them turns it into an unsolvable mess.
- Using the parallel axis theorem about the wrong axis. The transfer distance is measured from the composite centroid to the individual shape's centroid, not from the edge of the section. Measuring from an edge is the single most common moment-of-inertia error.
- Assuming friction is at its maximum. The product of the friction coefficient and the normal force is the maximum available friction, not the friction actually acting. When a body is in equilibrium and not sliding, friction is whatever equilibrium requires.
- Sign confusion on moments. Pick one positive sense, write it on the diagram, and keep it for the whole problem. Most sign errors come from switching convention halfway through a summation.
Frequently Asked Questions
How many statics questions are on the FE Mechanical exam?
NCEES specifies 9-14 questions out of 110, roughly 8-13 percent. Only Dynamics, Fluid Mechanics, Thermodynamics and Mechanical Design carry comparable or greater weight.
Method of joints or method of sections for truss questions?
Use sections when the question asks for one specific member, especially a diagonal, because a single cut and one moment equation can deliver it. Use joints when you need several members or when the geometry makes a clean cut impossible. Recognising which is faster is worth practising deliberately.
Do I need to memorise moment of inertia formulas?
No. The handbook tabulates the standard shapes along with the parallel axis theorem. What you need is speed at decomposing a composite section and discipline about measuring transfer distances from the correct centroid.
How does FE Mechanical statics differ from FE Civil statics?
The mechanics is identical. The framing differs: mechanical problems lean toward machine frames, linkages and brackets, while civil problems lean toward trusses and structural members. Both are 8-14 questions, so neither discipline can afford to skip it.
Keep Going
These topics feed into each other on the exam:
- FE Mechanical Mechanics of Materials practice problems — 9-14 questions on the exam
- FE Mechanical Dynamics, Kinematics, and Vibrations practice problems — 10-15 questions on the exam
- FE Mechanical Mechanical Design and Analysis practice problems — 10-15 questions on the exam
Browse every knowledge area from the free FE Mechanical practice problem hub, see what the full bank covers on the FE Mechanical exam prep page, or plan your schedule with the FE study timeline.