Free-body diagrams, equilibrium and section properties: the foundation for mechanics of materials and machine design.
Choose any section below to get a free practice problem. Work it with the FE Reference Handbook open, tap your answer, then check the solution.
Break every force into x and y (and z) components, add the components, then rebuild the resultant with the Pythagorean theorem.
What are the x and y components of a 500 N force at 30° above the +x axis?
Fx = 500 cos 30° = 433 N, Fy = 500 sin 30° = 250 N: (433, 250) N.
Common trap: (D) swaps sine and cosine.
StaticsResultantMomentThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
A body at rest has ΣFx = 0, ΣFy = 0 and ΣM = 0.
A 3 m cantilever carries 5 kN at its free end. What is the moment at the fixed support?
M = PL = 5(3) = 15 kN·m.
Equilibriumreactionsfree-body diagramThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
Truss members carry only axial force, tension or compression.
A symmetric triangular truss spans 8 m with its apex 3 m high. A 20 kN load acts at the apex. What is the bottom chord force?
Each support carries 10 kN. Sloped members are 5 m long (3-4-5), so Fslope(3/5) = 10 and Fslope = 16.7 kN compression. Bottom chord = 16.7(4/5) = 13.3 kN tension.
Common trap: (D) is the force in the sloped members, not the bottom chord.
Trussesmethod of jointsmethod of sectionsThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
Static friction can grow up to μsN before slipping starts; once sliding, kinetic friction is μkN.
A block on an adjustable ramp has μs = 0.3. At what angle does it start to slide?
tan θ = 0.3, θ = 16.7°.
Common trap: (D) treats 0.3 as radians.
Frictionbelt frictionThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
For a composite area, the centroid is the area-weighted average of each piece’s centroid: ȳ = ΣAiyi/ΣAi.
What is the moment of inertia of a 100 mm diameter circle about its centroid?
I = πd4/64 = π(108)/64 = 4.91 × 106 mm4.
Common trap: (A) is the polar moment, πd4/32.
CentroidsMoment of InertiaParallel Axis TheoremThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
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