Statics

Concurrent force systems

Moments and couples

Building the free-body diagram

Equilibrium in two and three dimensions

Exam strategy

Key equations

Worked examples

Common pitfalls

• •Modeling a pin as a roller (or vice versa). A roller/cable/smooth surface gives ONE reaction along a known line; a pin gives TWO components. Miscounting makes a determinate beam look unsolvable — or hides indeterminacy.
• •Forgetting the moment arm is the PERPENDICULAR distance. $M=Fd$ needs $d$ measured perpendicular to the line of action, not the slant distance to the force's point of application.
• •Using $\arctan$ blindly for resultant direction. A calculator returns one quadrant; check the signs of $\sum F_x$ and $\sum F_y$ to place the angle in the correct quadrant.
• •Leaving a distributed load as $w$ in the equilibrium equations. Replace it by its resultant $W=wL$ at the load-diagram centroid before summing forces and moments.
• •Treating a couple as a force. A couple has zero net force but a nonzero, position-independent moment — it shows up only in $\sum M=0$, never in $\sum F=0$.
• •Mixing sign conventions mid-problem. Declare CCW-positive (or CW) and up/right-positive once, and a negative answer then honestly means the reaction points opposite to your assumed arrow.
• •Trying to solve a statically indeterminate body with equilibrium alone. When reactions exceed 3 (2-D) or 6 (3-D), you need compatibility/material relations — recognize it rather than forcing a wrong split.

References

• NCEES FE Reference Handbook — Statics
• Hibbeler, Engineering Mechanics: Statics — force systems, moments, equilibrium of rigid bodies