Statics Tutoring

Statics is the first real engineering course most students take, and it filters hard: the math is just algebra and trig, but the modeling is new. Students who never learn to draw a correct free-body diagram spend the whole semester guessing. STEM Tutor 360's statics tutoring fixes the root skill first — reading a physical situation and turning it into a complete, correct FBD — because every equilibrium equation downstream depends on it.

From there, sessions build the standard toolkit systematically: 2D and 3D equilibrium, trusses by the method of joints and sections, frames and machines, friction problems, centroids, and moments of inertia. We work from your professor's problem sets and past exams, so the difficulty level matches what you'll actually face.

A typical truss problem, worked

A simple triangular truss has a pin support at A, a roller at B 6 m to the right, and an apex C that sits 3 m across and 4 m up. A 12 kN load hangs straight down from C. Find the force in every member.

Reactions first, from the whole truss. The load is centered, so the vertical reactions are 6 kN at A and 6 kN at B, and the horizontal reaction at A is zero.

Now joint A. Member AC rises 4 m over 3 m, a 3-4-5 slope, so its vertical component is $\tfrac{4}{5}$ of its force. Assume every member is in tension and let the sign speak. Vertical balance at A: $6 + \tfrac{4}{5} F_{AC} = 0$, so $F_{AC} = -7.5\ \text{kN}$, meaning 7.5 kN in compression. Horizontal balance: $F_{AB} + \tfrac{3}{5}(-7.5) = 0$, so $F_{AB} = 4.5\ \text{kN}$ in tension.

By symmetry BC is also 7.5 kN in compression. Check at joint C: the two compression members push up with $2 \times 7.5 \times \tfrac{4}{5} = 12\ \text{kN}$, which exactly balances the load.

The habit that matters is assuming tension everywhere. You never have to guess a direction, and a negative answer simply means compression.

How the course usually runs

Hibbeler, Beer & Johnston, and Meriam & Kraige all build statics in about this order. I follow your book's layout and your professor's problem sets.

• Force vectors in two and three dimensions
• Equilibrium of a particle
• Moments, couples, and equivalent force systems
• Rigid-body equilibrium and support reactions
• Structural analysis: trusses, frames, and machines
• Internal forces, including shear and bending moment diagrams
• Friction, including wedges and belts in some courses
• Centroids, distributed loads, and area moments of inertia

Where students get stuck

• A free-body diagram missing a force, most often a support reaction or the weight.
• Modeling a support wrong, such as giving a roller a horizontal reaction or forgetting the moment at a fixed support.
• Moment sign errors, or using a distance that isn't perpendicular to the force.
• Not spotting two-force members, which turns an easy problem into a long one.
• In frames, forgetting that the forces two members exert on each other at a shared pin are equal and opposite.

Stuck on statics homework?

Almost every statics homework problem goes wrong at the free-body diagram. In a session we draw the diagram together on a similar problem until you can do it without prompting, then you work your own set while I check each diagram before you write equations.

I won't complete graded assignments for you, because the free-body diagram is the skill your exams test. Sessions are 60 minutes, online on a shared whiteboard or in person near Richmond, Sugar Land, and Katy.