Engineering question: How do we isolate a system to identify the forces that act on it?
Follow the modules in order. Pause the videos and draw on paper before viewing the solutions.
An FBD is a simplified drawing of one isolated body with all external forces and relevant external moments acting on that body.
A box, lamp, beam or an entire structure can be our body. Redraw it alone as a simplified line, rectangle or point. Remove the table, cables, ground or supports from the isolated view.
We select the system boundary first: only interactions that cross this boundary create external loads on our FBD.
Every interaction with something outside the body becomes a force or moment as appropriate. Include gravity, applied loads and reactions. Draw and label arrows with correct directions.
Important: Do not draw both members of a Newton's third-law pair on the same body's FBD. The table's upward force on a box belongs; the box's downward force on the table does not.
Weight: W = mg = (12 kg)(9.8 m/s²) = 117.6 N downward. The stationary crate receives an upward normal reaction N = 117.6 N. The table itself does not appear in the isolated crate diagram.
Each arrow must have a known or assumed direction, a label and a point or line where it acts.
An ideal pin can exert horizontal and vertical forces, but no reaction moment. An ideal roller on flat ground exerts one vertical normal reaction. A roller on a sloping surface reacts perpendicular to that surface.
A fixed support can exert horizontal force, vertical force and a resisting moment. A taut cable only pulls along the cable. We will calculate reaction moments later in Unit 2.
Begin with the engineering mechanics introduction. Use the second video for everyday weight, tension, friction and normal-force situations. If embedded playback is blocked, use the YouTube links.
While watching: Pause at the simply supported beam and write down which reactions the supports can supply.
Watch directly on YouTube ↗While watching: Sketch a hanging object, then compare your chosen arrows with the explanation.
Watch directly on YouTube ↗While watching: Notice that engineers draw a beam FBD before evaluating its internal shear and bending moments.
Watch directly on YouTube ↗Internal shear/moment diagrams and their calculations are beyond Lesson 2.4. Use the video to preview why an accurate FBD matters for later engineering analysis.
A simply supported beam carries a 60 N downward point load at its midpoint, with pin A and roller B 4 m apart. Neglect the beam's self-weight.
Identify the beam as the body. The load, pin and roller interact with it from the outside.
Remove the physical support symbols and add their possible reactions. Here Aₓ = 0 N because there is no horizontal load.
Do not split off-center loads equally. For an off-center point load, support reactions differ. We'll solve those cases using moments in Lesson 2.6.
Before pressing each button, predict what the drawing should contain. Then adjust the centered load to test whether your reaction forces still balance.
The beam is alone. Which forces from the original physical setup will act on this body?
Teaching model: single centered vertical load, equal span halves, no beam self-weight or horizontal loading. Assumes ideal pin/roller supports.
A good FBD works for more than beams: the same reasoning applies to lamps, signs, crates and components.
A lamp weighs 90 N and hangs from one vertical cable. If motionless, T = W = 90 N for this simplified example.
The taut cable pulls the lamp toward its attachment. The lamp's weight acts downward.
A 12 kg crate remains stationary while a person pushes horizontally to the right with 30 N on a rough floor.
ΣFₓ = +30 −30 = 0; ΣFᵧ = +117.6 −117.6 = 0. Actual static friction is the amount needed to prevent sliding, up to its maximum; it is not always μₛN.
Use the Lesson 2.4 practice worksheet or engineering notebook. The answers are intentionally hidden so you can test your understanding.
Draw all external forces on a 5 kg crate at rest on a level table. Use g = 9.8 m/s².
Weight = 49 N downward; normal = 49 N upward. With no horizontal interactions, no horizontal forces are needed.
Draw the FBD for a pin-and-roller beam with a centered downward 100 N load. Neglect self-weight. Find the reactions.
Aₓ = 0; Aᵧ = 50 N upward; Bᵧ = 50 N upward. Include 100 N downward at midpoint. The geometry and load are symmetric.
A box stays still when pushed left by 25 N across a rough level floor. Name the force types and directions.
Applied force 25 N left; static friction 25 N right (if sufficient friction); weight down; normal up.
Which support can resist x and y translation yet allows rotation? Which support also prevents rotation?
An ideal pin resists horizontal and vertical translation but allows rotation. A fixed support additionally resists rotation via a moment reaction.
A beam has a downward point load close to A, far from B. Can the reactions simply be divided equally?
No. The symmetric 50/50 shortcut applies only to centered loads with symmetric supports. Moment equilibrium is needed for off-center reaction magnitudes.
Two bars are joined by a pin. When drawing the FBD of the entire two-bar assembly, why is their internal pin force omitted?
Both bars are inside the system boundary, so their mutual forces are internal and cancel. If you isolate just one bar, the connecting pin force becomes external and must appear.
Open-access materials can reinforce the lesson and extend your knowledge.
Five-step FBD method, examples and full 2D reaction table.
Engineering Statics — Free-Body Diagrams ↗Explanations of pin, roller and fixed constraints.
Engineering Mechanics — Supports ↗Open engineering textbook examples of isolated systems.
Engineering LibreTexts — FBDs ↗Boundary: the body/system selected. Reaction: force or moment from a restraint. Equilibrium: net force and net moment are zero. External load: force exerted from outside the system boundary.
Complete your POE 2.4 Free-Body Diagrams classwork and homework worksheet (or notebook equivalent if directed). Use the site to learn and check, but turn in your own annotated diagrams and explanations.
Due: See the Daily Agenda for the current deadline and use your instructor's submission method.
