Dawson 203-SNE-DW Tutoring & Exam Help

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Share a load between two supports

If beam analysis is on your outline, try this original statics model. Other engineering-physics chapters may use different models.

A uniform rigid beam of length $L=4\,\mathrm m$ is horizontal and at rest. A pin at its left end $A$ and a roller at its right end $B$ support it. The beam’s weight is $W=120\,\mathrm N$ , acting at its midpoint. A separate downward point load $P=300\,\mathrm N$ acts $a=1\,\mathrm m$ to the right of $A$ . Find the vertical support reactions $R_A$ and $R_B$ , taking upward as positive. Predict which support carries more load. There are no other forces; the pin’s horizontal reaction is zero because all applied loads are vertical. Ignore deformation and strength limits: this classroom model does not establish whether a real structure is safe.

Show a hint

Sketch the two upward reactions and both downward loads. Choose A as the moment point so that the unknown reaction at A has zero lever arm. Use force balance afterward.

Show the reasoning

1. Balance moments about $A$ , taking counterclockwise as positive. All forces are perpendicular to the beam, so the lever arms are their horizontal distances from $A$ . The reaction at $A$ has zero moment there:

$R_B L-W\frac L2-Pa=0.$

Substituting gives $4R_B-120(2)-300(1)=0$ , so $R_B=135\,\mathrm N$ . The products in the moment equation are in newton-metres.

2. Balance vertical forces: $R_A+R_B-W-P=0$ . Thus $R_A=120+300-135=285\,\mathrm N$ . The left support carries more because the added load is nearer the left end.

3. Check about $B$ . The left reaction turns clockwise; both downward loads turn counterclockwise: $-285(4)+120(2)+300(3)=0$ . Also $285+135=420$ N, the total downward load. Equal reactions of 210 N would satisfy force balance but would fail moment balance.

Your turn: move the load

Keep the beam, supports and weights unchanged, but place the 300 N point load $a=3\,\mathrm m$ from $A$ . Predict which reaction increases, then calculate both reactions. Explain why their sum stays the same while their individual values change.

Check both balances

Moments about $A$ give $4R_B=120(2)+300(3)=1140$ , so $R_B=285\,\mathrm N$ . Vertical force balance gives $R_A=420-285=135\,\mathrm N$ . The reactions exchange values because the point load is now equally close to the opposite end of the uniform beam.

The total weight remains 420 N, fixing $R_A+R_B$ . Moving the point load two metres right increases the magnitude of its clockwise moment about $A$ by $300(2)=600\,\mathrm{N\,m}$ ; the reaction at $B$ must therefore rise by $600/4=150$ N. The reaction at $A$ drops by the same amount.

Review pivot choices and torque signs Use the force and moment checks, then compare the bar and cable examples.

Bring your force diagram and chosen moment point. A tutor can check which forces have zero lever arm and whether both balance equations describe the same beam.

Related subject areas

Choose the area that matches the chapter you’re studying.

MechanicsElectricity & magnetismWaves, optics & modern physics

Common difficulties

Turning the situation into a model
Using vectors, signs, and units consistently
Selecting the relevant physical principle

How tutoring can help

We confirm support and availability for your chapter before booking. For beam equilibrium, a tutor can help you draw the forces, measure each moment arm from the chosen pivot and explain why that choice removes an unknown. You can build the equations together from the example above or another permitted question.

Exam preparation for 203-SNE-DW

If statics is included in your assessment, try the moved-load question with the solution closed. Predict which support reaction increases, then calculate both reactions with their units. Check vertical force balance and take moments about the other support; satisfying only one balance does not establish equilibrium.

Use your section’s outline to choose the chapters to review. We work through permitted practice and comparable problems, without completing graded assignments or exams on your behalf.

Useful links for preparation or further study—not transfer equivalencies or a required registration sequence.

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203-SNE-DW · official course reference