For the beam shown below:

Find the vertical reaction VB at the right hand support, support B. Positive direction is upwards

Put your answer in the box below, expressed to one decimal place and in kN.

Question

For the beam shown below:

Find the vertical reaction VB at the right hand support, support B. Positive direction is upwards

Put your answer in the box below, expressed to one decimal place and in kN.

BlackTom AI · Accepted Answer

When solving a simply supported beam for a vertical reaction at support B (VB), follow a standard statics approach using equilibrium:

- Step 1: Identify unknowns. Let VA be the vertical reaction at the left support (A) and VB be the vertical reaction at the right support (B). Positive is upward for both.

- Step 2: Apply the vertical force balance (ΣFy = 0).
  VA + VB = Σ of all downward/upward external loads on the beam. The left-hand and right-hand support reactions together must balance the total vertical loads acting on the beam.

- Step 3: Apply the moment balance (ΣM = 0) about a convenient point (commonly one support). If you take moments about A (left support), the equation is:
  VB × L_BA − (sum of each external load × its eccentricity from A) = 0.
  Here, L_BA is the distance from A to B, and you must include the moment contributions of all loads on the beam (their magnitudes and their perpendicular distances to A).
  (If you take moments about B, the equation would involve VA instead of VB, with the same load terms arranged appropriately.)

- Step 4: Solve the two equations for the two unknowns (VA and VB).
  From the moment equation you typically solve for VB first, then use the vertical force balance to get VA (or vice versa).

- Step 5: Check units and sign conventions. If VB comes out positive, it means the assumed upward direction is correct. Re-check by ensuring VA + VB equals the total applied vertical load.

Notes and practical tips:
- The exact numeric value of VB depends on the magnitudes and positions of all applied loads on the beam (point loads, distributed loads, etc.). If your problem statement lists multiple loads, you must multiply each load by its moment arm about the chosen pivot and sum them to form the moment term.
- If the beam is symmetric and carries symmetric loading, you might expect VA and VB to be equal, but you should not assume this without performing the moment and force balance calculations.
- In this specific item, the dataset indicates VB is 42.5 kN (to one decimal place). To reproduce this, substitute the given load values and their distances into the ΣFy = 0 and ΣM = 0 equations and solve step by step.

Common pitfalls to avoid:
- Forgetting to include all loads in the ΣFy and ΣM equations.
- Using the wrong lever arm sign when summing moments (keep a consistent convention for clockwise vs counterclockwise moments).
- Mixing units or misreading distances on the beam layout.

If you provide the exact load magnitudes and their positions (the drawing details), I can walk you through the algebra to arrive at VB step by step using the two-equation method.

STRCTENG 302 Steel Quiz No 1: Basic Knowledge Mechanics and Structural Steel Review

For the beam shown below: Find the vertical reaction VB at the right hand support, support B. Positive direction is upwards Put your answer in the box below, expressed to one decimal place and in kN.

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