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Technology and EngineeringMadrid 2026Question 3.1Free lesson

Overhanging beam: reactions, shear force and bending moment

From the equilibrium of the beam to its internal-force diagrams: why it is solved this way

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Problem statement

For the beam shown in the figure:

[Figure: horizontal beam of $[[L]]$ m, with a fixed pinned support $A$ at the left end and a roller support $B$ at $[[b]]$ m from $A$. At $[[a]]$ m from $A$ there is an upward vertical force of $[[P1]]$ N, and at the right end, on the overhang $[[c]]$ m beyond $B$, a downward vertical force of $[[P2]]$ N.]

a) Calculate the reactions at the supports. (0.5 marks)

b) Draw the shear force and bending moment diagrams. (1.5 marks)

Source: Madrid university entrance exam (PAU, Spain) · 2025-2026 · Ordinary session · Technology and Engineering · Question 3.1. Official exam set by the public universities of the Community of Madrid, to whom it belongs; translated from Spanish and reproduced with its source in order to explain it for teaching purposes.

What this lesson answers

  1. What does the figure tell us before we calculate anything?
  2. a) Why take moments exactly at a support?
  3. a) What are the reactions, and what does it mean when one comes out negative?
  4. b) Why is the shear force constant between loads and jumps at each one?
  5. b) Why is the bending moment the accumulated area of the shear force?
  6. b) What does the bending moment look like, and where is its maximum?
  7. Is there another route that gives the same answer?
  8. The answers and how to check them
  9. Common mistakes to avoid
  10. Exam tips
  11. If you want top marks

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