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Queensferry

Module 3 · Lesson 3.3

Building the diagrams

Predict the shape, then calculate the values.

Why this matters

These two diagrams are how engineers see a beam. They tell you where the beam is working hardest, which section size you need, and where to put reinforcement. An engineer who can sketch them by eye can check a computer output in seconds.

By the end of this lesson you should be able to

  • Work out reactions, then shear, then moment, in that order
  • Sketch each diagram before finding numbers
  • Read the key values off the diagrams

The order never changes. Find the reactions. Then work along the beam from one end building the shear force diagram. Then build the bending moment diagram from the shear. Doing it in any other order makes life much harder.

Two rules cover most of what shear does. At a point load, the shear diagram takes a vertical step equal to that load. Under a UDL, the shear slopes steadily downwards at a rate equal to the load intensity. Where there is no load at all, the shear stays flat.

Predict first

A simply supported beam carries only a uniformly distributed load. What shape is the bending moment diagram?

Try it

Beam laboratory

Change the beam, then reveal one diagram at a time. Predict each shape before you reveal it.

Beam type

m

kN (0 to remove)

m from left

kN/m (0 to remove)

Reveal

Simply supported beam of span 6 metres20 kN6 m
Shear force and bending moment diagrams for an eight metre beam carrying a five kilonewton per metre uniform load and a forty kilonewton point load at three metres.5 kN/m40 kN45.00 kN35.00 kNShear force V (kN)45.00Bending moment M (kN·m)112.50
The completed diagrams for the beam from Modules 3 and 4. Note the step in shear under the point load, and that the moment peaks exactly where shear crosses zero.

Worked example

Full diagrams for a beam with a UDL and a point load

Full diagrams for a beam with a UDL and a point load5 kN/m40 kN45.00 kN35.00 kN

Given

  • Span 8.0 m, simply supported
  • UDL 5 kN/m over the whole span; point load 40 kN at 3.0 m
  • Reactions already found: RA = 45 kN, RB = 35 kN

Find

The shear force and bending moment diagrams, and the maximum moment.

    Practice

    A simply supported beam spans 8.0 m with a single point load of 32 kN at 3.0 m from the left support. What is the left-hand reaction?

    Practice

    For that same beam, what is the maximum bending moment?

    Practice

    For the same beam, what is the shear force just to the right of the 32 kN load?

    Summary

    • Reactions first, then shear, then moment
    • Point load: step in shear. UDL: sloping shear, curved moment
    • Maximum moment where shear crosses zero
    • Moment must be zero at a simple end support — always check it
    Progress is kept in this browser only.

    This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint