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Structural Analysis Fundamentals / module 17

Influence lines and moving loads

What happens when the load will not stay still: influence lines, the Müller-Breslau principle, and finding the worst position of a load train.

What you will understand

  • Explain what an influence line is and how it differs from a bending moment diagram
  • Construct influence lines for reaction, shear and bending moment on a simple span
  • Use the Müller-Breslau principle to sketch an influence line without calculation
  • Find the effect of a distributed load from the area under an influence line
  • Locate the worst position of a train of moving loads

Lessons

  1. What an influence line actually is

    The one diagram people consistently misread — and why.

  2. Shear, moment and the Müller-Breslau principle

    A way to draw an influence line by releasing the structure instead of calculating.

  3. Moving loads and load trains

    Find the vehicle positions that produce the governing action.

  4. Influence lines for trusses and indirect loading

    When the load reaches the girder through cross beams, and how truss members respond to it.

Module summary
  • An influence line fixes one *effect* and moves the load; a bending moment diagram fixes the load and moves the section
  • Reaction influence line for a simple span: a straight line from 1 at the support to 0 at the far end
  • Shear influence line has a unit jump at the section; moment influence line is a triangle peaking at a(L − a)/L
  • Müller-Breslau: release the effect you want and the deflected shape *is* the influence line
  • The effect of a distributed load is w × (area under the influence line)
  • For a load train, the worst position places a heavy axle at or near the peak — but it must be checked, not assumed
Teaching basis and review status

These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.

Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.

Read the lesson register and outstanding review notes

Check your understanding

Check yourself

What does the horizontal axis of an influence line represent?

Practice

A simply supported beam spans 8.00 m. What is the peak ordinate of the influence line for bending moment at mid-span, in metres?

Practice

For a simply supported span of 8.00 m, what is the magnitude of the jump in the shear influence line at a section 3.00 m from the left support?

Check yourself

To maximise an effect using a distributed live load, which parts of the structure should be loaded?