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Bridge Design

Middle schoolInterdisciplinaryTwin planar pin-jointed elastic trusses with equal load sharing, direct stiffness analysis and ideal member capacity checks

Click a member to inspect or remove it. Drag the orange top handle to change truss height. Disabled members remain as faint guides so they can be restored.

3D

Drag the apparatus to adjust it. Drag the background to rotate. Scroll to zoom.

Stable elastic truss

Measurement notebook

Change the setup, test a prediction and save the result. Up to 12 snapshots are kept.

About this experiment

Build a bridge that has to carry a load. Inspect the axial force in each member, remove a diagonal and see when the frame becomes a mechanism. Change height, span and member area, then ramp the load while the deformed shape develops. The experiment solves a small stiffness matrix instead of deciding strength from the appearance of the drawing.

Learning goals

  • Distinguish tension, compression and a geometric mechanism
  • Explain why triangulation stabilises a pin-jointed frame
  • Relate member stiffness to elastic modulus, area and length
  • Check support equilibrium against the total applied deck load
  • Compare yielding and ideal Euler buckling as different member limits

How to use it

  1. 1Run the default load test and inspect an orange member and a blue member. Record their signed forces.
  2. 2Choose Toggle member and remove a diagonal, or choose Rectangles only. Explain why an elastic displacement cannot be reported for a mechanism.
  3. 3Restore triangulation. Increase the truss height while keeping span and load fixed, and compare displacement and member forces.
  4. 4Double member area and repeat the same load test. Compare stiffness, mass and compression capacity.
  5. 5Move the load to a support, then return it to midspan. Verify the change in reactions and deformation.

The model

Assemble axial-member stiffness and solve the restrained system
Signed axial member force, with positive tension
Ideal pinned buckling load for a circular member

Assumptions

  • Two identical planar side trusses share the vertical deck load equally. Their transverse coupling is ideal; deck and crossbeam mass and bending stiffness are excluded.
  • Members are straight axial bars with pinned joints. Small displacement, linear elasticity and no prestress are assumed. The drawing magnifies displacement and caps that magnification for readability.
  • Member sections are solid circles. Density is held at 7850 kg/m³ and nominal yield stress at 250 MPa while elastic modulus can be varied independently. This is a parameter experiment, not a material catalogue.
  • Compression capacity is the smaller of axial yield capacity and ideal pinned Euler buckling capacity. Imperfections, connection failure, lateral bracing details and post-buckling response are excluded.
  • An unstable stiffness matrix is reported as a mechanism. Capacity ratios above one flag an elastic extrapolation beyond a member limit; actual fracture or collapse is not simulated.

Try this in class

  1. Q1Why does removing a diagonal matter even if all remaining bars are very stiff?
  2. Q2Why can a compression member buckle before its material reaches yield stress?
  3. Q3Which support reaction changes when the load moves to one end?
  4. Q4Is the lightest stable bridge necessarily the one with the lowest capacity ratio?

Frequently asked questions

Why are missing members still faintly visible?

They are restoration guides. They contribute no stiffness, mass or force until enabled again.

Does the magnified shape change the force solution?

No. All forces and millimetre readouts use the small-displacement solution. Magnification affects only the drawing.

Is this a bridge design approval tool?

No. It is an ideal classroom truss model with explicitly limited failure checks, not a structural design standard or a construction specification.