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More Bridge Building

Age 16 to 18
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Newton, from Macquerie Fields primary school thinks that the bridges of even length will be the most stable and not feel any forces at the joints. Is he right? Can you use vectors and mechanics to help?
 
Fygliwu presents a very intuitive mechanical explanation:

A bridge of even length should be less stable due to the fact that it has a central point which bears a load. On a bridge of uneven length this load is shared between a set of three points, the two in the middle on the bottom and the one in the middle on the top. This therefore means that the load of an uneven bridge is spread out and therefore dissapated whilst the load of an uneven bridge in focused on a single joint.  
 
Can anyone supply mathematical justification?
 

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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