Lever arms, moments and structural engineering basics, thanks to Paul Cuddy

We have a couple of projects on site at the moment with some tricky structural detailing; both involve cantilevered roofs that (with the help of structural engineer Paul Cuddy – Tel: 086 306 1608) poses and answers some interesting structural basics that I thought I’d share with you.

Lever arms and Moments:

Take an eraser:

Draw 2 lines as shown

Bend the eraser

Watch how the lines get closer at the top, wider at the bottom but are the same at the centre:

rubber_analogy

Maximum tension occurs at the bottom and dissipates linearly to the centre

Maximum compression occurs at the top and dissipates linearly to the centre

The diagram below shows what’s happening to these forces:

lever_arm_diagram

What we have here therefore is a Lever Arm “the tendency of a force to rotate an object about an axis” – for more information on Lever Arms CLICK HERE

These two forces (compression & tension) are acting in parallel and opposite each other; the amount of these forces and the distance between them (the lever arm) create a bending moment.

Bending Moment = The Force x The Lever arm

This lever arm is therefore critical in steelwork design; the larger the lever arm, the greater the span.

This is why columns and beams are the shape they are; with the flanges at the top and bottom, the centre of gravity of a beam moves to the top and bottom of the beam:

centre_of_gravity

Why is this important and where else can it be used?

  • The moment determines the deflection on a beam and the amount of deflection determines whether you’re ceilings are going to crack (best case scenario!)
  • These calculations determine the size of steelwork required in order to support the forces that are applied on them; this determines whether your building will fail (or not)
  • This is why it’s essential to commission a structural engineer to undertake these calculations for you.

    The incredible thing is that what seems a simple proposition can more often than not be a complex structural problem that’s waiting to fail (if not handled and calculated correctly).

    Back to the projects on site…

    We have a cantilevered roof and through the structural calculations it was determined that there would be excessive deflection in the rafters that would crack a plastered ceiling. In order therefore to increase the lever arm of the rafters we had to increase the thickness at this point by using a plywood sheathing which effectively converted the rafters into a large spanning beam.

    How do you calculate the thickness of the ply? What type of plywood do you use, for that you need a structural engineer – a special thanks again to Paul Cuddy (Tel: 086 306 1608) for the advice and help in this post and allowing me to plagiarise his images and analogies.

    Comments welcome.

    DISCLAIMER:

    Mark Stephens RIBA MRIAI is an architect living working in the west of Ireland, he is not a structural engineer and the above post does not offer any specific advice of a structural nature. e&oe

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