Internal lever arm

[bojoka4052]

I am reading a text about bridge cross section and lever arm. The lever arm is mentioned in relation to calculation of section properties of the bridge. I was wondering if having a big lever arm in the cross-section (generally speaking) is good or bad? Is it conservative to assume a small lever arm?

 

[driftLimiter]

Well the lever arm in a a cross section comes from a simplification of material mechanics.

If you take an internal slice of any section in bending, there is some distribution of stresses from the bending where the top and bottom have opposite directions (one way bending).

If one solves for the stress resultant of the tension and compression side of the stress distribution you get a force, and a line of action for those forces.

The distance between these forces could loosely be called the sections 'lever arm'.

Basically a bigger lever arm leads to two outcomes,
-first it often comes along with an increased moment of inertia for the section (which means it will deflect less under loads).
-The section has a tendency to distribute stress over more depth, which loosely can be related to its moment strength.

There are some drawbacks of simply increasing the lever arm distance of a cross section,
-the section can become slender or have slender elements making it prone to instabilities
-weight of the cross section increases


You might investigate a few topics to further understanding of this concepts:
- Normal Stresses due to Bending.
- Deflection of beams.
- Bending strength of concrete beams.