Engineering - For beginners Part 8

[RAB]

Engineering - For beginners Part 8
The role of Shape and Size influence on beam design

Parts 1-5 Gave examples of how deflection is most often the controlling element in residential design. Below are a few examples and key ideas on how shape and size can control deflection.

  Beams have a Stiffness Factor based on size and shape.
     --The Stiffness Factor is calculated from the outside edge to outside edge of the beam
     --The Stiffness formula gives more attention to height (depth) rather than width --

-Beam depth is the controlling variable more so than its width
-Engineers call shape related stiffness the Moment of Inertia
-MoI=Im = How much force to bend=Shape Stiffness multiplier
-Beam cost is related to its shape

Solid beams with similar Inertia and included cost factors
3.5 x 15  =1
5.5x13    =1.5
10.5 x 10.5 =2
20 x 8.5 = 3  (8.5 x 20 turned sideways)

Interested readers – this is a multipart series.
Engineers please excuse the simplification that this forum dictates.

Ryan B

[John Raabe]

In beams, the material at the top and the bottom is doing the real work of tension and compression. You can actually carve out much of the middle of a beam and not reduce its strenth or stiffness by much.

This is why steel I beams and wood I joists are shaped the way they are. They are trying to do the most work they can with the least material.

[Amanda_931]

And the round-wood people swear that peeled logs work better than cut?

Even after being notched a bit to fit?

[Ryan B]

The image below shows cross sections of different sized beams.  All have the same Moment of Inertia (shape related stiffness). All can hold the same uniform load with the same deflection.
The red shaded area gives you some idea of areas of importance/influence – the wider portion of the triangle carries the load rather the center part of the beam. Design codes allow for holes in the center portion of a beam due to this nature of influence.

*Key Elements in beam shape*
If deflection is equal -
As depth decreases - costs increase.
As depth decreases - bracing issues decrease.
As cross section area increases – cost increase.

8x16 Steel I-beam is used floor systems that need higher shear factors.
3.5x16 manufactured joist is quite common in big box store roof systems.
5.5x13 is often found in residential use as a ridge beam.
10.5x10.5 can be used as a hidden beam in a floor/ceiling system.
20x9 can be used as a simple bridge.