Span length vs strength

If you have a beam with a load in the center (worst case), for the same bending moment, the force that the beam could support would be half as much for an 8 foot span as a 4 foot span.

So 100 lb in the center of an 8 ft beam would cause the same bending as 2 200 lb weights in the center of two 4 ft spans (the 8 ft span with center support).

Free Online Beam Calculator | SkyCiv Engineering

?? If it's a central point load, with a centre support there is no bending or shear stress in the 2 halves. Failure would be due to local compression. Different of course if it's a UDL, but type of loading is not given.

Wood timbers fail in a number of ways, the most common being compression (crushing) of the upper surface.

This describes the various failure modes.

Failures In Timber Beams (chestofbooks.com)

https://theconstructor.org/practical-guide/bending-test-wooden-beam/2459/

https://www.woodweb.com/knowledge_base/Lumber_Strength_Dimensions_Orientation.html

I like your links but that drawing has a serious flaw. The board assumes to be the solitary cant cut from a log.

Most of the boards from a log will not include this center core.

Also, the center of the cant cut is the mature wood and not the juvenile. All of the other boards cut from a log will have the more mature wood on one side or the other.

The explanation of compression, tension and shear forces applied to a board spanning a section is spot on.

Yeah I don't know why they call it juvenile wood, I would call it heartwood, and it probably contains the most sap ...

What I would call the sapwood here in these walnut boards is the darker grain..

So the type of cut must be taken into account...

"The most recently formed tree ring is the new wood near the outer part of a tree's trunk, just beneath the bark. The oldest rings are smaller and near the center."

For a high strength beam I would consider laminated wood...

...and arched for an extended span....

A little more info:

Consider all materials of the same type and quality for the full length of the span.

The point load is centered on each span,both the 4 ft example and the 8 ft example span.

It seems logical that it would be twice as strong on the shorter span,but somehow,I think it may be more complicated.

Perhaps it is very simple after all.

It's not that much to assume every piece of wood is unique, and properties may vary according to this uniqueness....and certainly characteristics change over time as the wood ages...and environment is going to have some effect..not to mention grain orientation and type...

A further clarification,and a new example:

What if the beams are the same material:steel I beams in OP.

Would the answer still be the same for strength when reducing the span by 50%?

Load W and a single span gives maximum tensile and compressive stress T (at the centre). With a centre support, for the same stress, each half can take 2W (as stress varies as L, and L is halved). So total load = 4W.

That's if design is limited by stress. Often deflection (as a fraction of length) is the limiting factor, and this varies as L². In that case each half can take 4W, total 8W. But you need to re-check the stress at 8W.

Look at it this way. You have an external downward force W in the center and upward forces (W/2) on the supports at the ends. These forces are bending the beam. The top of the beam is under compression and the bottom is under tension to counteract these external forces.

The longer the beam (L), the greater the lever arm of the external forces. The internal forces have a fixed lever arm defined by the thickness of the beam.

Bottom line: The internal forces times beam thickness is proportional to external forces times length, so the force needed to reach the internal force breaking point is inversely proportional to length.

Once again you have asked a seemingly simple question with so few details that I doubt you grasp the complexity of the engineering discipline you question.

Strength of uniform materials does not change with how the materials are used. Soft yellow pine is a relatively cheap, plentiful renewable material that is rarely uniform.

The multiple metrics of material strength (tensile, compressive, shear, strain, etc.) include some additional variable (area, elongation, etc.) that applies to how the material gets used in a structural design. You present very little information about your structural design for anyone to expound about the strength of your design.

I'll present a few hyperbolic scenarios that meets your sparse information but will result in very different results. A knife edge contact in the middle of the span will greatly reduce the amount force needed to deform and/or shear the pine. This is a common approach used in splitting wood. A slim wooden dowel contacting at midpoint will not provide much additional support but can be a great method of allowing mechanical vibrations to transfer to and from the wood. This approach can be found in many acoustic string instruments. In contrast supporting the wood mid point with a dampening material can significantly reduce the likelihood of material fatigue from vibrations.

The <...strength...> of each half is the same, because of the inherent properties of the material used. However, because of the additional support, the ability of the structure to support a given load will increase.

The centre of a log has different properties to the outer edges; not every piece of timber is suitable for the same purpose. Timber has shakes, splits, twists, inclusions, voids and knots as a normal feature, and decays at a rate over time that varies according to what it is exposed to. It is easy to imagine over-designing support structures by a factor of 5 times theoretical new material when made in timber.

The American Forest and Paper Association publishes a wood structural design manual. This has standardized allowable loads for wood. You can find a pdf version at ...

https://awc.org/publications/wood-structural-design-data/

Plus, in the beginning pages there are all sorts of loading scenarios to assist the designer in determining maximum moment and shear values.

As already pointed out to you by others, wood has many design characteristics that differentiate it from steel and concrete. All things being equal, the load factors will cancel out and therefore are not applicable to your question.

Western Woods used to publish standardized allowable loads based on species. A very quick search on the internet indicates my copy may be a collector's item now. :)

I assume uniform loading and that when you place a support in the middle, you do not cut the beam in the middle so that the beam remains continuous. These loading situations are shown on pages 41 and 55 of the aforementioned manual.

If I did my math correctly, placing a support in the middle of the beam makes it about 7 times stronger.

The reason I posed the original question is that I read in a carpenter's design handbook that it would make it 8 times stronger,and that did not seem right to me.

So I rounded down because I calculated 7.1 times stronger. If you cut the beam so that is it not continuous, then it is only 4 times stronger.

That's what I said in #12, but only if the design is limited by deflection, not stress, or any local point stresses

Wood beam max loading by species...and other variables...

https://www.omnicalculator.com/construction/wood-beam-span