Compare Bending Resistance of Dimension Lumber used as Joist

[PAUL GRAHAM]

Two 2 x 4s are laminated by means of glue and screws to form a horizontal beam 3.5" deep x 3" wide supported at the ends and uniformly loaded by static compression. Compare the bending resistance of this beam to that of a single 2 x 6 which is 5.25" deep x 1.5" wide under the same load.

 

[Baluncore]

Welcome to PF.

Is this homework?

If you place two identical beams next to each other, the deflection is halved, since each only has half the load.

If you increase the depth of a beam, is the deflection reduced: (1) In proportion to the change in depth, (2) By the square of the change in depth, or (3) By the cube of the change in depth.

 

[PAUL GRAHAM]

Not homework as in "assigned" study.

I am designing a post-and-beam table, 48" x 18", to safely carry an 800 lb static load (an aquarium), with legs in each of the four corners. Except for the tops of the horizontal elements (beams), there is no top surface. The weight bears uniformly around the perimeter. So two 4' beam spans, front and back, are joists supported at the ends. There are no center posts, and it is desirable to minimize beam depth.

Assuming that single 2 x 6 joists are satisfactory for this load, is it acceptable to substitute the doubled 2 x 4? I understand that doubling the beam width halves the deflection, but is this at least equal to the capacity of a single 2 x 6? I'm not a structural engineer, but I believe intuitively that it is considerably more resistant to bending. I thought it would be useful to ask someone who knows. How does the deflection reduction vary with beam depth? Certainly it is proportional in some way, but by what order of change I do not know.

Since the weight of the aquarium is bearing on the perimeter and is distributed equally to each of the four legs, the axial loading of the leg is a significant consideration. The 30" leg is a glued and screwed assembly of three 2 x 4s. I don't question the adequacy of this, but am open to comment.

I appreciate your response. Thanks for the interest.

 

[Baluncore]

How does the deflection reduction vary with beam depth? Certainly it is proportional in some way, but by what order of change I do not know.

An assigned study requires that you must do some research.
You must learn to do your own research. You have been given a clue.
If we do the research for you, there is no advantage to you, and you will not learn.

 

[Dale]

There are a lot of online calculators you can find. Those will be easiest to use. Here is one:

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

You will have a 4 ft span carrying a 100 lb/ft load

Note that the lumber grade will make a big difference here. Cheap “studs” will fail in bending, but higher grade lumber will be ok.

 

[PAUL GRAHAM]

Baluncore;
As stated this is not assigned study, but a hobby project. I am a 78 year old retiree whose education is in historical geology and environmental engineering. I am not a PE and am not in training to become one. I know just enough about some things to frame an intelligent question on occasion. If I'm working a problem at the edge of my understanding, I seek opinion and guidance. Your admonition is well-taken, but, although my interest is keen, I just don't have the time. For my edification I always want a better understanding of technical detail and underlying principles but I don't seek to acquire expertise outside my field or area of interest.

Dale;
Thank you for guiding me to this calculator. Although aware of these aids, I did not feel competent to use them correctly as I have no training in the nomenclature or mathematics. I will be using off-the-shelf #2 S/P/F for this project. I am inclined to use laminated 2 x 6s and call it good by a wide margin. The aquarium seals must not fail, which in time they will if the construction is not robust. I very much appreciate your interest. Thanks for the consult.

 

[Dale]

I will be using off-the-shelf #2 S/P/F for this project. I am inclined to use laminated 2 x 6s and call it good by a wide margin.

That should be more than enough. When laminating be sure to use enough glue and screws so that you get good “squeeze out” pretty evenly everywhere.

The aquarium seals must not fail, which in time they will if the construction is not robust.

I think that for that the most important metric will be deflection. The calculator estimates a .007” maximum deflection. If you can give it an upward bow of that amount then you should have perfect support. A few passes with a hand plane can get you there.

Be sure to make your joints solid to avoid racking.

 

[Baluncore]

@PAUL GRAHAM
If you can place a strip or sheet, of foam or rubber, under the aquarium, that will tend to reduce point loads between the glass and the timber.

 

[PAUL GRAHAM]

Actually, a 5/8" MDF panel goes on top of the space-frame and a 0.2" high-impact neoprene mat goes on this. The aquarium bottom is elevated by the thickness of its plastic rim. That rim is transferring the weight of a full aquarium to the space-frame and the mat eliminates point stresses. The use of these mats is common practice for stands for large aquariums. I have also seen styrofoam sheets used for this.

The laminations and all other contacts between members will use best quality carpenter's glue and tightly spaced screw patterns. Load carrying main joints at sheer-lines will use Timberlok lags of appropriate lengths.

A bonus with glulam doubling is you get a crack stop.

Thanks again guys!

 

[berkeman]

I am designing a post-and-beam table, 48" x 18", to safely carry an 800 lb static load (an aquarium), with legs in each of the four corners. Except for the tops of the horizontal elements (beams), there is no top surface. The weight bears uniformly around the perimeter. So two 4' beam spans, front and back, are joists supported at the ends. There are no center posts, and it is desirable to minimize beam depth.

Be sure to make your joints solid to avoid racking.

I'm not sure that just solid corner joints will prevent racking. @PAUL GRAHAM I see from your Profile/About page that you are in the US, and using my Mentor/Admin superpowers I see that earthquakes are not common in your area where you live. But still, you could have a child or adult stumble and bump the side of your table/aquarium, generating some racking moments. Are you sure you don't want to add some triangular braces or some sheets to the back and sides?

 

[PAUL GRAHAM]

The base of this space-frame surrounds the perfectly vertical legs, 3" x 5" in section, with 2 x 4, having a perimeter congruent with the top, now 2 x 6, platform. Attachment of all 2-by members to the legs is by Timberlok lags, two lags at each end and staggered with those used on the members at the perpendiculars. These Timberloks make very strong connections, and all contact surfaces will be glued. A floor of 5/8" MDF will be attached tying all the base members together. I have some large steel angles which I plan to use to keep the legs rigidly perpendicular during assembly. I have already allowed the possibility of leaving them attached. I want this space-frame to be open on all sides with no enclosing panels or gussets (it's an architectural thing), but this aquarium stand will be pretty much unitized and rock-solid stable.

Just For Fun, Since You Mentioned It.....

I am in the Kansas City area. It is thought that a quake of sufficient energy in the New Madrid fault system, on the other side of Missouri, could cause some damage here and would certainly be felt. That quake will come one day surely. The building codes in my area emphasize a seismic zone in eastern Kansas, practically in my backyard, called the Nemaha Ridge which is a feature connected to a deep fault underlying the Flint Hills. There has been no movement in that fault for a very long time, but if it does move it could be severe.

 

[Dale]

With members that large most traditional joints will be very strong and stable. You could easily get 30 or more square inches of long grain glue surface per joint with a half lap or mortise and tenon or similar.

The Timberlok screws are very strong in shear, but they will not prevent racking alone. Even if you use several, the wood fibers will just crush around them and the joint will work loose. They are a great idea in addition to glue and surface area, but not a substitute (in my very amateur opinion)

 

[PAUL GRAHAM]

Certainly not a substitute for glue. Joints are simple lap overlay. Contact surface area where upper platform frame attaches to leg is 18.375 sq in on one side and 26.25 sq in on the perpendicular side, and, similarly, 12.25 and 17.5 where base frame attaches to leg. A minimum of three Timberloks at each joint restrain rotation (great shear strength), and the legs are restrained at both ends. Apart from improper screwdriving technique, I associate fiber crushing with repeated forcible movement over time. This is a lot of dead-load mass, not so readily set in motion by uncommon and random events that could happen inside a home inhabited by an old guy. Since it is always true that only a very few things are actually impossible, I will just say this type of joint deterioration does not seem likely in this case. However, the glue is indispensable - absolutely. I get that racking is a serious consideration, but it will yield to proper design and careful build. Now in the design phase, anything goes still, so if you have serious concerns please speak further.

Anyone who knows what Timberloks are is no amateur.

 

[Dale]

I associate fiber crushing with repeated forcible movement over time.

That is true enough. I used Timberloks for our chicken houses and goat shed. All are subject to repeated forcible movements over time. Your aquarium is not the same kind of load.

 

[berkeman]

The base of this space-frame surrounds the perfectly vertical legs, 3" x 5" in section, with 2 x 4, having a perimeter congruent with the top, now 2 x 6, platform.

Can you post a sketch of this table design? That would help a lot, IMO. Thanks.

 

[PAUL GRAHAM]

Well you're right about that berkeman.
After today's input I am starting working drawings. I'll have something as you suggest in a couple of days.