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Are 2 2x4 as strong as a 4x4?

2 2x4s glued together should be stronger than 1 4x4 because of the glue, but not necessarily stronger in the case of the OP's planks screwed together.

physicsforums.com - Why are two pieces of wood stronger when bound together?

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jrmichler said: Two possible reasons:

1) Real world 2 X 4's have knots in them. With doubled 2 X 4's, the knots do not line up, so the assembly is stronger. 2) If it's used as a long column, the maximum load is limited by buckling in the thin direction. The thin direction is twice as thick in doubled 2 X 4's, so has eight times the resistance to buckling. Caveat: The above is simplified. The reality is much more complex, but does not change the overall conclusions. Adding the mention of knots adds to the discussion. This is essentially the same thing as discussing the grain. As you say, some wood types have larger knots, some smaller and some wood (much more expensive have cuts without the knots. Lumberyard employees and owner are well-aware of the strength characteristics of wood and they are priced accordingly. The initial question was for two pieces of wood. No two are exactly alike in strength. The piecing together has been mentioned with the word glulum which is later defined in a comment. Different forms of laminates, including the use of wood in lamination, as well as the use of plywood of different grades, all attempt to answer the needs that are raised by the question. I brought out the bonding aspect of glue in my initial answer and a couple of people then brought that out without reference. One person thoughtfully brought up kiln drying which is one way of speeding up the curing process. Sufficiently dried lumber does not exhibit the characteristic of, "bleeding." When new support posts were installed under my lanai, I observed for several months, bleeding of sap or pitch from various openings or pores. It Kind of bothered me since I both asked for the more expensive support 4X4's in which had already been, "bled." "Wet," lumber will have the tendency to, "bend," under load as it does its job. Variables include the types of bonding agents and the methods of application of those agents. Some of these questions are theoretical, in which the variables are sort of eliminated in use of computer aided analysis of strengths with a sort of constant built in. Those figures are predetermined by prior testing limits for the certain kinds of woods selected. The physics of the answer must include a lot of variables to be valid in its answer, and also in its practical application. Some bonding agents mixed with sawdust, to make various by-product wood products can actually be quite weak.

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Can you sister floor joists with 2x4?

Yes, it will add some strength, although calculating just how much strength it will add may be difficult. This is true, but only to a point. If you were to add 2x4s to 20 foot 2x12s, for example, you'd be adding weight without any significant increase in rigidity.

diy.stackexchange.com - Can you sister floor joists with smaller boards?

Joists and beams are sized based on 3 conditions: 1) bending, 2) shear, and 3) deflection. However, only one of these elements will “govern”. That is to say, one will fail before the others. Long spans usually fail in bending or deflection, while short spans with heavy loads fail in shear. Adding smaller boards to existing joists is called a “composite” joist. Each member has certain characteristics and determining how (and where) to fasten them together is critical. If additional boards are not added uniformly then the joist can be eccentrically loaded, which will cause it to twist and possibly fail. Because of the complexity of calculating these loads (and connections), generally we design joists so loading is evenly distributed to the top of joists (and sistered joists) so the load is applied uniformly to all members. Therefore, we like all members to align on top. If one member is smaller (or has many knots and is not as good of grade) it doesn’t matter, as the load will transfer to adjacent members. Also, your question about sistered joists not “going the full length” is important, because when joists bend they have tension on the bottom edge and compression on the top edge. So, if the sistered joist is not continuous on the bottom, then it can’t carry the tension throughout the joist. But if it’s discontinuous on top, the ends of each piece just presses against one another and is effective...if ends are pressed against each other tightly.