I have two 3"x10" 18' long wood beam across the living room supporting the 2nd floor. The beams are sitting on top of two wood columns (6"x6") on each side of the beam. Also, there is an about 1/8" steel in between this two beams that are all bolt together. The beams have put up for about 2 weeks and I noticed that there are about 1/4" of deflection toward the middle section. I want to know if this is strong enough supporting the 2nd floor, since I am worried about the strength of the beams. I want to mention that the living room was supported by two 12' long of 2"x8" and two 6' long of 2"x8" wood beam before, which means there were 3 columns supporting. And now I only 2 columns.

Thanks.

Your beams are 18 feet long...that's 216 inches. A common criterium for deflection is 1/360 of the span. Divide 216 inches by 360, and you get 0.6 inches, or nearly 5/8 inch. That would be the maximum deflection allowable for your beams. The deflection you measure is less than half of that, so it is within the limits normally allowed.

It is nearly impossible, and certainly not economical or practical, to make a beam absolutely stiff so that there would never be deflection.

Thanks for the response. I thought the deflection would be worst once there is more loads on the 2nd floor. Wouldn't it?

Well, there are real life loads and there are design loads. We design professionals have to work with design loads. Generally in a house, the first floor contains the living spaces, and the building code requires us to design for 40 pounds per square foot live load. The second floor typically contains bedrooms, and the code permits a design live load of only 30 pounds per square foot for floors containing sleeping rooms. Attic floor loads and roof loads are generally carried directly on walls or beams, and not transmitted to a floor below.

However, if your living spaces are lightly furnished, and your bedrooms have, say, Aunt Mabel's heavy old antiques and lots of them, it is possible that in real life, the loads on the second floor could exceed the loads on the first floor. However, they are not likely to exceed the design live load of 30 pounds per square foot.

For same size beams spanning the same distance, deflection is basically proportional to load, so you could assume that generally, the load on your second floor is actually less than half the 30 pound design live load, when averaged over the entire area carried by the beams.