Part 2 of the solved problem 7-2 for K values for columns in a frame.

23a-Solved problem 7-2 for k value for frame 2/3.

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Solved problem 7-2 for k value for frame 2/3.

Side-sway Uninhibited frame calculation for the solved problem 7-2.

K value for frame-K value for column CD.

The author gives the Ix/L values for both columns and beams and places them between brackets. For the sake of checking, two elements are selected for a random check. The first column, DC, has a section of W12x40 and a height of 15′. The second element is beam DH, which has a section W18x50 and a length of 30′.

For column Dc with W12x40,Ix value=307.0 inch4,vL=15′, the Ix/h=307/15=20.466 inch4/ ft.

For the beam of W18x50, Ix=800 inch4, l=30, then Ix/l for the beam=800/30=26.666=26.67 inch4/ft.

First, for the G at Joint D, there is only one column at joint D, so G= sum of (EI/L) for one column/ sum(EI/L )for one girder, G=20.47/26.67 =0.7675, at joint C

There are two columns and one girder, G= sum (20.47+23.20)/(70) =0.6238.

Solved problem 7-2-random check on Ix/l values.

Using the French equation k=sqrt((1.6*GA*Gb+4*(GA+Gb)+7.5))/ sqrt(Ga+Gb+7.5), for the unbraced frame, substitute the values of GA as 0.7675 and Gb=0.6238) in both the numerator and denominator. We get k=1.247, which is close to k=1.225, and the error value is small.

K value for column Dc.

Side-sway inhibited frame calculation for the solved problem 7-2.

K value for frame-K value for column BC.

We check the other column BC, Gc=0.6238  for joint B, two columns and one girder Gb=sum(23.2+23.2)/70=0.6628; the web plane is in the frame direction if we have a look at the elevation of the section.

The two flanges are on the left and right. This section will intersect with the girder section’s two webs, and the column and girder will intersect in the frame elevation. I have written the values of Ix for the different sections.
If we divide the inertia value over the length or -Ix/L for the girder, we get the same figures between brackets. After estimating Gb and Gc, knowing that the frame is a braced frame at that level since the joints C and B are not moving, the next slide shows the calculation for Gc and Gb.

Solved problem 7-2 for k value for frame 2/2
Solved problem 7-2 for k value for frame 2/2

Here is the graph. The values of both Gc and Gb can be found as—Gc=0.6238, Gb=0.6628. The k value will be obtained from the Nomograph for a braced frame by marking the different values of Gc and Gb on the graph.

Solved problem 7-2 -Using french equation compared with the Alignment chart to get K value for column CB.

K value for frame-K value for column BA.

Now, we will consider column BA, for which there is no sway Relative to each other, GA=10 since the support is hinged.

GA and GB for column BA

For column Gb, as estimated earlier, Gb=(23.2+23.2)/70=0.6628, GA=10. Now, we will consider column BA, for which, Relative to each other, there is no Sway, GA=10 since the support is hinged. In the next slide, we will estimate the k value by both methods, the nomograph and the French equation.

K value for column BA.

We use the Nomograph for the braced frame. Here, G=0.6628, Gb=10. The line joining represents column BA. It will intersect with the middle line, and then k=0.83.

K  value for column AB.

Using the French equation, substitute with 0.6628 and 10 for the braced frame, and we get k=0.8343. We will check column HG. and continue the next time in part 3 of the solved problem 5-2.

Chapter 7 – Concentrically Loaded Compression, Members is a useful external link.

The next post is Solved Problem 7-2 For K Factor part 3.

 

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