Built-Up Columns with Components in Contact with Each Other

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1 CHAPTER Structural Steel Design LRFD Method Third Edition DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS A. J. Clark School of Engineering Department of Civil and Environmental Engineering Part II Structural Steel Design and Analysis 6b FALL 00 By Dr. Ibrahim. Assakkaf ENCE 55 - Introduction to Structural Design Department of Civil and Environmental Engineering University of Maryland, College Park CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. 1 If a column consists of two equal size plates as shown in Fig. 1, and if those plates are not connected together, each plate will act as a separate column, and each will resist approximately half of the total column load. This means that the total moment of inertia of the column will equal two times the moment of inertia of one plate. 1

2 CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. Figure 1. Column consisting of two plates not connected to each other bd bd I 1 6 b Plates deform equal amounts d d (a) Column cross section (b) Deformed shape of Columns CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. The two columns will act the same and have equal deformation, as shown in part (b) of Fig. 1. If the two plates are connected together sufficiently to prevent slippage on each other, they will act as a unit as shown in Fig.. Their moment of inertia may be computed for the whole built-up section.

3 CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. 4 Figure. Column consisting of two plates fully connected to each other I ( d ) b 1 b 1 4 bd 6 ( 8d ) Plates deform equal amounts CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. 5 The moment of inertia for this built-up section will be four times as large as it was for the column of Fig 1, where slipping between plates was possible. Also, the column of Fig will deform different amounts as the column bends laterally.

4 CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. 6 Should the plates be connected in a few places, the strength of the resulting column would be somewhere in between the two cases just described. The greatest displacement between the two plates in Fig 1 tend to occur at the ends and the least displacement tends to occur at middle depth. CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. 7 Greatest Strength of Built-up Column As a result, connections placed at column ends which will prevent slipping between the parts have the greatest strengthening effect, while those at middepth have the least effect 4

5 CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. 8 The following example presents the design of member built up from two channels that are not in contact with each other. The parts of such members need to be connected or laced together across their open sides. CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. 9 Example 1 Select a pair of 1-in standard channels for the column and load shown using F y 50 ksi. For connection purposes, the back-toback distance of the channels is to be 1 in. 5

6 CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No k 0 ft 1 in 580 k CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. 11 KL Assume 50 r Then from Table.50 of φ c A F cr required 5.40 ksi Pu φ F c cr the LRFD Manual, 16.8 in Try C1 0 s (for each channel, A 8.81 in, I x 16 in 4, I y 5.1 in 4, x in ) 6

7 CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. 1 LRFD Manual Design Tables (P. 16.I-145) CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. 1 6 in I I x y 16 4 in [ ( 5.6) ] in distance of channels Note that 5.6 x in 4 x 7

8 CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. 14 I x rx A I y ry A r x K ( 8.81) 510 ( 8.81) 4.9 in to be used 4.9 in 5.8 in ( From Table1, pinned ends) Controls CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. 15 Table 1 8

9 c P φ F n c the Manual and by interpolation : cr A g.8 ( 8.

9 CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. 16 KL ( 1.0)( 0) 0 ft KL r From Table.50of φ c F cr KL r x.8 ksi Therefore, φ c P φ F n c the Manual and by interpolation : cr A g.8 ( 8.81) 596 k > 580 k OK Thus, USE C1 0 CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. 17 LRFD Manual Design Tables (P. 16.I-145) 9

10 CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. 18 Checking width/thickness ratios: d 1.0 in, b f C1 0 tw 0.51in, k.17 in, t f 5.1 in 1 1 in 1.15 in 8 CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. 19 b t f f h t w < 0.56 ( ) E F 19.1 < 1.49 y E F y OK 5.88 OK USE C1 0, F y 50 ksi 10

11 CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. 0 Built-Up Columns Figure 4. Limiting Width-Thickness Ratios for Compression Elements CHAPTER 6b. DESIGN OF AXIALLY LOADED COMPRESSION MEMBERS Slide No. 1 Built-Up Columns Figure 4. (cont d) Limiting Width-Thickness Ratios for Compression Elements Stiffened Elements 11

Revision and Errata List AISC Steel Construction Manual, 13 th Edition, Third Printing (Revision 2 June 2010)

Revision and Errata List AISC Steel Construction Manual, 13 th Edition, Third Printing (Revision 2 June 2010) The following list represents corrections that have been made in the Fourth Printing of the