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AISC Column Design Logic Makes Sense for Composite Columns, Too.pdf

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AISC Column Design Logic Malconcrete compres- sion members
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  AISC Column Design Logic Mal<es Sense for Composite Columns,  Too RICH RD  W.  FURLONG STRUCTURAL  engineers of North America have regarded the composite column generally as a curious stepchild who does not quite belong to a family, yet appears to behave very well. Fathers of the American Concrete Institute have provided shelter by permitting their own ACI routines to be applied to concrete compression members reinforced longitudinally with structural steel shape, pipe, or tubing. ^ As a concrete compression member the stepchild is restrained from doing its own thing as effectively as its structural steel cousins are allowed to do. The ACI Building Code forbids consideration of axially loaded columns by insisting that all columns also function as beams. Within the structural steel shape^ and tubing-^ family, compression members can be assembled for design as axially loaded columns. Composite columns that are incorporated into structures with connections identical to those used for steel shapes or tubes ought to be considered analytically to behave exactly the same as the shapes or tubes. Composite columns possess better stiffness and local stability than their structural steel cousins, and they are much more reliable in shear and ductility than their reinforced concrete cousins. Even though they cost more to produce than either of the cousins, their potential benefit-cost ratio may make them a far more attractive sibling for any structural family—whether it be concrete, steel, or a new genre as yet unnamed. The following demonstration of composite column analysis and comparison with laboratory behavior is intended to encourage the steel family to consider the adoption of design rules for composite columns. XI LLY LO DED COMPOSITE COLUMNS The logic of the AISC Specification can be applied to axially loaded composite columns if the influence of concrete on the strength, stiffness, and cross-section slender-ness of composite columns is incorporated into effective parameters  Fy^  for strength,  E^  for stiffness and r* for composite section radius of gyration. Definitions of each equivalence parameter follow: Richard  W.  Furlong  is  Profet versity  of  Texas  at  Austin. ã of  Civil Engineering The Uni- Fy* = Fy +  0.85/; ^ A, r* = \/^ Js  + 0.5£,/, EsA,  + 0.5E,A, (1) 2) 3) in which A,  = As = Ec  = Es  = /'. = Fy  = /. = area of concrete in composite cross section area of steel in composite cross section modulus of elasticity for concrete modulus of elasticity for steel design compressive strength of concrete standard cylinders static yield strength of steel moment of inertia of concrete in composite cross section moment of inertia of steel in composite cross section These parameters were applied to 84 concrete-filled tube columns and 30 concrete-encased rolled-shape columns that had been tested in recent years. ^'^'^'^'^ The parameters were then used in AISC column strength formulas in order to compute allowable loads on each of the 114 specimens. Significant computed quantities are listed in Tables 1 and 2. The AISC strength formulas take the following form with the modified parameters: a 4) where  Cc  is the slenderness ratio dividing elastic from inelastic buckling. When the effective length  Kl  is less than the product r*Q, the axial stress  F^  should be computed: Fa=- Kl__l ( Kl \   3 8 r*C 5) FIRST QUARTER  / 1976  Ref. 5-1 c3 O Pd X5 0 '—5 G i3 13 T3 r3 1 ^ ^ 03 (U 0 OJ 0 o G Cj :_0 S -Q C/5 H r-* (U P^ O.D. (in.) 3.74 3.74 8.50 8.50 3.74 4.76 4.76 1.00 1.50 2.00 3.00 14.00 14.00 14.00 5.01 5.00 4.00 4.76 6.00 3.01 4.50 5.00 6.00 5.51 5.53 6.62 ^,(in.^) 5.07 1.63 4.22 6.13 1.63 2.14 3.11 0.11 0.48 0.40 0.59 18.7 8.07 13.50 0.99 1.78 1.49 2.33 2.29 0.63 1.72 1.46 1.14 6.14 3.25 3.62 Table 1. A^  (in.^) 5.92 9.36 52.5 50.6 9.36 15.6 14.7 0.68 1.29 2.74 6.47 135.0 146.0 140.0 18.7 17.9 11.1 15.5 26.0 6.5 14.2 18.2 27.1 17.7 20.8 30.8 Axially Loa fy  (ksi) 39.9 50.7 42.3 41.7 56.8 50.8 49.0 45.2 49.8 76.0 76.0 76.0 76.0 51.5 40.1 51.5 53.8 47.7 53.8 47.7 87.8 65.5 60.2 52.7 60.0 42.0 48.0 38.5 39.0 41.9 43.2 43.2 ded Steel Tubes Filled with Concrete f c  (ksi) 2.94 3.62 3.32 4.32 3.32 4.32 3.49 3.06 3.51 3.06 3.51 3.06 3.51 3.06 3.51 4.04 4.04 4.04 3.95 5.52 4.76 3.04 3.40 9.6 9.6 9.6 9.6 4.95 4.52 4.99 4.29 3.76 3.03 3.62 5.93 3.76 4.20 5.10 3.05 3.75 4.66 4.66 4.74 4.74 4.56 6.26 3.34 Kl  (in.) 33.9 55.9 78.0 33.9 55.9 78.0 87.4 87.4 87.4 87.4 80.0 41.3 41.3 91.0 91.0 41.3 41.3 91.0 91.0 42.0 42.0 42.0 42.0 22.0 22.0 21.1 21.5 19.7 19.7 20.0 20.0 60.0 60.0 41.3 41.3 41.3 66.0 60.0 24.0 24.0 33.0 59.0 59.0 59.0 16.0 16.0 16.0 16.0 32.0 32.0 32.0 Kl 7^ 0.353 0.582 0.812 0.383 0.632 0.882 0.421 0.443 0.453 0.449 0.890 0.348 0.354 0.768 0.781 0.359 0.354 0.791 0.781 1.44 1.00 0.736 0.474 0.169 0.165 0.153 0.187 0.222 0.218 0.206 0.201 0.566 0.563 0.245 0.290 0.286 0.348 0.616 0.266 0.248 0.238 0.346 0.303 0.312 0.079 0.079 0.079 0.079 0.139 0.152 0.137 Pax  (kips) 113.0 96.9 76.4 57.3 47.6 35.6 164.0 182.0 241.0 245.0 34.0 72.0 75.7 51.0 53.0 100.6 99.7 69.8 69.9 1.31 10.7 15.3 32.3 910.0 361.0 402.0 622.0 115.0 112.0 136.0 130.0 80.2 78.6 121.0 113.0 109.0 107.0 23.0 36.0 29.6 84.5 81.7 72.9 82.2 181.0 183.0 130.0 132.0 160.0 184.0 141.0 Pfest  (kips) 229.0 209.0 203.0 150.0 131.0 119.0 371.0 509.0 549.0 645.0 104.0 162.0 192.0 143.0 163.0 227.0 245.0 180.0 195.0 3.52 24.7 27.1 72.0 2576.0 2408.0 791.0 1671.0 289.0 289.0 293.0 293.0 184.0 180.0 260.0 246.0 214.0 211.0 198.0 55.0 92.5 74.2 160.0 170.0 141.0 140.0 148.0 153.0 162.0 165.0 663.0 663.0 410.0 410.0 451.0 502.0 475.0 392.0 Pjest p 2.02 2.16 2.66 2.62 2.75 3.34 2.26 2.79 2.27 2.63 3.06 2.25 2.54 2.80 3.08 2.26 2.46 2.58 2.79 2.69 2.31 1.77 2.24 2.83 2.80 1.97 2.69 2.49 2.58 2.15 2.25 2.29 2.29 2.16 2.18 1.96 1.85 2.39 2.57 2.51 1.89 2.01 1.79 1.73 1.71 1.81 2.10 1.97 2.01 3.67 3.63 3.15 3.10 2.81 2.73 2.58 2.79 ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION  Table 1 (cont'd) Ref. y c 0 u r^ V ^ (L) S-i o <u QJ :3 IJ <u 13 ^ O.D. (in.) 3.50 3.50 6.64 6.64 6.62 6.64 A,  (in.^) 2.36 0.55 2.13 2.13 2.89 3.98 A^  (in.^) 7.26 7.74 32.5 32.5 31.5 30.6 fy  (ksi) 58.0 70.0 43.2 46.0 32.1 37.8 f'c  (ksi) 5.81 5.75 5.65 6.06 5.92 6.00 5.36 5.92 2.60 4.95 5.30 4.87 3.86 4.75 4.77 3.98 Kl  (in.) 68.0 56.0 44.0 32.0 20.0 68.0 56.0 44.0 32.0 20.0 10.0 12.0 78.0 12.0 78.0 12.0 78.0 12.0 78.0 12.0 90.0 12.0 90.0 12.0 90.0 12.0 90.0 Kl r*Cc 0.758 0.625 0.491 0.358 0.223 0.805 0.638 0.512 0.372 0.232 0.116 0.051 0.335 0.058 0.375 0.059 0.384 0.058 0.379 0.046 0.345 0.048 0.359 0.045 0.337 0.044 0.328 Pax  (kips) 64.9 74.1 81.6 90.8 96.6 27.7 31.4 36.6 40.1 43.1 45.1 97.2 86.6 136.0 118.0 145.0 125.0 138.0 120.0 117.0 103.0 131.0 115.0 163.0 145.0 151.0 135.0 Pfest  (kips) 138.0 160.0 161.0 206.0 223.0 50.5 66.2 80.0 90.0 110.0 119.2 298.0 185.0 274.0 206.0 294.0 170.0 299.0 155.0 350.0 213.0 322.0 236.0 442.0 254.0 446.0 262.0 Pfest Pax 2.13 2.16 1.97 2.27 2.31 1.82 2.11 2.19 2.24 2.55 2.64 3.06 2.14 2.01 1.74 2.03 1.36 2.17 1.29 3.00 2.24 2.46 2.05 2.71 1.75 2.95 1.94 When the effective length  Kl  is greater than  r^^C^^  the axial stress  Fn  should be taken as: Fa = 12 TT^E* (6) 23  (Kl/r*)^ Finally, the allowable axial load  Pax  is determined as the product of allowable stress and  steel  area: P = F A ã'ãax  ^  a^^s 7) Range of Al  S Safety Factors M ^ ~rr 114 SPECIMENS 84 Filled Tubes 30 Encased Steel Shapes juR. 1.5 2.0 2.5 3.0 3 5 RATIO  ^^ ãAX Fig. 1. Axially loaded composite column The right-hand columns of Table 1 and Table 2 contain ratios of the reported test load  P^x  to the computed values  Ptest-  The ratios vary from a low value of 1.29 to a high value of 3.67. The mean value for 114 composite specimens was 2.28, with an 18.4 percent coefficient of variation. AISG safety factors are intended to be in the range 1.67 to 1.92. The frequency distribution for all 114 tests appears in Fig. 1, and the AISC safety domain is shown as a shaded region of that diagram. The two ratios that were less than 1.40 involved steel tubes fabricated from welded spiral plate stock, and perhaps such tubes require special attention. AISC FORMAT FOR BEAM-COLUMNS Frequently it is necessary to proportion compression members to resist flexural forces in addition to thrust. All columns that are used in frames constructed with moment resistant connections must be considered as beam-columns. The AISC requirements for designing beam-columns are based on limits to the total stress generated by both thrust and flexure. However, composite columns present FIRST QUARTER / 1976  Reference c > GO ^ 㧠H rh OJ 0^ C 03 '—2 ^ iT) ^ Concr. Size (in.) 5   3.5 7   6.5 10   8 12   10 14   12 16   12 9.5   9.5 Steel Size (in.) 3   1.5 5   4.5 8X6 8X6 8X6 12   8 5.5   5.5 Table 2. Axially Loaded Encased Steel Shapes A,  (in.^) 1.18 5.88 10.3 ã10.3 10.3 19.1 6.66 A,  (in.^) 16.32 39.6 69.7 110.0 158.0 173.0 82.6 f'c  (ksi) 2.60 1.60 2.60 2.60 2.60 2.60 4.66 4.28 4.77 4.29 4.24 4.24 4.27 4.77 4.39 4.30 fy  (ksi) 36.0 36.0 36.0 36.0 36.0 36.0 41.5 42.7 40.2 40.0 55.0 72.6 70.8 72.5 41.5 70.7 Kl r^Cc 0.398 0.550 0.707 0.864 1.015 1.172 1.329 0.054 0.272 0.490 0.707 0.917 0.472 0.479 0.441 0.091 0.183 0.274 0.365 0.457 0.664 0.545 0.381 0.157 0.561 0.779 0.635 0.442 0.576 0.694 Pax  (kips) 40.0 36.0 31.2 25.8 20.0 15.0 11.6 177.0 163.0 143.0 119.0 90.6 255.0 300.0 354.0 627.0 608.0 583.0 556.0 525.0 255.0 268.0 310.0 271.0 294.0 298.0 322.0 384.0 239.0 303.0 Ptest  (kips) 81.4 71.5 63.0 43.6 50.6 36.1 33.9 352.0 308.0 317.0 288.0 231.0 568.0 704.0 836.0 1051.0 990.0 926.0 937.0 933.0 482.0 526.0 590.0 572.0 528.0 528.0 554.0 545.0 513.0 517.0 Pfest ax 2.04 1.99 2.02 1.69 2.53 2.41 2.92 1.99 1.89 2.22 2.42 2.55 2.22 2.34 2.42 1.68 1.63 1.59 1.69 1.78 1.89 1.96 1.90 2.11 1.80 1.77 1.72 1.42 2.14 1.71 unique problems associated with estimates of stress, either in concrete or in steel. Again a pseudo-allowable bending stress, J^^*, can be defined as the product of allowable moment and the steel section modulus, and all other components of AISC design equations can be applied. The moment capacity of composite cross sections can be determined analytically only by means of rather tedious calculations involving the equilibrium of post-elastic stress conditions associated with compatible strains near ultimate flexural loads. Estimates of a reliable moment capacity  Mo  can be taken far more simply by using the product of yield stress and the plastic section modulus of the steel in the cross section of filled tubes and encased shapes that are bent about the major axis. Minor axis bending strength estimates should include not only the weak axis plastic moment for steel, but also the capacity of a concrete section reinforced by the web of the steel shape. For encased shapes bent about the minor axis, Mo = ZyFy  +  A^F^ (b A^hy\ \2 \Jfch)  (J) where Zy =  weak axis plastic section modulus of rolled shape b =  width of concrete section parallel to steel flanges h  = depth of concrete section in the web direction Ayj =  area of web of steel shape The allowable flexural stress for composite sections should be taken as * 5 .S' (8) where  S =  section modulus of steel in plane of bending. The AISC equation for allowable combinations of thrust and flexural stress then can be used: Ja  J ^m 9) ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION

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