COLUMNS = Slenderness Ratio r = Least radius of gyration, inches SHORT COLUMNS LONG COLUMNS Fail by crushing, cracking Fail by buckling = Slenderness Ratio r = Least radius of gyration, inches E = Modulus of elasticity, ksi Fy = Yield strength of steel, ksi

Fe = Euler’s Buckling Stress, ksi CRITICAL STRESS, ksi (Fcr) SHORT COLUMNS LONG COLUMNS SLENDERNESS RATIO

Pn = Nominal Strength (Failure Strength) of Column = Fcr. Ag, kips Design strength of column = 0.9 x Pn FOR LRFD DESIGN STRENTH DESIGN LOAD Pn Pu = Resistance Factor for Compression, 0.9

Fixed Pin Free

EFFECTIVE LENGTH FACTOR , K RECOMMENDED VALUES OF EFFECTIVE LENGTH FACTOR , K POINT OF INFLECTION PIN FIXED FIXED FIXED PIN PIN K = 0.65 K = 1.0 K = 0.8

FREE TO ROTATE & TRANSLATE FIXED K = 2.1

PROBLEM # 1 Determine the available strength of the compression member shown in Figure 1, in each of the following ways: Use AISC Equation E3-2 or E3-3. Compute both the design strength for LRFD and the allowable strength for ASD. Use table 4-22 from Part 4 of the Manual. Compute both the design strength for LRFD and the allowable strength for ASD. FIXED HSS 10x6x ½ ASTM A500, Grade B steel (Fy = 46ksi) Figure 1 K = 0.65 FIXED

PROBLEM # 1 Figure 1 Find Slenderness Ratio FIXED OK 2) Find Euler’s Buckling Stress HSS 10x6x ½ ASTM A500, Grade B steel (Fy = 46ksi) 3) Find if Short or Long Column K = 0.65 SHORT COLUMN FIXED 4) Find Fcr Figure 1 Fcr

PROBLEM # 1 5) Design Strength of Column = 0.9 x Fcr x Ag = 0.9 x 39.15 x 13.5 = 475.7 kips Page # 4-31 Effective length KL = 0.65 x 15 = 9.75’ *By interpolation = 486 - = 474 kips

PROBLEM # 1 Page # 4-319 49 35.2 Load = 35.2 x 13.5 = 475.2 kips

For the conditions shown in Figure 1, use LRFD and PROBLEM # 2 For the conditions shown in Figure 1, use LRFD and D = 90k L= 260k Select a W12 of A992 steel. Select a steel pipe. Select a square HSS. Select a rectangular HSS. FLANGES WEB Pu = 1.2D + 1.6L = 1.2 x 90 + 1.6 x 260 = 524 kips KL = 0.65 x 15.33’ = 9.97’ A 992 STEEL W12 PIPE, RECTANGULAR HSS, SQUARE HSS Figure 1

PROBLEM # 2 W12 Page # 4-18

PROBLEM # 2 W12 COLUMN DESIGNATION WEIGHT (lbs/ft) LOAD CAPACITY Pn (kips) STRENGTH REQUIRE (Pu) W12 53 590 524 kips

PROBLEM # 2 ROUND HSS Page # 4-64

PROBLEM # 2 ROUND HSS Page # 4-65

PROBLEM # 2 ROUND HSS Page # 4-65

PROBLEM # 2 ROUND HSS Page # 4-66

PROBLEM # 2 ROUND HSS COLUMN DESIGNATION WEIGHT (lbs/ft) LOAD CAPACITY Pn (kips) STRENGTH REQUIRE (Pu) HSS 16.000x0.375 62.6 630 524 kips HSS 16.000x0.312 52.3 528 HSS 14.000x0.375 54.6 545 HSS 10.750x0.500 54.8 531

PROBLEM # 2 SQUARE HSS Page # 4-48

PROBLEM # 2 SQUARE HSS Page # 4-49

PROBLEM # 2 SQUARE HSS Page # 4-51