Tiêu đề PSAD 29 - Steel Design - Combined Axial and Bending.pdf ✅

PSAD 29: Steel Design – Combined Axial and Bending Video Transcript SITUATION 1: A W410×100 steel column 5.0 meters long is fixed to a footing at the base and pin connected at the top. It carries a total axial load of 180 kN and is subjected to the end moments: Mx = 80 kNm CCW (at the base) & Mx = 80 kNm CW (at the top). Sidesway is prevented about the x-axis and y-axis (k = 0.7) Use NSCP 2001. Properties of the W410X100 column: A = 12600 mm2 bf = 259 mm rx = 177 mm tf = 17 mm ry = 62.5 mm Sx = 1920 x 103 mm3 E = 200 GPa Sy = 380 x 103 mm3 tw = 10 mm rT = 70 mm Fy = 248 MPa d = 414 mm Zx = 2.15 × 106 mm3 1. Compute for the allowable axial compressive stress (MPa) if axial force alone existed. Use NSCP 2001. 2. Compute for the allowable compressive bending stress (MPa) about the x- axis if bending moment alone existed. Assume compact section and Cb = 1.3. Use NSCP 2001. 3. Compute for the total ratio of actual to allowable axial and bending stresses in the column. Use NSCP 2001. Solution: For the slenderness ratio, since no lateral bracing is provided at the interior of the column, the effective length of the column on both axes is the same. The maximum slenderness ratio will be on the axis with the smallest radius of gyration. Use k = 0.7 for pin and fixed. kL r = 0.7(5000) 62.5 = 56 Compare critical slenderness ratio with Cc Cc = √ 2π 2E Fy Cc = √ 2π 2(200000) 248 = 126.169 Since kL r < Cc , the case falls under Section (505.3.1.), Fa = 1 − ( kL r ) 2 2Cc 2 5 3 + 3 8 kL r Cc − ( kL r ) 3 8Cc 3 Fy

Check against the allowable bending stress in tension, Fbt = 0.60Fy = 0.6(248) = 148.8 MPa The smaller value governs, Fb = 148. 8 MPa. Computing the actual stresses, fa = 180000 12600 = 14.286 MPa fbx = 80 × 106 1920 × 103 = 41.667 MPa Checking which case, fa Fa = 14.286 122.694 = 0.116 When fa Fa < 0.15, IV = fa Fa + fbx Fbx + fby Fby ⏞ zero since there is no bending in this axis IV = 14.286 122.694 + 41.667 148.8 + 0 IV = 0. 396 SITUATION 2: The pinned ends steel WF column shown is subjected to concentrated loads. The column is braced against joint translation about the x-axis and y-axis (k = 1). Column Properties: A = 11000 mm2 bf = 254 mm d = 310 mm tf = 16 mm tw = 9 mm FY = 345 MPa Zx = 1.66 × 106 mm3 Fbx = 0.60 Fy Fby = 0.75 Fy Ix = 198 x 106 mm4 rx = 134 mm Iy = 45 x 106 mm4 ry = 64 mm E = 200 GPa Moment Magnification Factor = 1.0 Compute for the following: 1. Computed (actual) bending stress, fbx (MPa) 2. Computed (actual) bending stress, fby (MPa) 3. The total ratio of actual to allowable axial and bending stresses in the column from NSCP 2001.