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W12x26 A992 beam-column, 20 ft long and braced at 10 ft, under 20 kips, 60 and 3 kip-ft and 20 kips shear: AISC 360-16 E3, F2, F6, G2 and H1-1a (LRFD)

Tool	Steel Beam and Column Design
Source	American Institute of Steel Construction (2016). Specification for Structural Steel Buildings. ANSI/AISC 360-16, Chicago, IL. Chapters B4, E3, E4, E7, F2, F6, G2 and H1 (equations as mathematics); Varma, A. H. (2017). CE 470: Design of Steel Structures, Chapters 4-6. Lecture notes, Purdue University (the Examples 4.2, 5.4, 5.6, 6.1 and 6.2 the test reproduces).
Level	Undergraduate

Problem

A W12x26 of ASTM A992 steel (F_y = 50 ksi, E = 29,000 ksi) is 20 ft long, pinned about both axes (K = 1.0) and braced laterally at mid-length (L_b = 10 ft, C_b = 1.0). It carries a factored axial compression of 20 kips, strong- and weak-axis moments of 60 and 3 kip-ft and a shear of 20 kips, and a service load of 0.8 kip/ft on the 20 ft span. Classify the flange and web, find the design compressive, flexural and shear strengths and the H1 interaction, and check the deflection against L/360. The section is built from its plate dimensions (d 12.2, b_f 6.49, t_f 0.38, t_w 0.23, k 0.68 in) with the fillets ignored.

Inputs to Enter

W12X26 from the dimension list; A992: F_y 50 ksi, F_u 65 ksi, E 29,000 ksi, G 11,200 ksi; LRFD; compression
P 20 kips, M_x 60,000 lb-ft, M_y 3,000 lb-ft, V 20 kips; L_x = L_y = L_z = 20 ft, K_x = K_y = K_z = 1.0; L_b 10 ft, C_b 1.0 entered
Service load 800 lb/ft on 20 ft, limit L/360

Open the Steel Beam and Column Design tool (loaded with this example)

Answers

Plate closed forms: A 7.564 in² (Manual 7.65), I_x 201.0 in⁴ (204), I_y 17.32, Z_x 36.68 (37.2), J 0.284 (0.30), C_w 605 in⁶ (607), r_y 1.513 in, r_ts 1.762 in, b_f/2t_f 8.54, h/t_w 47.1
B4: flange compact (8.54 < 9.15) and nonslender (< 13.49); web compact in flexure (47.1 < 90.6) but slender in compression (47.1 > 35.9), E7 reduces nothing because λ < λ_r √(F_y/F_cr) = 80.3
E3: KL/r_x 46.6, KL/r_y 158.6 > 4.71 √(E/F_y) = 113.4 so elastic, F_e 11.38 ksi, F_cr = 0.877 F_e = 9.98 ksi; torsional F_e 28.3 ksi does not govern; P_n 75.5 kips, φP_n 67.95 kips
F2: M_p 152.8 kip-ft, L_p 64.15 in (5.35 ft), L_r 179.0 in (14.9 ft), L_b = 120 in inelastic: M_n 125.2 kip-ft, φM_n 112.7 kip-ft; F6: φM_ny 30.58 kip-ft; G2.1(a): h/t_w < 53.9, C_v1 = 1, V_n 84.2 kips, φ_v = 1.00
H1-1a: 0.294 + (8/9)(0.532 + 0.098) = 0.855, margin +0.17 (governing); deflection 0.494 in < 0.667 in

Notes

The tool's default inputs are this case; press Submit. The loads are illustrative (the brief's 40 kips and 90 kip-ft fail H1 at 1.44). The Manual's W12x26 properties typed in give L_p 63.74 in, L_r 178.8 in and M_n 1,522,000 lb-in at L_b = 120 in (the Lateral-Torsional Buckling tool's values, Table 3-2 5.31 / 14.9 ft); the plate forms sit 1.3 % lower. test_steel_beam_column.php (2,404 checks) reproduces the Purdue CE 470 examples (W14x74 φP_n 431.4 kips; W12x65 φ_cP_n 685 and φ_bM_n 345 / 356 kip-ft, interaction 0.819; W16x67 328 kip-ft; W21x48 / W18x55 / W21x55 312 / 335 / 376 kip-ft), FHWA-HIF-16-002 Table 3 and twenty seeded sections against numpy.