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Structural Steel Designers Handbook Part 7

Tham khảo tài liệu 'structural steel designers handbook part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | DESIGN OF BUILDING MEMBERS 7.15 TABLE 7.2 Properties of Selected W Shapes for LRFD Property W18 X 35 grade 36 W18 X 40 grade 50 W21 X 50 grade 50 W21 X 62 grade 50 ỘMp kip-ft 180 294 413 540 Lp ft 5.1 4.5 4.6 6.3 Lr ft 14.8 12.1 12.5 16.6 ỘMr kip-ft 112 205 283 381 S in3 57.6 68.4 94.5 127 X1 ksi 1590 1810 1730 1820 x2 1 ksi2 0.0303 0.0172 0.0226 0.0159 ry in 1.22 1.27 1.30 1.77 In this example then the 20-ft unbraced beam length exceeds Lr. For this condition the nominal bending capacity Mn is given by Eq. 6.54 Mn Mcr CnMr. For a simple beam with a concentrated load the moment gradient Cb is unity. From the table in the manual for the W18 X 40 grade 50 design strength ộMr 205 kip-ft 277.5 kip-ft. Therefore a larger size is necessary. The next step is to find a section that if its Lr is less than 20 ft its Mr exceeds 277.5 kip-ft. The manual table indicated that a W21 X 50 has the required properties Table 7.2 . With the aid of Table 7.2 the critical elastic moment capacity ộMcr can be computed from ộMcr 0.90 CbSxX1V2 Ị X12X2 Lb r y 1 2 L rỹ 2 7.22 The beam slenderness ratio with respect to the y axis is Lb ry 20 X 12 1.30 184.6 Thus the critical elastic moment capacity is 1 X 94.5 X 1 730V2 Ị 1 7302 X 0.0226 Mc - 0.90 184.6 ự1 2 184.6 2 1 591 kip-in 132.6 kip-ft 277.5 kip-ft The W21 X 50 does not have adequate capacity. Therefore trials to find the lowest-weight larger size must be continued. This trial-and-error process can be eliminated by using beamselector charts in the AISC manual. These charts give the beam design moment corresponding to unbraced length for various rolled sections. Thus for ộMr 277.5 kip-ft and L 20 ft the charts indicate that a W21 X 62 of grade 50 steel satisfies the criteria Table 7.2 . As a check the following calculation is made with the properties of the W21 X 62 given in Table 7.2. For use in Eq. 7.22 the beam slenderness ratio is Lb ry 20 X 12 1.77 135.6 From Eq. 7.22 the critical elastic moment capacity is 1 X 127 X 1820V2 18202 X .