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The beam shown will be constructed from a standard steel W-shape using an allowable bending stress of 106.5 ksi. Assume P = 61 kips, L₁ = 8.0 ft, and L₂ = 24.0 ft. (a) Determine the minimum section modulus required for this beam. (b) From the table below, select the lightest W shape that can be used for this beam. (c) What is the total weight of the steel beam itself (i.e., not including the loads that are carried by the beam)? A L₁ B L2 P L₁ b₂ X

The beam shown will be constructed from a standard steel W-shape using an allowable bending stress of 106.5 ksi. Assume P = 61 kips, L₁ = 8.0 ft, and L₂ = 24.0 ft. (a) Determine the minimum section modulus required for this beam. (b) From the table below, select the lightest W shape that can be used for this beam. (c) What is the total weight of the steel beam itself (i.e., not including the loads that are carried by the beam)? A L₁ B L2 P L₁ b₂ X

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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The beam shown will be constructed from a standard steel W-shape using an allowable bending stress of 106.5 ksi. Assume P = 61 kips, L₁ = 8.0 ft, and L₂ = 24.0 ft. (a) Determine the minimum section modulus required for this beam. (b) From the table below, select the lightest W shape that can be used for this beam. (c) What is the total weight of the steel beam itself (i.e., not including the loads that are carried by the beam)? A L₁ B L2 Wide-Flange Sections or W Shanes US Customary Units P L₁ bf X
Transcribed Image Text:The beam shown will be constructed from a standard steel W-shape using an allowable bending stress of 106.5 ksi. Assume P = 61 kips, L₁ = 8.0 ft, and L₂ = 24.0 ft. (a) Determine the minimum section modulus required for this beam. (b) From the table below, select the lightest W shape that can be used for this beam. (c) What is the total weight of the steel beam itself (i.e., not including the loads that are carried by the beam)? A L₁ B L2 Wide-Flange Sections or W Shanes US Customary Units P L₁ bf X
Wide-Flange Sections or W Shapes-U.S. Customary Units Designation W24 x 94 24 x 76 24 × 68 24 x 55 W21 x 68 21 x 62 21 x 50 21 x 44 W18 x 55 18 x 50 18 x 40 18 x 35 W16 x 57 16 x 50 16 x 40 16 x 31 W14 x 68 14 x 53 14 x 48 14 x 34 14 x 30 14 x 26 14 x 22 Area Depth A d in.² 27.7 22.4 20.1 16.2 20.0 18.3 14.7 13.0 16.2 14.7 11.8 10.3 16.8 14.7 11.8 9.13 20.0 15.6 14.1 10.0 in. 24.3 23.9 23.7 23.6 21.1 21.0 20.8 20.7 18.1 18.0 17.9 17.7 16.4 16.3 16.0 15.9 14.0 13.9 13.8 14.0 8.85 13.8 7.69 13.9 6.49 13.7 Web thickness tw in. 0.515 0.440 0.415 0.395 0.430 0.400 0.380 0.350 0.390 0.355 0.315 0.300 0.430 0.380 0.305 0.275 0.415 0.370 0.340 0.285 0.270 0.255 0.230 Flange Flange width thickness bf tf in. 9.07 8.99 8.97 7.01 8.27 8.24 6.53 6.50 7.53 7.50 6.02 6.00 7.12 7.07 7.00 5.53 10.0 8.06 8.03 6.75 6.73 5.03 5.00 in. 0.875 0.680 0.585 0.505 0.685 0.615 0.535 0.450 0.630 0.570 0.525 0.425 0.715 0.630 0.505 0.440 0.720 0.660 0.595 0.455 0.385 0.420 0.335 Ix in.4 2700 2100 1830 1350 1480 1330 984 843 890 800 612 510 758 659 518 375 722 541 484 340 291 245 199 Sx in.³ 222 176 154 114 140 127 94.5 81.6 98.3 88.9 68.4 57.6 92.2 81.0 64.7 47.2 103 77.8 70.2 48.6 42.0 35.3 29.0 in. 9.87 9.69 9.55 9.11 8.60 8.54 8.18 8.06 7.41 7.38 7.21 7.04 6.72 6.68 6.63 6.41 Iy in.4 109 82.5 70.4 29.1 64.7 57.5 24.9 20.7 44.9 40.1 19.1 15.3 43.1 37.2 28.9 12.4 6.01 121 5.89 5.85 5.83 5.73 5.65 5.54 57.7 51.4 23.3 19.6 8.91 7.00 Sy in.3 24.0 18.4 15.7 8.30 15.7 14.0 7.64 6.37 11.9 10.7 6.35 5.12 12.1 10.5 8.25 4.49 24.2 14.3 12.8 6.91 5.82 3.55 2.80 in. 1.98 1.92 1.87 1.34 1.80 1.77 1.30 1.26 1.67 1.65 1.27 1.22 1.60 1.59 1.57 1.17 2.46 1.92 1.91 1.53 1.49 1.08 1.04
Transcribed Image Text:Wide-Flange Sections or W Shapes-U.S. Customary Units Designation W24 x 94 24 x 76 24 × 68 24 x 55 W21 x 68 21 x 62 21 x 50 21 x 44 W18 x 55 18 x 50 18 x 40 18 x 35 W16 x 57 16 x 50 16 x 40 16 x 31 W14 x 68 14 x 53 14 x 48 14 x 34 14 x 30 14 x 26 14 x 22 Area Depth A d in.² 27.7 22.4 20.1 16.2 20.0 18.3 14.7 13.0 16.2 14.7 11.8 10.3 16.8 14.7 11.8 9.13 20.0 15.6 14.1 10.0 in. 24.3 23.9 23.7 23.6 21.1 21.0 20.8 20.7 18.1 18.0 17.9 17.7 16.4 16.3 16.0 15.9 14.0 13.9 13.8 14.0 8.85 13.8 7.69 13.9 6.49 13.7 Web thickness tw in. 0.515 0.440 0.415 0.395 0.430 0.400 0.380 0.350 0.390 0.355 0.315 0.300 0.430 0.380 0.305 0.275 0.415 0.370 0.340 0.285 0.270 0.255 0.230 Flange Flange width thickness bf tf in. 9.07 8.99 8.97 7.01 8.27 8.24 6.53 6.50 7.53 7.50 6.02 6.00 7.12 7.07 7.00 5.53 10.0 8.06 8.03 6.75 6.73 5.03 5.00 in. 0.875 0.680 0.585 0.505 0.685 0.615 0.535 0.450 0.630 0.570 0.525 0.425 0.715 0.630 0.505 0.440 0.720 0.660 0.595 0.455 0.385 0.420 0.335 Ix in.4 2700 2100 1830 1350 1480 1330 984 843 890 800 612 510 758 659 518 375 722 541 484 340 291 245 199 Sx in.³ 222 176 154 114 140 127 94.5 81.6 98.3 88.9 68.4 57.6 92.2 81.0 64.7 47.2 103 77.8 70.2 48.6 42.0 35.3 29.0 in. 9.87 9.69 9.55 9.11 8.60 8.54 8.18 8.06 7.41 7.38 7.21 7.04 6.72 6.68 6.63 6.41 Iy in.4 109 82.5 70.4 29.1 64.7 57.5 24.9 20.7 44.9 40.1 19.1 15.3 43.1 37.2 28.9 12.4 6.01 121 5.89 5.85 5.83 5.73 5.65 5.54 57.7 51.4 23.3 19.6 8.91 7.00 Sy in.3 24.0 18.4 15.7 8.30 15.7 14.0 7.64 6.37 11.9 10.7 6.35 5.12 12.1 10.5 8.25 4.49 24.2 14.3 12.8 6.91 5.82 3.55 2.80 in. 1.98 1.92 1.87 1.34 1.80 1.77 1.30 1.26 1.67 1.65 1.27 1.22 1.60 1.59 1.57 1.17 2.46 1.92 1.91 1.53 1.49 1.08 1.04
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