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The beam shown will be constructed from a standard steel W-shape using an allowable bending stress of 50.6 ksi. Assume P = 61 kips. L₁ = 3.8 ft, and L₂ = 11.4ft. (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 C L₁ D X

The beam shown will be constructed from a standard steel W-shape using an allowable bending stress of 50.6 ksi. Assume P = 61 kips. L₁ = 3.8 ft, and L₂ = 11.4ft. (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 C L₁ D 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 50.6 ksi. Assume P = 61 kips. L₁ = 3.8 ft, and L2 = 11.4 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 4₁ Designation W24 x 94 24 x 76 24 x 68 24 x 55 W21 x 68 21 x 62 21 x 50 21 x 44 WI8 x 55 18 x 50 Wide-Flange Sections or W Shapes-U.S. Customary Units Flange Flange 18 x 40 18 x 35 W16 x 57 16 x 50 16 x 40 16 x 31 Answer: W14 x 68 14 x 53 14 14 x 34 x 48 14 x 30 14 x 26 14 x 22 (a) Smin= (b) Wi (c) W = 1 B i in.² 27.7 22.4 Web Area Depth thickness width A d 4 bf in. 20.1 16.2 20.0 18.3 14.7 13.0 16.8 14.7 11.8 16.2 18.1 14.7 18.0 11.8 17.9 10.3 17.7 9.13 20.0 15.6 in. 24.3 23.9 23.7 23.6 21.1 21.0 20.8 20.7 14.1 10.0 L₂ 14.0 13.9 16.4 0.4.30 16.3 0.380 16.0 0.305 15.9 0.275 in. 0.515 0.440 0.415 0.395 0.430 0.400 0.380 0.350 X 0.390 0.3.5.5 0.315 0.300 13.8 0.340 14.0 0.285 8.85 13.8 0.270 0.255 7.69 6.49 13.9 13.7 0.230 lb 0.415 0.370 D 3 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 L₁ 8.03 6.75 6.73 5.03 5.00 thickness ts in. 0.875 0.680 0.585 0.505 0.535 0.450 2700 2100 1830 1350 0.685 1480 0.615 1330 984 843 0.630 0.570 0.525 0.425 0.715 0.630 0.505 0.440 0.720 0.660 D 0.595 0.455 0.385 0.420 0.335 1₁ in.* 890 800 612 $10 758 659 518 375 722 541 484 340 291 245 199 S₂ in.³ F 222 176 154 114 140 127 94.5 81.6 98.3 88.9 92.2 81.0 64.7 47.2 7.41 7.38 68.4 7.21 57.6 7.04 1003 "z 1, in. in.* 9.87 9.69 9.55 9.11 77.8 70.2 48.6 8.60 8.54 8.18 8.06 6.72 6.68 6.63 6.41 6.01 5.89 5.85 5.83 42.0 5.73 35.3 5.65 29.0 5.54 109 82.5 70.4 29.1 44.9 40.1 19.1 15.3 8.30 64.7 15.7 57.5 14.0 24.9 20.7 121 57.7 51.4 23.3 I 19.6 S, in.¹ 8.91 7.000 24.0 18.4 15.7 43.1 12.1 37.2 10.5 28.9 12.4 7.64 6.37 11.9 10.7 6.35 5.12 8.25 4.49 24.2 14.3 N de ", 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 12.8 1.91 6.91 1.5.3 5.82 1.49 3.55 1.08 2.80 1.04
Transcribed Image Text:The beam shown will be constructed from a standard steel W-shape using an allowable bending stress of 50.6 ksi. Assume P = 61 kips. L₁ = 3.8 ft, and L2 = 11.4 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 4₁ Designation W24 x 94 24 x 76 24 x 68 24 x 55 W21 x 68 21 x 62 21 x 50 21 x 44 WI8 x 55 18 x 50 Wide-Flange Sections or W Shapes-U.S. Customary Units Flange Flange 18 x 40 18 x 35 W16 x 57 16 x 50 16 x 40 16 x 31 Answer: W14 x 68 14 x 53 14 14 x 34 x 48 14 x 30 14 x 26 14 x 22 (a) Smin= (b) Wi (c) W = 1 B i in.² 27.7 22.4 Web Area Depth thickness width A d 4 bf in. 20.1 16.2 20.0 18.3 14.7 13.0 16.8 14.7 11.8 16.2 18.1 14.7 18.0 11.8 17.9 10.3 17.7 9.13 20.0 15.6 in. 24.3 23.9 23.7 23.6 21.1 21.0 20.8 20.7 14.1 10.0 L₂ 14.0 13.9 16.4 0.4.30 16.3 0.380 16.0 0.305 15.9 0.275 in. 0.515 0.440 0.415 0.395 0.430 0.400 0.380 0.350 X 0.390 0.3.5.5 0.315 0.300 13.8 0.340 14.0 0.285 8.85 13.8 0.270 0.255 7.69 6.49 13.9 13.7 0.230 lb 0.415 0.370 D 3 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 L₁ 8.03 6.75 6.73 5.03 5.00 thickness ts in. 0.875 0.680 0.585 0.505 0.535 0.450 2700 2100 1830 1350 0.685 1480 0.615 1330 984 843 0.630 0.570 0.525 0.425 0.715 0.630 0.505 0.440 0.720 0.660 D 0.595 0.455 0.385 0.420 0.335 1₁ in.* 890 800 612 $10 758 659 518 375 722 541 484 340 291 245 199 S₂ in.³ F 222 176 154 114 140 127 94.5 81.6 98.3 88.9 92.2 81.0 64.7 47.2 7.41 7.38 68.4 7.21 57.6 7.04 1003 "z 1, in. in.* 9.87 9.69 9.55 9.11 77.8 70.2 48.6 8.60 8.54 8.18 8.06 6.72 6.68 6.63 6.41 6.01 5.89 5.85 5.83 42.0 5.73 35.3 5.65 29.0 5.54 109 82.5 70.4 29.1 44.9 40.1 19.1 15.3 8.30 64.7 15.7 57.5 14.0 24.9 20.7 121 57.7 51.4 23.3 I 19.6 S, in.¹ 8.91 7.000 24.0 18.4 15.7 43.1 12.1 37.2 10.5 28.9 12.4 7.64 6.37 11.9 10.7 6.35 5.12 8.25 4.49 24.2 14.3 N de ", 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 12.8 1.91 6.91 1.5.3 5.82 1.49 3.55 1.08 2.80 1.04
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