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Question 3.12: For the beam shown in Figure 3-16. the load F due to the pip...

For the beam shown in Figure 3-16. the load F due to the pipe is 12 000 lb. The distances are a = 4 ft and b = 6 ft. Determine the required section modulus for the beam to limit the stress due to bending to 30 000 psi, the recommended design stress for a typical structural steel in static bending.

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Objective         Compute the required section modulus 5 for the beam in Figure 3-16.
Given                The layout and the loading pattern are shown in Figure 3-16.

Lengths: Overall length = L = 10 ft; a = 4 ft; b = 6 ft.
Load = F = 12 000 lb.
Design stress = σ_d= 30 000 psi.

Analysis U.se Equation (3-25) to compute the required section modulus 5. Compute the maximum bending moment that occurs at the point of application of the load using the formula shown in Part (b) of Figure 3-16.

Results    M_{max}=R_ja=\frac{Fba}{a+b}=\frac{(12 000 \ lb)(6ft)(4ft)}{(6 ft + 4 ft)} =28 800 lb.ft

S=\frac{M}{\sigma _d}=\frac{28 800 \ lb . ft}{30 000 \ lb/in^2}\frac{12 \ in}{ft} =11.5 \ in^3

Comments A beam section can now be .selected from Tables A16-3 and A 16-4 that has at least this value for the section modulus.

TABLE A16-3 Propertes of steel wide-flange shapes, W
-shapes*
Flange Axis X-X Axis
Y-Y
Designation Area
(in^2)		 Depth
(in)		 Web
thickness
(in)		 Width
(in)		 Thickness
(in)		 I
(in^4)		 S
(in^3)		 I
(in^4)		 S
(in^3)
W24 × 76 22.4 23.92 0.44 8.99 0.68 2100 176 82.5 18.4
W24 × 68 20.1 23.73 0.415 8.965 0.585 1830 154 70.4 15.7
W21 × 73 21.5 21.24 0.455 8.295 0.74 1600 151 70.6 17
W21 × 57 16.7 21.06 0.405 6.555 0.65 1170 111 30.6 9.35
W18 × 55 16.2 18.11 0.39 7.53 0.63 890 98.3 44.9 11.9
W18 × 40 11.8 17.9 0.315 6.015 0.525 612 68.4 19.1 6.35
W14 ×43 12.6 13.66 0.305 7.995 0.53 428 62.7 45.2 11.3
W14 × 26 7.69 13.91 0.255 5.025 0.42 245 35.3 8.91 3.54
W12 × 30 8.79 12.34 0.26 6.52 0.44 238 38.6 20.3 6.24
W12 × 16 4.71 11.99 0.22 3.99 0.265 103 17.1 2.82 1.41
W10 × 15 4.41 9.99 0.23 4 0.27 69.8 13.8 2.89 1.45
W10 × 12 3.54 9.87 0.19 3.96 0.21 53.8 10.9 2.18 1.1
W8 × 15 4.44 8.11 0.245 4.015 0.315 48 11.8 3.41 1.7
W8 × 10 2.96 7.89 0.17 3.94 0.205 30.8 7.81 2.09 1.06
W6 × 15 4.43 5.99 0.23 5.99 0.26 29.1 9.72 9.32 3.11
W6 × 12 3.55 6.03 0.23 4 0.28 22.1 7.31 2.99 1.5
W5 × 19 5.54 5.15 0.27 5.03 0.43 26.2 10.2 9.13 3.63
W5 × 16 4.68 5.01 0.24 5 0.36 21.3 8.51 7.51 3
W4 × 13 3.83 4.16 0.28 4.06 0.345 11.3 5.46 3.86 1.9
*Data are taken from a variety of sources. Sizes listed represent a small sample of the sizes available.
Notes: Example designation: W14 x 43
14 = nominal depth (in); 43 = weight per unit length (lb/ft)
I = moment of inertia; 5 = section modulus.

 

TABLE A16-4 Properties of American Standard steel beams. S-shapes^*
Flange Axis X-X Axis
Y-Y
Designation Area
(in^2)		 Depth
(in)		 Web
thickness
(in)		 Width
(in)		 Average
thickness
(in)		 I
(in^4)		 S
(in^3)		 I
(in^4)		 S
(in^3)
S24× 90 26.5 24 0.625 7.125 0.87 2250 187 44.9 12.6
S20 × 96 28.2 20.3 0.8 7.2 0.92 1670 165 50.2 13.9
S20 × 75 22 20 0.635 6.385 0.795 1280 128 29.8 9.32
S20 × 66 19.4 20 0.505 6.255 0.795 1190 119 27.7 8.85
S18 × 70 20.6 18 0.711 6.251 0.691 926 103 24.1 7.72
S15 × 50 14.7 15 0.55 5.64 0.622 486 64.8 15.7 5.57
S12 × 50 14.7 12 0.687 5.477 0.659 305 50.8 15.7 5.74
S12 × 35 10.3 12 0.428 5.078 0.544 229 38.2 9.87 3.89
S10 X 35 10.3 10 0.594 4.944 0.491 147 29.4 8.36 3.38
S10 × 25.4 7.46 10 0.311 4.661 0.491 124 24.7 6.79 2.91
S8 × 23 6.77 8 0.441 4.171 0.426 64.9 16.2 4.31 2.07
S8 ×18.4 5.41 8 0.271 4.001 0.426 57.6 14.4 3.73 1.86
S7 × 20 5.88 7 0.45 3.86 0.392 42.4 12.1 3.17 1.64
S6 × 12.5 3.67 6 0.232 3.332 0.359 22 1 7.37 1.82 1.09
S5 × 10 2.94 5 0.214 3.004 0.326 12.3 4.92 1.22 0.809
S4 × 7.7 2.26 4 0.193 2.663 0.293 6.08 3.04 0.764 0.574
S3 × 5.7 1.67 3 0.17 2.33 0.26 2.52 1.68 0.455 0.39
*Data are taken from a variety of sources. Sizes listed represent a small sample of the sizes available.
Notes: Example designation: S10 × 35
10 = nominal depth (in); 35 = weight per unit length (lb/ft)
I = moment of inertia; S = section modulus.

The lightest .section, typically preferred, is the W8×15 wide flange shape with S = 11.8 in^3

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