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A simply supported wood beam AB with span length L = 8 m carries a uniform load of intensity q = 10.8 kN/m and a concentrated load P= 25 kN at a distance a = 2.5 m from RH end (see figure). a. Calculate the maximum bending stress due to the load if the beam has a rectangular cross section with width b = 150 mm and height h=320 mm. You will need to set up Shear and Moment functions to determine MMax. b. Calculate the shear stresses in the beam (at the location of maximum shear force) at points located at the Neutral Axis and 40 mm, 80 mm, 120 mm and 160 mm from the N/A of the beam. From these calculations, plot a graph showing the distribution of shear stresses from top to bottom of the beam. L a H P h

A simply supported wood beam AB with span length L = 8 m carries a uniform load of intensity q = 10.8 kN/m and a concentrated load P= 25 kN at a distance a = 2.5 m from RH end (see figure). a. Calculate the maximum bending stress due to the load if the beam has a rectangular cross section with width b = 150 mm and height h=320 mm. You will need to set up Shear and Moment functions to determine MMax. b. Calculate the shear stresses in the beam (at the location of maximum shear force) at points located at the Neutral Axis and 40 mm, 80 mm, 120 mm and 160 mm from the N/A of the beam. From these calculations, plot a graph showing the distribution of shear stresses from top to bottom of the beam. L a H P h

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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1. A simply supported wood beam AB with span length L = 8 m carries a uniform load of intensity q = 10.8 kN/m and a concentrated load P= 25 kN at a distance a = 2.5 m from RH end (see figure). a. Calculate the maximum bending stress due to the load if the beam has a rectangular cross section with width b = 150 mm and height h=320 mm. You will need to set up Shear and Moment functions to determine MMax. b. Calculate the shear stresses in the beam (at the location of maximum shear force) at points located at the Neutral Axis and 40 mm, 80 mm, 120 mm and 160 mm from the N/A of the beam. From these calculations, plot a graph showing the distribution of shear stresses from top to bottom of the beam. P - L 2. Using the results from problem 1 above and assuming the allowable stress Allow = 150 MPa, calculate the following: 9 a. The required section modulus S. Then select the most economical wide-flange beam (W shape) from Table F-1(b) in Appendix F (attached), b. Recalculate S, taking-into-account the weight (IE deadload) of the beam. Select a new beam if necessary L h a H I
Transcribed Image Text:1. A simply supported wood beam AB with span length L = 8 m carries a uniform load of intensity q = 10.8 kN/m and a concentrated load P= 25 kN at a distance a = 2.5 m from RH end (see figure). a. Calculate the maximum bending stress due to the load if the beam has a rectangular cross section with width b = 150 mm and height h=320 mm. You will need to set up Shear and Moment functions to determine MMax. b. Calculate the shear stresses in the beam (at the location of maximum shear force) at points located at the Neutral Axis and 40 mm, 80 mm, 120 mm and 160 mm from the N/A of the beam. From these calculations, plot a graph showing the distribution of shear stresses from top to bottom of the beam. P - L 2. Using the results from problem 1 above and assuming the allowable stress Allow = 150 MPa, calculate the following: 9 a. The required section modulus S. Then select the most economical wide-flange beam (W shape) from Table F-1(b) in Appendix F (attached), b. Recalculate S, taking-into-account the weight (IE deadload) of the beam. Select a new beam if necessary L h a H I
Table F-1(b) Properties of Wide-Flange Sections (W Shapes) - SI Units (Abridged List) Flange Mass per Web Designation meter Area Depth thickness kg mm² mm W 760 X 314 314 W 760 X 196 196 W 610 X 241 241 W 610 X 140 140 W 460 X 177 177 W 460 x 106 106 W 410 X 149 W 410 X 114 W 410 X 85 W 410 x 46.1 W 360 x 179 W 360 x 122 W 360 x 79 W 360 x 39 W 310 X 129 W 310 x 74 W 310 X 52 W 310 X 21 W 250 x 89 W 250 x 67 W 250 X 44.8 W 250 x 17.9 149 114 85.0 46.1 179 122 129 74.0 52.0 21.0 40,100 785 25,100 770 89.0 67.0 44.8 17.9 30,800 635 17,900 617 22,600 483 13,400 470 19,000 432 14,600 419 10,800 417 5890 404 79.0 39.0 4960 22,800 368 15,500 363 10,100 353 353 16,500 318 9420 310 6650 318 2680 302 11,400 259 8580 257 5700 267 2280 251 W 200 X 52 6650 206 W 200 X 41.7 52.0 41.7 31.3 5320 205 W 200 x 31.3 3970 210 W 200 x 22.5 22.5 2860 206 Note: Axes 1-1 and 2-2 are principal centroidal axes. mm 19.7 15.6 17.9 13.1 16 17 66 16.6 12.6 14.9 11.6 10.9 6.99 15.0 13.0 9.40 6.48 13.1 10.7 8.89 7.62 4.83 Width Thickness I mm 384 267 330 230 287 194 307 9.40 205 7.62 167 5.08 101 264 262 181 140 mm 33.5 25.4 7.87 204 7.24 166 6.35 134 6.22 102 31.0 22.2 26.9 20.6 373 23.9 257 21.7 205 16.8 128 10.7 25.0 19.3 18.2 11.2 20.6 16.3 13.2 5.72 257 17.3 204 15.7 148 13.0 101 5.33 12.6 11.8 10.2 Axis 1-1 S x 105 mm² x 10³ mm³ 8.00 4290 2400 2150 1120 912 487 620 462 316 156 574 367 225 102 308 163 119 36.9 142 103 70.8 22.4 52.9 40.8 31.3 20.0 10,900 6230 6780 3640 3790 2080 2870 2200 1510 773 r mm 328 310 264 251 201 191 180 178 171 163 3110 158 2020 154 1270 150 578 144 1090 112 805 110 531 111 179 Axis 2-2 I S × 105 mm² × 10³ mm³ mm 99.1 315 81.6 184 45.4 105 25.1 77.4 57.4 17.9 5.16 206 61.6 24.0 1930 137 100 1050 132 747 133 244 117 3.71 23.4 10.2 0.982 48.3 22.2 6.95 0.907 511 89.2 17.7 398 87.6 9.03 298 88.6 4.07 193 83.6 1.42 1640 610 1120 393 736 259 585 441 198 73.6 1110 480 234 58.2 651 228 122 19.5 377 218 94.2 18.0 174 109 60.8 27.9 r 88.6 57.2 77.5 50.3 68.3 43.2 63.8 62.7 40.6 29.7 95.0 63.0 48.8 27.4 78.0 49.8 39.1 19.1 65.3 51.1 34.8 19.9 51.6 41.1 32.0 22.3
Transcribed Image Text:Table F-1(b) Properties of Wide-Flange Sections (W Shapes) - SI Units (Abridged List) Flange Mass per Web Designation meter Area Depth thickness kg mm² mm W 760 X 314 314 W 760 X 196 196 W 610 X 241 241 W 610 X 140 140 W 460 X 177 177 W 460 x 106 106 W 410 X 149 W 410 X 114 W 410 X 85 W 410 x 46.1 W 360 x 179 W 360 x 122 W 360 x 79 W 360 x 39 W 310 X 129 W 310 x 74 W 310 X 52 W 310 X 21 W 250 x 89 W 250 x 67 W 250 X 44.8 W 250 x 17.9 149 114 85.0 46.1 179 122 129 74.0 52.0 21.0 40,100 785 25,100 770 89.0 67.0 44.8 17.9 30,800 635 17,900 617 22,600 483 13,400 470 19,000 432 14,600 419 10,800 417 5890 404 79.0 39.0 4960 22,800 368 15,500 363 10,100 353 353 16,500 318 9420 310 6650 318 2680 302 11,400 259 8580 257 5700 267 2280 251 W 200 X 52 6650 206 W 200 X 41.7 52.0 41.7 31.3 5320 205 W 200 x 31.3 3970 210 W 200 x 22.5 22.5 2860 206 Note: Axes 1-1 and 2-2 are principal centroidal axes. mm 19.7 15.6 17.9 13.1 16 17 66 16.6 12.6 14.9 11.6 10.9 6.99 15.0 13.0 9.40 6.48 13.1 10.7 8.89 7.62 4.83 Width Thickness I mm 384 267 330 230 287 194 307 9.40 205 7.62 167 5.08 101 264 262 181 140 mm 33.5 25.4 7.87 204 7.24 166 6.35 134 6.22 102 31.0 22.2 26.9 20.6 373 23.9 257 21.7 205 16.8 128 10.7 25.0 19.3 18.2 11.2 20.6 16.3 13.2 5.72 257 17.3 204 15.7 148 13.0 101 5.33 12.6 11.8 10.2 Axis 1-1 S x 105 mm² x 10³ mm³ 8.00 4290 2400 2150 1120 912 487 620 462 316 156 574 367 225 102 308 163 119 36.9 142 103 70.8 22.4 52.9 40.8 31.3 20.0 10,900 6230 6780 3640 3790 2080 2870 2200 1510 773 r mm 328 310 264 251 201 191 180 178 171 163 3110 158 2020 154 1270 150 578 144 1090 112 805 110 531 111 179 Axis 2-2 I S × 105 mm² × 10³ mm³ mm 99.1 315 81.6 184 45.4 105 25.1 77.4 57.4 17.9 5.16 206 61.6 24.0 1930 137 100 1050 132 747 133 244 117 3.71 23.4 10.2 0.982 48.3 22.2 6.95 0.907 511 89.2 17.7 398 87.6 9.03 298 88.6 4.07 193 83.6 1.42 1640 610 1120 393 736 259 585 441 198 73.6 1110 480 234 58.2 651 228 122 19.5 377 218 94.2 18.0 174 109 60.8 27.9 r 88.6 57.2 77.5 50.3 68.3 43.2 63.8 62.7 40.6 29.7 95.0 63.0 48.8 27.4 78.0 49.8 39.1 19.1 65.3 51.1 34.8 19.9 51.6 41.1 32.0 22.3
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