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A W 310 X 52 steel beam is subjected to a point load P = 56 kN and a transverse load V = 15kN at B. The beam has length L = 2 m. See the table for beam properties. (Assume that the structure behaves linearly elastically and that the stresses caused by two or more loads may be superimposed to obtain the resultant stresses acting at a point. Consider both in-plane and out-of-plane shear stresses unless otherwise specified. (Do not use rounded intermediate values in your calculations) (a) Calculate the principal normal stresses and the maximum shear stress on element D located on the web right below the top flange and near the fixed support. Neglect the weight of the beam. (Enter your answers in MPa. For the normal stresses, use the deformation sign convention. For the shear stress, enter the magnitude.) σ1 = MPa σ2 = MPa τmax = MPa (b) Calculate the principal normal stresses and the maximum shear stress on an element at centroid C (see figure). Neglect the weight of the beam. (Enter your answers in MPa. For the normal stresses, use the deformation sign convention. For the shear stress, enter the magnitude.) σ1 = MPa σ2 = MPa τmax = MPa

A W 310 X 52 steel beam is subjected to a point load P = 56 kN and a transverse load V = 15kN at B. The beam has length L = 2 m. See the table for beam properties. (Assume that the structure behaves linearly elastically and that the stresses caused by two or more loads may be superimposed to obtain the resultant stresses acting at a point. Consider both in-plane and out-of-plane shear stresses unless otherwise specified. (Do not use rounded intermediate values in your calculations) (a) Calculate the principal normal stresses and the maximum shear stress on element D located on the web right below the top flange and near the fixed support. Neglect the weight of the beam. (Enter your answers in MPa. For the normal stresses, use the deformation sign convention. For the shear stress, enter the magnitude.) σ1 = MPa σ2 = MPa τmax = MPa (b) Calculate the principal normal stresses and the maximum shear stress on an element at centroid C (see figure). Neglect the weight of the beam. (Enter your answers in MPa. For the normal stresses, use the deformation sign convention. For the shear stress, enter the magnitude.) σ1 = MPa σ2 = MPa τmax = MPa

Welding: Principles and Applications (MindTap Course List)
Welding: Principles and Applications (MindTap Course List)
8th Edition
ISBN:9781305494695
Author:Larry Jeffus
Publisher:Larry Jeffus
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A W 310 X 52 steel beam is subjected to a point load P = 56 kN and a transverse load V = 15kN at B. The beam has length L = 2 m. See the table for beam properties. (Assume that the structure behaves linearly elastically and that the stresses caused by two or more loads may be superimposed to obtain the resultant stresses acting at a point. Consider both in-plane and out-of-plane shear stresses unless otherwise specified. (Do not use rounded intermediate values in your calculations)

(a) Calculate the principal normal stresses and the maximum shear stress on element D located on the web right below the top flange and near the fixed support. Neglect the weight of the beam. (Enter your answers in MPa. For the normal stresses, use the deformation sign convention. For the shear stress, enter the magnitude.)

σ1 =                            MPa

σ2 =                            MPa

τmax =                            MPa

(b) Calculate the principal normal stresses and the maximum shear stress on an element at centroid C (see figure). Neglect the weight of the beam. (Enter your answers in MPa. For the normal stresses, use the deformation sign convention. For the shear stress, enter the magnitude.)

σ1 =                            MPa

σ2 =                            MPa

τmax =                            MPa

D- A Z L y C D h₁/2 B i
Transcribed Image Text:D- A Z L y C D h₁/2 B i
Properties of Wide-Flange Sections (W Shapes) SI Units (Abridged List) Mass Flange per Designation Meter Area Depth mm² mm kg W 760 x 314 314 40100 785 W 760 x 196 196 25100 770 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 W410 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 × 89 W 250 x 67 W 250 x 44.8 W 250 x 17.9 Web Thick- ness Width mm mm 19.7 15.6 30800 635 17.9 330 17900 617 13.1 230 22600 483 16.6 287 13400 470 12.6 194 149 19000 432 114 14600 419 85.0 10800 417 10.9 46.1 5890 404 6.99 129 16500 318 74.0 9420 310 52.0 6650 318 21.0 2680 302 384 33.5 267 25.4 14.9 264 11.6 262 181 140 179 122 15500 363 13.0 79.0 10100 353 9.40 39.0 4960 353 6.48 22800 368 15.0 373 257 205 128 13.1 307 9.40 205 7.62 167 5.08 101 89.0 11400 259 10.7 257 8.89 204 67.0 8580 44.8 17.9 257 5700 267 7.62 148 2280 251 4.83 101 W 200 X 52 52.0 6650 206 W 200 X 41.7 41.7 5320 205 31.3 3970 210 W 200 x 31.3 6.35 134 W 200 X 22.5 22.5 2860 206 6.22 102 Note: Axes 1-1 and 2-2 are principal centroidal axes. Thick- ness I S r mm x 10 mm x 10³ mm³ mm 31.0 22.2 26.9 20.6 25.0 19.3 18.2 11.2 23.9 21.7 16.8 10.7 20.6 16.3 13.2 5.72 17.3 15.7 13.0 5.33 7.87 204 12.6 7.24 166 11.8 10.2 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 Axis 1-1 52.9 40.8 31.3 20.0 10900 328 6230 310 6780 264 3640 251 3790 201 2080 191 2870 180 2200 178 1510 171 773 163 3110 158 2020 154 1270 150 578 144 1930 137 1050 132 747 133 244 117 1090 112 805 110 531 179 $11 398 87.6 298 88.6 193 83.6 I S x 105mm x 10³ mm³ mm 1640 88.6 610 57.2 315 81.6 184 45.4 105 25.1 77.4 57.4 17.9 5.16 206 61.6 24.0 3.71 100 23.4 10.2 0.982 48.3 22.2 6.95 0.907 99.1 89.2 17.7 9.03 4.07 1.42 Axis 2-2 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 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 $1.6 41.1 60.8 32.0 27.9 22.3
Transcribed Image Text:Properties of Wide-Flange Sections (W Shapes) SI Units (Abridged List) Mass Flange per Designation Meter Area Depth mm² mm kg W 760 x 314 314 40100 785 W 760 x 196 196 25100 770 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 W410 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 × 89 W 250 x 67 W 250 x 44.8 W 250 x 17.9 Web Thick- ness Width mm mm 19.7 15.6 30800 635 17.9 330 17900 617 13.1 230 22600 483 16.6 287 13400 470 12.6 194 149 19000 432 114 14600 419 85.0 10800 417 10.9 46.1 5890 404 6.99 129 16500 318 74.0 9420 310 52.0 6650 318 21.0 2680 302 384 33.5 267 25.4 14.9 264 11.6 262 181 140 179 122 15500 363 13.0 79.0 10100 353 9.40 39.0 4960 353 6.48 22800 368 15.0 373 257 205 128 13.1 307 9.40 205 7.62 167 5.08 101 89.0 11400 259 10.7 257 8.89 204 67.0 8580 44.8 17.9 257 5700 267 7.62 148 2280 251 4.83 101 W 200 X 52 52.0 6650 206 W 200 X 41.7 41.7 5320 205 31.3 3970 210 W 200 x 31.3 6.35 134 W 200 X 22.5 22.5 2860 206 6.22 102 Note: Axes 1-1 and 2-2 are principal centroidal axes. Thick- ness I S r mm x 10 mm x 10³ mm³ mm 31.0 22.2 26.9 20.6 25.0 19.3 18.2 11.2 23.9 21.7 16.8 10.7 20.6 16.3 13.2 5.72 17.3 15.7 13.0 5.33 7.87 204 12.6 7.24 166 11.8 10.2 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 Axis 1-1 52.9 40.8 31.3 20.0 10900 328 6230 310 6780 264 3640 251 3790 201 2080 191 2870 180 2200 178 1510 171 773 163 3110 158 2020 154 1270 150 578 144 1930 137 1050 132 747 133 244 117 1090 112 805 110 531 179 $11 398 87.6 298 88.6 193 83.6 I S x 105mm x 10³ mm³ mm 1640 88.6 610 57.2 315 81.6 184 45.4 105 25.1 77.4 57.4 17.9 5.16 206 61.6 24.0 3.71 100 23.4 10.2 0.982 48.3 22.2 6.95 0.907 99.1 89.2 17.7 9.03 4.07 1.42 Axis 2-2 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 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 $1.6 41.1 60.8 32.0 27.9 22.3
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