Please write the complete solutions and Legibly. Thumbs up will given!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 = MPaσ2 = MPaτmax = 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 = MPaσ2 = MPaτmax = MPa D-AZLyCDh₁/2Bi Properties of Wide-Flange Sections (W Shapes) SI Units (Abridged List)MassFlangeperDesignation Meter Area Depthmm² mmkgW 760 x 314 314 40100 785W 760 x 196196 25100770W 610 x 241 241W 610 x 140140W 460 x 177 177W 460 x 106106W 410 x 149W 410 x 114W 410 X 85W410 x 46.1W 360 x 179W 360 x 122W 360 x 79W 360 x 39W 310 X 129W 310 x 74W 310 X 52W 310 x 21W 250 × 89W 250 x 67W 250 x 44.8W 250 x 17.9WebThick-ness Widthmm mm19.715.630800 635 17.933017900 617 13.1 23022600 483 16.6 28713400 470 12.6 194149 19000 432114 14600 41985.0 10800 417 10.946.1 5890 4046.99129 16500 31874.0 9420 31052.0 6650 31821.0 2680 30238433.5267 25.414.926411.6 26218114017912215500 363 13.079.0 10100 353 9.4039.0 49603536.4822800 368 15.0 37325720512813.1 3079.40 2057.62 1675.0810189.0 11400 259 10.7 2578.89 20467.0 858044.817.92575700 2677.62 14822802514.83101W 200 X 5252.0 6650206W 200 X 41.741.7 532020531.3 3970 210W 200 x 31.36.35 134W 200 X 22.5 22.5 2860 206 6.22 102Note: Axes 1-1 and 2-2 are principal centroidal axes.Thick-ness ISrmm x 10 mm x 10³ mm³ mm31.022.226.920.625.019.318.211.223.921.716.810.720.616.313.25.7217.315.713.05.337.87 20412.67.24 166 11.810.28.00429024002150112091248762046231615657436722510230816311936.914210370.822.4Axis 1-152.940.831.320.010900 3286230 3106780 2643640 2513790 2012080 1912870 1802200 1781510 17177316331101582020 1541270 150578 14419301371050 132747133244 1171090 112805 110531179$11398 87.629888.6193 83.6ISx 105mm x 10³ mm³ mm164088.661057.231581.618445.410525.177.457.417.95.1620661.624.03.7110023.410.20.98248.322.26.950.90799.189.2 17.79.034.071.42Axis 2-2112039373625958544119873.6111048023458.265122812219.537721894.218.017410977.550.368.343.263.862.740.629.795.063.048.827.478.049.839.119.165.351.134.819.9$1.641.160.832.027.9 22.3

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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

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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Please write the complete solutions and Legibly. Thumbs up will given!

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

τ_max= 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

τ_max= MPa

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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