1. A beam is loaded and supported as shown below. (a) Using the coordinate system shown, determine the equation of the elastic curve in terms of x, w, L, E, and I by integrating the beam deflection equation. Determine the deflection at B for a structural steel S203 × 34 American standard beam, if L = 5 m and w = 2 kN/m. (b) Y A W B

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1. A beam is loaded and supported as shown below.
(a) Using the coordinate system shown, determine the equation of the elastic curve
in terms of x, w, L, E, and I by integrating the beam deflection equation.
Determine the deflection at B for a structural steel S203 x 34 American standard
beam, if L = 5 m and w = 2 kN/m.
(b)
Y
A
X
W
L
|B
Transcribed Image Text:1. A beam is loaded and supported as shown below. (a) Using the coordinate system shown, determine the equation of the elastic curve in terms of x, w, L, E, and I by integrating the beam deflection equation. Determine the deflection at B for a structural steel S203 x 34 American standard beam, if L = 5 m and w = 2 kN/m. (b) Y A X W L |B
TABLE A-4 American Standard Beams (Sl Units)
Desig-
nation*
S610 x 180
x 158
x 149
X 134
x 119
S508 x 143
x 128
X 112
x 98
S457 X 104
X 81
S381 X 74
X 64
$305 x 74
x 61
X 52
X 47
S254 x 52
x 38
$203 × 34
X 27
S178 X 30
x 23
S152 X 26
X 19
S127 X 22
V LE
Area
(mm²)
22970
20130
18900
17100
15160
18190
16320
14190
12520
13290
10390
9485
8130
9485
7740
6645
6030
6645
4815
4370
3490
3795
2905
3270
2370
I
2800
1006
Depth
(mm)
622.3
622.3
609.6
609.6
609.6
515.6
515.6
508.0
508.0
457.2
457.2
381.0
381.0
304.8
304.8
304.8
304.8
254.0
254.0
203.2
203.2
177.8
177.8
152.4
152.4
127.0
FLANGE
Width
(mm)
204.5
199.9
184.0
181.0
177.8
182.9
179.3
162.2
158.9
158.8
152.4
143.3
139.7
139.1
133.4
129.0
127.0
125.6
118.4
105.9
101.6
98.0
93.0
90.6
84.6
83.4
Thick-
ness
(mm)
27.7
27.7
22.1
22.1
22.1
23.4
23.4
20.2
20.2
17.6
17.6
15.8
15.8
16.7
16.7
13.8
13.8
12.5
12.5
10.8
10.8
10.0
10.0
9.1
9.1
8.3
Web
Thick-
ness
(mm)
20.3
15.7
18.9
15.9
12.7
20.3
16.8
16.1
12.8
18.1
11.7
14.0
10.4
17.4
11.7
10.9
8.9
15.1
7.9
11.2
6.9
11.4
6.4
11.8
5.9
12.5
[
(106
mm²)
1315
1225
995
937
874
695
658
533
495
358
335
202
186
127
113
95.3
90.7
61.2
51.6
27.0
24.0
17.6
15.3
10.9
AXIS X-X
S
(10³
mm³)
9.20
6.33
4225
3935
3260
3065
2870
2705
2540
2100
1950
1690
1465
1060
977
832
744
626
596
482
408
265
236
198
172
144
121
X-
99.8
(mm)
240
247
229
234
241
196
200
194
199
170
180
146
151
·X
116
121
120
123
96.0
103
78.7
82.8
68.3
72.6
57.9
62.2
47.5
(106
mm¹)
34.7
32.1
19.9
18.7
17.6
20.9
19.5
12.4
11.5
10.0
8.66
6.53
5.99
6.53
5.66
4.11
3.90
3.48
2.83
1.79
1.55
1.32
1.10
0.961
0.758
0.695
AXIS X-Y
S
(103
mm³)
339
321
216
206
198
228
218
153
145
127
114
91.3
85.7
94.1
84.6
63.7
61.3
55.4
47.7
33.9
30.5
26.9
23.6
21.3
17.9
16.6
Y
(mm)
38.9
39.9
32.3
33.0
34.0
33.8
34.5
29.5
30.2
27.4
29.0
26.2
27.2
26.2
26.9
24.1
25.4
22.9
24.2
20.3
21.1
18.6
19.5
17.1
17.9
15.7
Transcribed Image Text:TABLE A-4 American Standard Beams (Sl Units) Desig- nation* S610 x 180 x 158 x 149 X 134 x 119 S508 x 143 x 128 X 112 x 98 S457 X 104 X 81 S381 X 74 X 64 $305 x 74 x 61 X 52 X 47 S254 x 52 x 38 $203 × 34 X 27 S178 X 30 x 23 S152 X 26 X 19 S127 X 22 V LE Area (mm²) 22970 20130 18900 17100 15160 18190 16320 14190 12520 13290 10390 9485 8130 9485 7740 6645 6030 6645 4815 4370 3490 3795 2905 3270 2370 I 2800 1006 Depth (mm) 622.3 622.3 609.6 609.6 609.6 515.6 515.6 508.0 508.0 457.2 457.2 381.0 381.0 304.8 304.8 304.8 304.8 254.0 254.0 203.2 203.2 177.8 177.8 152.4 152.4 127.0 FLANGE Width (mm) 204.5 199.9 184.0 181.0 177.8 182.9 179.3 162.2 158.9 158.8 152.4 143.3 139.7 139.1 133.4 129.0 127.0 125.6 118.4 105.9 101.6 98.0 93.0 90.6 84.6 83.4 Thick- ness (mm) 27.7 27.7 22.1 22.1 22.1 23.4 23.4 20.2 20.2 17.6 17.6 15.8 15.8 16.7 16.7 13.8 13.8 12.5 12.5 10.8 10.8 10.0 10.0 9.1 9.1 8.3 Web Thick- ness (mm) 20.3 15.7 18.9 15.9 12.7 20.3 16.8 16.1 12.8 18.1 11.7 14.0 10.4 17.4 11.7 10.9 8.9 15.1 7.9 11.2 6.9 11.4 6.4 11.8 5.9 12.5 [ (106 mm²) 1315 1225 995 937 874 695 658 533 495 358 335 202 186 127 113 95.3 90.7 61.2 51.6 27.0 24.0 17.6 15.3 10.9 AXIS X-X S (10³ mm³) 9.20 6.33 4225 3935 3260 3065 2870 2705 2540 2100 1950 1690 1465 1060 977 832 744 626 596 482 408 265 236 198 172 144 121 X- 99.8 (mm) 240 247 229 234 241 196 200 194 199 170 180 146 151 ·X 116 121 120 123 96.0 103 78.7 82.8 68.3 72.6 57.9 62.2 47.5 (106 mm¹) 34.7 32.1 19.9 18.7 17.6 20.9 19.5 12.4 11.5 10.0 8.66 6.53 5.99 6.53 5.66 4.11 3.90 3.48 2.83 1.79 1.55 1.32 1.10 0.961 0.758 0.695 AXIS X-Y S (103 mm³) 339 321 216 206 198 228 218 153 145 127 114 91.3 85.7 94.1 84.6 63.7 61.3 55.4 47.7 33.9 30.5 26.9 23.6 21.3 17.9 16.6 Y (mm) 38.9 39.9 32.3 33.0 34.0 33.8 34.5 29.5 30.2 27.4 29.0 26.2 27.2 26.2 26.9 24.1 25.4 22.9 24.2 20.3 21.1 18.6 19.5 17.1 17.9 15.7
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