A simple beam of length L- 5 m carries a uniform load of intensity = 5.8 kN/m and a concentrated load 22.5 kN (see figure). P=22.5 kN] q=5.8 kN/m The 1-1 and 2-2 axes are labeled on the cross section below. E (a) Assuming 1.5m 113 MPa, calculate the required section modulus S (in mm³). (At this point, disregard the weight of the beam.) mm³ Select the most economical wide-flange beam (W shape) from this table, and recalculate S (in mm³), taking into account the weight of the beam. Select a new beam if necessary. mm³ What is the suitable beam size?
A simple beam of length L- 5 m carries a uniform load of intensity = 5.8 kN/m and a concentrated load 22.5 kN (see figure). P=22.5 kN] q=5.8 kN/m The 1-1 and 2-2 axes are labeled on the cross section below. E (a) Assuming 1.5m 113 MPa, calculate the required section modulus S (in mm³). (At this point, disregard the weight of the beam.) mm³ Select the most economical wide-flange beam (W shape) from this table, and recalculate S (in mm³), taking into account the weight of the beam. Select a new beam if necessary. mm³ What is the suitable beam size?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:A simple beam of length L = 5 m carries a uniform load of intensity q = 5.8 kN/m and a concentrated load 22.5 kN (see figure).
P = 22.5 kN
1
q= 5.8 kN/m
The 1-1 and 2-2 axes are labeled on the cross section below.
H
-L-5 m-
(a) Assuming allow = 113 MPa, calculate the required section modulus S (in mm³). (At this point, disregard the weight of the beam.)
mm 3
Select the most economical wide-flange beam (W shape) from this table, and recalculate S (in mm³), taking into account the weight of the beam. Select a new beam if necessary.
mm3
What is the suitable beam size?
● W 200 x 41.7
●W 250 x 89
W 360 x 39
● W 360 x 79
● W 200 x 31.3
necessary.
1.5 m
(b) Now assume that the design requires that the W shape must be used in weak axis bending (i.e., it must bend about the 2-2 (or y-) axis of the cross section). Select the most economical wide-flange beam (W shape) from this table, and recalculate S (in mm³), taking into account the weight of the beam. Select a new beam if
mm
What is the suitable beam size?
● W 200 x 41.7
●W 250 x 89
●W 360 x 39
●W 360 x 79
W 200 x 31.3
Transcribed Image Text:Properties of Wide-Flange Sections (W Shapes)—SI Units (Abridged List)
Mass
Web
Flange
per
Thick-
Thick-
Designation Meter Area Depth ness Width ness
kg mm² mm mm mm
W 760 x 314 314
W 760 X 196
196
W 610 x 241
W 610 x 140
W 460 X 177 177
W 460 X 106
106
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
241
140
W 250 X 89
W 250 X 67
W 250 X 44.8
W 250 X 17.9
W 200 X 52
W 200 X 41.7
W 200 x 31.3
W 200 X 22.5
40100 785 19.7 384
25100 770 15.6 267
30800 635 17.9
17900 617
W 410 x 149 149 19000 432 4.9
W 410 x 114 114 14600 419 11.6
W 410 X 85 85.0 10800 417
W 410 x 46.1 46.1 5890 404
10.9
22600 483
13400 470 12.6
179 22800
122 15500
79.0 10100
39.0 4960
368
363
353
353
330
13.1 230
129 16500 318
74.0 9420 310
52.0 6650 318
21.0 2680 302
89.0 11400 259
67.0 8580 257
44.8 5700 267
17.9 2280 251
16.6 287 26.9
194
20.6
6.99
15.0
373
13.0 257
9.40
205
6.48
128
13.1 307
9.40 205
7.62
5.08
10.7
257
8.89
204
7.62 148
4.83
101
264 25.0
262
19.3
181
18.2
140
11.2
Note Axes 1-1 and 2-2 are principal centroidal axes
33.5
25.4
206
7.87 204
52.0 6650
41.7 5320
31.3 3970
205
7.24 166
210
6.35
134
22.5 2860 206 6.22
102
S
mm x 106mm x 10³ mm³ mm x 10mm
31.0
22.2
20.6
16.3
167 13.2
101
5.72
23.9
21.7
16.8
10.7
17.3
15.7
13.0
5.33
12.6
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
3640
3790
2080
28
2200
1510
264
251
180
178
171
773 163
201
191
3110
158
2020
154
1270 150
578
144
511
398
1090 112
805
110
531 111
179
315
99.1
81.6
184
45.4
105
25.1
77.4
57.4
17.9
5.16
206
1930 137 100
1050 132
747
133
244 117
61.6
24.0
3.71
23.4
10.2
0.982
48.3
22.2
6.95
0.907
89.2 17.7
87.6
9.03
298 88.6
193 83.6
Axis 2-2
4.07
1.42
S
× 10³mm³ mm
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
88.6
57.2
الا نیا
77.5
50.3
68.3
43.2
63.
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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