The cantilever beam shown is an aluminum pipe that has an outside diameter of 114 mm and an inside diameter of 97.3 mm. A moment of 3 kN-m is applied at the free end. Find the rotation at the free end of the pipe. Neglect the weight of the pipe. M = 3 KN.m 2m Mod. of Mod. of Coet. of Thermal Expansion a Peisson's Elasticity Rigidity Density Ultimate Strength MPa Tensile Yield MPa x 10 Strength F, MPa Ratio x 10 x 10 Tens. Comp. Shear * 10 Material Steel ASTM A6 or AS01 785 207 83 250 400 11.7 0.25 185 Steel (high-strength low-alloy) ASTM A992 207 83 345 450 11.7 0.25 Steel AISI 1020 hot-rolled 785 207 79.3 210 380 11.7 0.25 Steel ASI 1040 785 207 79.3 290 520 11.7 0.25 hot-rolled Stainless steel (annealed) 200 80 280 580 410 11.7 0.25 Cast iron gray) 721 103 41 140 550 220 10.6 0.26 Aluminum aloy 6061-16 2.64 70 28 240 260 190 23.6 0.33 Magnesium aloy 1.794 45 17 210 280 140 26.1 0.34 Titanium aloy 4.40 114 45 900 970 690 9.7 Inside Diameter Nominal Outside Diameter Wall Thickness Diameter Mass kg/m mm 10 mm 10' mm mm mm mm Standard Weight 51 60.50 525 3.91 544 658 0.261 8.65 20.1 102 114.00 102 6.02 16.10 1910 284 49.7 38.4
The cantilever beam shown is an aluminum pipe that has an outside diameter of 114 mm and an inside diameter of 97.3 mm. A moment of 3 kN-m is applied at the free end. Find the rotation at the free end of the pipe. Neglect the weight of the pipe. M = 3 KN.m 2m Mod. of Mod. of Coet. of Thermal Expansion a Peisson's Elasticity Rigidity Density Ultimate Strength MPa Tensile Yield MPa x 10 Strength F, MPa Ratio x 10 x 10 Tens. Comp. Shear * 10 Material Steel ASTM A6 or AS01 785 207 83 250 400 11.7 0.25 185 Steel (high-strength low-alloy) ASTM A992 207 83 345 450 11.7 0.25 Steel AISI 1020 hot-rolled 785 207 79.3 210 380 11.7 0.25 Steel ASI 1040 785 207 79.3 290 520 11.7 0.25 hot-rolled Stainless steel (annealed) 200 80 280 580 410 11.7 0.25 Cast iron gray) 721 103 41 140 550 220 10.6 0.26 Aluminum aloy 6061-16 2.64 70 28 240 260 190 23.6 0.33 Magnesium aloy 1.794 45 17 210 280 140 26.1 0.34 Titanium aloy 4.40 114 45 900 970 690 9.7 Inside Diameter Nominal Outside Diameter Wall Thickness Diameter Mass kg/m mm 10 mm 10' mm mm mm mm Standard Weight 51 60.50 525 3.91 544 658 0.261 8.65 20.1 102 114.00 102 6.02 16.10 1910 284 49.7 38.4
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:The cantilever beam shown is an aluminum pipe that has an outside diameter of 114 mm and
an inside diameter of 97.3 mm. A moment of 3 kN-m is applied at the free end. Find the
rotation at the free end of the pipe. Neglect the weight of the pipe.
М 33KN.m
2m
Mod. of
Mod. of
Coeff, of
Elasticity Rigidity
G
Thermal
Ultimate Strength
Density
kg /m3
x 10
Tensile Yield
Strength
F, MPa
Expansion a
m/m/C
x 10-6
Poisson's
MPa
MPa
MPa
Ratio
Material
x 10
x 10
Tens.
Comp.
Shear
Steel ASTM A36
or A501
7.85
207
83
250
400
11.7
0.25
Steel (high-strength
low-alloy) ASTM
A992
7.85
207
83
345
450
11.7
0.25
Steel AISI 1020
hot-rolled
7.85
207
79.3
210
380
11.7
0.25
Steel AISI 1040
hot-rolled
7.85
207
79.3
290
520
11.7
0.25
Stainless steel
7.85
200
80
280
580
410
11.7
0.25
(annealed)
Cast iron (gray)
7.21
103
41
140
550
220
10.6
0.26
Aluminum allov
2.64
70
28
240
260
190
23.6
0.33
6061-T6
Magnesium alloy
1.794
45
17
210
280
140
26.1
0.34
Titanium alloy
4.40
114
45
900
970
690
9.7
Nominal
Outside
Inside
Wall
Diameter
Diameter
Diameter
Thickness
Mass
A
kg/m
mm2
106 mm
103 mm3
mm
mm
mm
mm
Standard Weight
51
60.50
52.5
3.91
5.44
658
0.261
8.65
20.1
102
114.00
102
6.02
16.10
1910
2.84
49.7
38.4
152
168.00
154
7.11
28.30
3350
11.0
131
57.2
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