M4.18 (Sl units) A bridge to be fabricated of steel girders is designed to be 500 m long and 12 m wideat ambient temperature (assumed 20°C). Expansion joints will be provided to compensate for thechange in length in the girders as the temperature varies. Each expansion joint can compensate for amaximum of 20 mm of change in length. From historical records it is estimated that the minimum andmaximum temperatures in the region wll be-35°C and 40°C, respectively. Determine (a) theminimum number of expansion joints required. Use Table 4.1from the book for reference. Round tothe nearest whole number of joints. Table 4.1 Volumetric properties in U.S. customary units for selected engineering materialsCoclicient of ThermalExpansion, aCx10F10Melting Point, TDensity, pg/emMaterialMetalsAluminum2.70(0.098)(13.3)660(1220)24Copper8.97(0.324)171083(1981)(94)Iron7.87(0.284)12.1(6.7)1539(2802)Lead11.35(0.410)29(621)(16.1)327Magnesium1.74(0.063)26(144)650(1202)Nickel8.92(0.322)13.3(7.4)(2651)1455Steel(0.284)7.8712(6.7)aTin7.3(0.264)23(12.7)232(449)Titanium4.51(0.163)8.6(4.7)1668(3034)Tungsten19.30(0.697)4.0(2.2)3410(6170)Zinc7.15(0.258)40(22.2)420(787)Ceramics and SiliconGlass2.5(0.090)1.8-9.0(1.0-5.0)Alumina3.8(0.137)9.0(5.0)2072(3762)Silica2.66(0.096)0.55(0.31)1600(2912)Silicon2.33(0.085)2.6(1.4)1414(2577)PolymersPhenol resins1.3(0.047)60(33)NylonPolyethyleneI.16(0042)100(55)260(500)0.92(0.033)180(100)115(240)Polystyrene1.05(0.038)70(39)240(464)Polyvinylchloride140(0.051)50(28)212(414)Compiled from. 121.131. 141. 15). and other sourcesMelting tesmperature depends on compositionLow-density polyethyleneChemically degrades at high temperanures because it is a thermosetting polymer, ocher polymers listed are thermoplastic

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Asked Nov 9, 2019
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M4.18 (Sl units) A bridge to be fabricated of steel girders is designed to be 500 m long and 12 m wide
at ambient temperature (assumed 20°C). Expansion joints will be provided to compensate for the
change in length in the girders as the temperature varies. Each expansion joint can compensate for a
maximum of 20 mm of change in length. From historical records it is estimated that the minimum and
maximum temperatures in the region wll be-35°C and 40°C, respectively. Determine (a) the
minimum number of expansion joints required. Use Table 4.1from the book for reference. Round to
the nearest whole number of joints.
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M4.18 (Sl units) A bridge to be fabricated of steel girders is designed to be 500 m long and 12 m wide at ambient temperature (assumed 20°C). Expansion joints will be provided to compensate for the change in length in the girders as the temperature varies. Each expansion joint can compensate for a maximum of 20 mm of change in length. From historical records it is estimated that the minimum and maximum temperatures in the region wll be-35°C and 40°C, respectively. Determine (a) the minimum number of expansion joints required. Use Table 4.1from the book for reference. Round to the nearest whole number of joints.

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Table 4.1 Volumetric properties in U.S. customary units for selected engineering materials
Coclicient of Thermal
Expansion, a
Cx10F10
Melting Point, T
Density, p
g/em
Material
Metals
Aluminum
2.70
(0.098)
(13.3)
660
(1220)
24
Copper
8.97
(0.324)
17
1083
(1981)
(94)
Iron
7.87
(0.284)
12.1
(6.7)
1539
(2802)
Lead
11.35
(0.410)
29
(621)
(16.1)
327
Magnesium
1.74
(0.063)
26
(144)
650
(1202)
Nickel
8.92
(0.322)
13.3
(7.4)
(2651)
1455
Steel
(0.284)
7.87
12
(6.7)
a
Tin
7.3
(0.264)
23
(12.7)
232
(449)
Titanium
4.51
(0.163)
8.6
(4.7)
1668
(3034)
Tungsten
19.30
(0.697)
4.0
(2.2)
3410
(6170)
Zinc
7.15
(0.258)
40
(22.2)
420
(787)
Ceramics and Silicon
Glass
2.5
(0.090)
1.8-9.0
(1.0-5.0)
Alumina
3.8
(0.137)
9.0
(5.0)
2072
(3762)
Silica
2.66
(0.096)
0.55
(0.31)
1600
(2912)
Silicon
2.33
(0.085)
2.6
(1.4)
1414
(2577)
Polymers
Phenol resins
1.3
(0.047)
60
(33)
Nylon
Polyethylene
I.16
(0042)
100
(55)
260
(500)
0.92
(0.033)
180
(100)
115
(240)
Polystyrene
1.05
(0.038)
70
(39)
240
(464)
Polyvinylchloride
140
(0.051)
50
(28)
212
(414)
Compiled from. 121.131. 141. 15). and other sources
Melting tesmperature depends on composition
Low-density polyethylene
Chemically degrades at high temperanures because it is a thermosetting polymer, ocher polymers listed are thermoplastic
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Table 4.1 Volumetric properties in U.S. customary units for selected engineering materials Coclicient of Thermal Expansion, a Cx10F10 Melting Point, T Density, p g/em Material Metals Aluminum 2.70 (0.098) (13.3) 660 (1220) 24 Copper 8.97 (0.324) 17 1083 (1981) (94) Iron 7.87 (0.284) 12.1 (6.7) 1539 (2802) Lead 11.35 (0.410) 29 (621) (16.1) 327 Magnesium 1.74 (0.063) 26 (144) 650 (1202) Nickel 8.92 (0.322) 13.3 (7.4) (2651) 1455 Steel (0.284) 7.87 12 (6.7) a Tin 7.3 (0.264) 23 (12.7) 232 (449) Titanium 4.51 (0.163) 8.6 (4.7) 1668 (3034) Tungsten 19.30 (0.697) 4.0 (2.2) 3410 (6170) Zinc 7.15 (0.258) 40 (22.2) 420 (787) Ceramics and Silicon Glass 2.5 (0.090) 1.8-9.0 (1.0-5.0) Alumina 3.8 (0.137) 9.0 (5.0) 2072 (3762) Silica 2.66 (0.096) 0.55 (0.31) 1600 (2912) Silicon 2.33 (0.085) 2.6 (1.4) 1414 (2577) Polymers Phenol resins 1.3 (0.047) 60 (33) Nylon Polyethylene I.16 (0042) 100 (55) 260 (500) 0.92 (0.033) 180 (100) 115 (240) Polystyrene 1.05 (0.038) 70 (39) 240 (464) Polyvinylchloride 140 (0.051) 50 (28) 212 (414) Compiled from. 121.131. 141. 15). and other sources Melting tesmperature depends on composition Low-density polyethylene Chemically degrades at high temperanures because it is a thermosetting polymer, ocher polymers listed are thermoplastic

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Expert Answer

Step 1

Refer Table 4.1, “Volumetric properties in U.S. customary units for selected engineering materials”, select the coefficient of thermal expansion for the steel.

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a 12 x10/C Write the formula for change in length of the steel girder (AL) AL aL (T-T) L2-LaL (T-T) (I) (12x10/°C)(500 m)(-35°C-20°C) L-500 m = -0.33 m L 0.33 m+500 m =499.67 m

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Step 2

Calculate the entire expansion over the temperature ...

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--(12x10°c) (499.67 m)(40°C-(-35°C)) = 0.4497 m 1000 mm = 0.4497 mx- 1m = 449.7 mm

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