All long iron trusses, say about eighty feet long, or over, should not be built-in solidly at both ends; otherwise the expansion and contraction due to variations of the temperature will either burst one of the supports, or else cause the truss to deflect so much, as to crack, and possibly endanger the work overhead. One end should be left free to move (lengthwise of truss) on rollers, but otherwise braced and anchored, the anchor sliding through slits in truss, as necessary. The expansion of iron for each additional single degree of temperature, Fahrenheit, is about equal to 1/145000 of its length, that is, a truss feet long at 10° Fahrenheit, would gain in length (if the temperature advanced to 100° Fahrenheit), - 90.145/145000=9/100 of a foot, or, say, 1 1/12 inches, so that at 100° Fahrenheit the truss would be 145 feet and 1 1/12 inches long; this amount of expansion would necessitate rollers under one end. Of course the contraction would be in the same proportion. The approximate expansion of other materials for each additional degree Fahrenheit would be (in parts of their lengths), as follows:

1 The point of greatest deflection can never be further from the centre of beam than 2-25 of the entire length of span. It can as a rule, therefore, be safely assumed to be at the centre. If it is desired to find its exact location, use

(43) where n=the distance from weight to nearer support; x = the distance of point of greatest deflection from farther support; and 1 = the length of span; x, I and m should all be expressed either in feet or inches. 2 Formula (42) is approximate only, but sufficiently exact for practical use.

 Wrought-iron 1145000 Cast-iron .... 1162000
 Steel............ 1151000 Antimony.............. 1166000 Gold, annealed............ 1123000 Bismuth................. 1130000 Copper.............. 1104000 Brass................... 195000 Silver.................. 195000 Gun metal................... 190000 Tin.............................. 167000 Lead.................. 163000 Solder................................. 170000
 Pewter....................................... 178000 Platina................... 120800 Zinc....................... 162000 Glass....................... 1210000 Granite...................... 1208000 Fire Brick................ 1365000 Hard Brick.................. 1600000 White Marble................. 1173000 Slate................. 1173000 Sandstone.................... 1103000 White pine................... 1440000 Cement................... 1120000

The tension due to each additional decree of Fahrenheit would be equal to the modulus of elasticity of any material multiplied by the above fraction; or about 186 pounds per square inch of cross-section, for wrought-iron. Above figures are for linear dimensions, the superficial extension would be equal to twice the linear, while the cubical extension would be equal to three times the linear.

Water is at its maximum density at about 39° Fahrenheit; above that it expands by additional heat, and below that point it expands by less heat. At 32° Fahrenheit water freezes, and in so doing expands nearly 1/12 part of its bulk, this strain equal to about 30,000 lbs.

per square inch will burst iron or other pipes not sufficiently strong to resist such a pressure. The above table of expansions might be useful in many calculations of expansions in buildings; for instance, were we to make the sandstone copings of a building in 10-foot lengths, and assume the variation of temperature from summer sun to winter cold would be about 150° Fahrenheit, each stone would expand

150.10/103000 = 1/68 of a foot, or say, about 1/6 inches, quite sufficient to open the mortar joint and let the water in. The stones should, therefore, be much shorter.