I BARNES-HAYWARD- EXPANSIVE FORCE OF ICE 47 



MCLEOD] 



"If ice is floating in water, the temperature of the surface in con- 

 tact with the water does not fall much below 32 °F. The variation 

 of the temperature at any point in the ice is nearly proportioned to 

 the distance from the surface in contact with the water, and is a 

 maximum at the surface in contact with the air. 



"The expansion of ice is a function of the change in temperature, 

 so that the tendency to expand is a maximum at the upper surface, 

 and is practically zero at the lower surface. If the ice is restricted 

 at the edges and is exposed to a rising temperature, the upper surface, 

 will be subject to compression. The unit compression decreases as 

 the distance from the upper surface, and is zero at the lower. 



"Then the maximum thrust that the ice can exert will be when 

 the upper surface is on the point of crushing. Taking this as 400 

 pounds per square inch, the thrust per linear foot of a sheet of ice (t) 

 inches thick = t v 2 X 12 X 400 = 2,400 t; that is the thrust of a 

 sheet of ice in pounds per linear foot is the thickness of the sheet 

 multiplied by 2,400. 



"Although ice forms in our northern rivers and lakes up to three 

 feet thick, it seems probable that the greatest ice pressures occur 

 when the ice is from a foot to a foot and a half thick,— that bemg 

 the greatest thickness at which ice reefs are formed. The thrust for 

 a sheet of ice 18 inches thick is 2,400 X 18 = 43,200 pounds per linear 

 foot, for a twenty-inch sheet 2,400 X 20 = 48,000 pounds. 



"There are only two references that give actual values of ice 

 thrust. The first is in the discussion of the New Croton Dam by 

 Professor Cain. He states that The ice between two bridge abut- 

 ments 90 feet apart, expanded during a rise in temperature and arched 

 so that the center was three feet above its original level.' He gives 

 the thrust for a 12-inch sheet of ice as 21,000 lbs. 



"The second reference is given in Volume 5, Part II, of the 

 Canadian Society of Civil Engineers by Duncan MacPherson, of a 

 bridge pier subjected to ice on one side only, which was shoved out 

 of line two inches, and held there under passing trains until a channel 

 was cut in the ice, when the pier settled back into its original position. 



"The thrust of the ice to tip the pier only was given as 14,600 

 pounds per linear foot for ice 12 inches thick. Taking the train load 

 at 3,000 pounds per linear foot, would bring the thrust up to 18,000 

 pounds for ice 12 inches thick. 



"Probably all that prevented rupture in the first case was that 

 there was not sufficient expansion. However, the thrust of the ice 

 would probably be much greater when the arch was flatter. 



"In the second case, the ice had not reached the point of failure, 

 and there is no information given from which to estimate it." 



