Continuous Beams over Three Spans

The matters of accessibility, natural light, and fresh air combine to make three-span construction more prevalent than any other series of multiple spans for buildings.In the colder, and even in the temperate, climates, office buildings, schools, hospitals, hotels, clubs, etc., generally provide for corridors in the center with rooms on either side. In the tropics the same classes of buildings, and also the dwellings, have rooms in the center with verandas on either side. Thus, the problems of two long side spans with a short center span, or two short side spans with a long center span, are constantly offered to the engineer for solution.For continuous construction, particularly prevalent on account of the increasing use of reinforced concrete, the proper solution of the moment equations is a most tedious task. It has come to be a very frequent custom, therefore, to neglect such important matters as the effect on moment factors of variability in spans, loads, and sections.This erroneous custom is sometimes very serious in its consequences. It reaches to all divisions of engineering-design, control, and execution; consultants, municipal authorities, and manufacturers of specialties, all are affected. Even engineering committees and technical schools seem to have avoided the problem or condoned the errors.In textbooks from Continental Europe, the problem is usually covered by the evolution of formulas which may be used in good faith and with good results, although they are generally tedious to apply.* Tables to facilitate the use of the formulas are generally missing, or are so elaborate as to be of no use for the most common problems of variable spans in commercial engineering work. The economic significance of the variables affecting the moment factors is also overlooked.This paper aims to provide the necessary tables showing moment factors for all the most common conditions, so that the moments may be found with the expenditure of less effort and time. It also shows the significance of the variables and the seriousness of the usual conventional errors. By the use of correct methods, safety and economy of materials are obtained simultaneously.