The Design of Arches of Minimum Weight Formed Along a String Curve with Their Elastic Compression Taken into Account

摘要

The author analyzes the effect of elastic compression on the value of a given relationship between the pitch and the span of an arch and also on the variation of the pitch of an arch. The study is confined to the elastic domain for a material which is uniform throughout and has the same modulus of elasticity. The unit weight of the material is also constant, and hence the law of weight variation is supplanted by a law of pitch variation. The analyses hold true for any arch cross section. The cases studied pertain to statically determinate arches, including a three-hinged arch supporting a uniform load distributed along the length of the span, and statically indeterminate arches including two-hinged circular, two-hinged parabolic, zero-hinge circular, and zero-hinge parabolic types. In the case of two-hinged parabolic arches, separate analyses are provided for arches of constant and of variable section heights.