On Some Common Errors in Iron Bridge Design

34 Manderla’s work is referred to in Bender’s “Economy of Design, of Metallic Bridges,” New York, 1885. Bender states that he has applied Manderla’s method to a number of examples, and that he has found in a “100 foot Whipple truss, 20 feet deep, a maximum secondary strain of 8 per cent.” in the centre of the top chord. He also says that he has found “Secondary strains of 172 per cent.” of the primary stresses in a triangular pin-jointed girder of 118 feet span and 12'5 feet deep in South Germany. Again he speaks of “secondary strains as high as 180 per cent.” over the middle piers of continuous bridges. Now, all this is most unsatisfactory and alarming. Unsatisfactory, because Bender gives no drawings or detailed dimensions of his bridges, nor does he show how he arrives at his results. Alarming because the only meaning that can be attached to his words is that the secondary stresses in structures of ordinary type may be greater than, in fact, nearly double of the primary stresses, and if this be the case, the structures affected must be most imminently dangerous, indeed it is difficult to understand why they have not long since fallen. Ritter’s work, as quoted by Koechlin in bis “Applications de la Statique Graphique,” Paris, 1889, is much fuller and more satisfactory, and his results more intelligible and less alarming. The maximum secondary stress that he arrives at in structures of ordinary proportions, is less than 30 per cent of the primary stress. Still, his method appears to the writer to be too general, and to fail in indicating exactly at what points of a frame the severest stress is to be expected. The writer has, after much consideration, arrived at a method, which he submits as giving, without inordinate labour, a fair approximation to the secondary stress in, at any rate, the simpler types of structure. It consists of the following operations (<7) From the primary stress and sectional area of each bar, and its known modulus of elasticity, its change in length is computed. This will be an elongation, or shortening, according as the primary stress is tensile or compressive. This change in length is exaggerated a convenient number of times. The writer increases it one hundred fold.