On Some Common Errors in Iron Bridge Design

35 (r) The frame is then re-plotted with the altered lengths of the bars. One result of this is that the pane] points of the top and bottom chords, instead of lying in straight lines, will lie in curves, which in most cases are approximately circular, but in others that have been tried, have a cusp at the centre, like a Gothic arch inverted. This cusp indicates a point of intense secondary stress. (t7) A smooth and regular curve (usually circular) is drawn through all these panel points, and at eacli panel point a tangent to this curve is drawn. This is most conveniently done by taking a well-tempered piece of spring steel and bending it so as to pass through all the points. (e) Lines are drawn, making the same angles with these tangents that the diagonals or web members made with the chords, when the structure was free from stress. If two such lines drawn from the two extre- mities of a diagonal or web member coincide, forming one straight line, that web member is free from secondary stress. But if, as is usually the cas •, they do not coincide, then the diagonal, which, by virtue of its rigid attachment to the chord is tangential to these lines at its ends, must be bent into a curve, usually of double curvature, or S curve as it is often called. This curve will present a point of contra- flexure and consequently of no bending moment at or near the mid-length of the bar and each part of the bar will be a cantilever, the deflection of the end of which can be measured on the exaggerate I scale adopted, and from this, its width, and the modulus of elasticity, the secondary stress can be computed. This secondary stress is usually least at the centre of the bar, increasing to a maximum at the ei (Is. To find the exact curve assumed the piece of spring steel mentioned before may be applied. (/) The secondary stress of the chords is computed from the radius of the curve zZ and in most cases is upproxi- mately uniform throughout.