Minutes of Proceedings of the Institution of Civil Engineers Volume 74 (188283) (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1883 Excerpt: ...where this is not the case, the mean sectional area of the two flanges may be substituted for their actual areas at any given section of the girder. It will further be assumed that tho girder is of wrought iron, whose extension or compression under a strain of 1 ton per square inch is equal to jaJjjth of its length; for any other material it is only necessary to substitute the corresponding modulus of elasticity. Note A.--In any diagram of moments the ordinates represent tho bending moments, and are measured on a certain scale of foot-tons. In a girder of uniform depth, the flange stress is also represented by the diagram of moments, the ordinates being measured on a certain scale of tons. In a girder of uniform depth and uniform section the intensity of flange-stress is also represented by the diagram of moments, the ordinates being measured on a ceitain scale of tons per square inch; the diagram may therefore be used as a diagram of stress or as a diagram of stress-intensity. Proposition I. Problem.--The diagram of stress-intensity in any girder of uniform depth being given, it is required to construct the deflection-curve, or to find the slope and deflection of the girder at any point. In Fig. 5, let B C represent tho whole or any portion of the length of the girder, and let A B C D be the diagram of stress-intensity due to a positive bending stress, i.e., let the ordinates A B, &e., represent tho intensity of tensilo stress in tho upper member, and of compressive stress in the lower member. Also in Fig. 6, let the straight line B C, represent the original unbended line of the girder, aud let the flexure commence at B, so that the line B 0, will be a tangent to the deflection-curve at that point; then the deflection C C, and the slope of the tangent...