Collapse loads of cantilever beams under end shear
TL;DR: In this article, the collapse loads of symmetrically tapered cantilever beams under a uniformly distributed end shear are extended to cover the entire range of geometric parameters, and an optimum design problem is considered: for fixed beam length and end load find the angle of taper which minimizes the weight.
Abstract: Results ofOnat andShield and ofGreen on the collapse loads of symmetrically tapered cantilever beams under a uniformly distributed end shear are extended to cover the entire range of geometric parameters. Close bounds are obtained except for very short beams. In addition, the effect of a parabolic distribution of end shear upon the lower bound is investigated and found to be small. For large beams complete solutions are exhibited. Finally, an optimum design problem is considered: for fixed beam length and end load find the angle of taper which minimizes the weight. The minimum is always achieved for a taper angle (top and bottom) between zero and fifteen degrees.
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TL;DR: In this paper, a plane-stress slip-line field analysis has been made of the possible plastic deformation modes of a built-in cantilever beam of rectangular cross-section subjected to a shear force at the free end with or without an axial load.
Abstract: A plane-stress slip-line field analysis has been made of the possible plastic deformation modes of a built-in cantilever beam of rectangular cross-section subjected to a shear force at the free end with or without an axial load Plastic-collapse loads for the several types of deformation patterns suggested are computed and the results presented in detail in the form of curves Some simple upper- and lower-bound estimates to the collapse load have also been determined and are compared with both the plane-stress slip-line results and those presented by Green (1), plane-strain conditions being assumed The agreement between the plane-stress slip-line fields and the assumed lower-bound results is found to be excellent
7 citations
5 citations
TL;DR: In this article, a slip line field is proposed for the incipient collapse of cantilevers yielding under combined axial and shear tip loading for plane stress conditions, which is then extended to fixed-ended haunched beams with uniformly distributed or concentrated central loading.
4 citations
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TL;DR: In this paper, the safe loads for a Prandtl-Reuss material subject to surface tractions or displacements which increase in ratio are extended to any perfectly plastic material and any history of loading.
Abstract: Earlier results [1,2]2 on safe loads for a Prandtl-Reuss material subject to surface tractions or displacements which increase in ratio are here extended to any perfectly plastic material and any history of loading.
636 citations
TL;DR: In this paper, it is shown that part of the plastic zone at the yield point, where deformation occurs, depends only on the current surface tractions and not on the previous loading programme.
Abstract: Summary The yield point of a plastic-rigid body is defined as the moment when deformation first becomes possible as the load is increased. The practical significance of the yield-point load for an actual plastic-elastic body is discussed. It is then shown that part of the plastic zone at the yield point, namely the part where deformation occurs, depends only on the current surface tractions and not on the previous loading programme. By means of the principle of maximum plastic work and its complimentary minimum principle (Hill 1950) approximations from above and below to the yield-point load can be obtained; some examples are given. Recent American work on the plastic limit design of structures is critically reviewed and shown, when properly regarded, to be a particular application of the principle of maximum plastic work.
157 citations
110 citations
TL;DR: In this article, the basic concepts of limit analysis are extended to members in which axial forces as well as bending moments must be taken into account, and methods of determining the critical load intensity of arches are developed and illustrated by numerical examples.
Abstract: In the limit analysis of frames it is usually assumed that the limiting bending moment of a cross section is not significantly reduced by the presence of axial forces. In the limit analysis of flat arches this assumption is not permissible as a rule. In the present paper the basic concepts of limit analysis are extended to members in which axial forces as well as bending moments must be taken into account. Methods of determining the critical load intensity of arches are developed and illustrated by numerical examples.
83 citations