【Daily Discussion】Public Utilities – Water Resources and Hydropower – 20210508
Thread Content
Briefly describe the basic principles of the crown beam method in the stress analysis of arch dams. Answer: The basic principle of the crown beam method is to divide the arch dam into a series of arch systems, considering only one cantilever beam at the arch crown. The load distribution across the arch beams is determined based on the condition that the radial displacements at the points where each layer of arch rings intersects the crown beam are identical ； Furthermore, the radial load distributed to the arch ring is evenly distributed from the crown of the arch to its ends; it is assumed that the stress conditions in the beam systems on both sides of the arch crown are the same as those in the arch crown beam itself. After load distribution, the stress in the rear arch is calculated using the pure arch method, while the stress in the beam is calculated as that of a cantilever beam. Feel free to participate actively in the discussions – the system offers generous rewards for answering questions from VIP members! ! !
The crown beam method is a preliminary approach for calculating the load distribution and stresses in arches, based on the principle that the central cantilever beam at the arch crown and several layers of horizontal arches must deform at the same point. This method can be further divided into those based on consistent radial deformation and those based on consistent vertical torsional deformation. It is usually used for preliminary calculations when the river valley is symmetrical. The corresponding multi-arch beam method is the most widely used approach in the design of medium and large arch dams. This method involves dividing the arch dam into several computational elements – horizontal arch systems and vertical cantilever beam systems. The external loads as well as the internal forces at the cut surfaces are applied as loads to the members of these elements, and the displacements and stresses of both the arch and beam systems are calculated separately.
The basic principle of the crown beam method is to divide the arch dam into a series of arch systems, considering only one cantilever beam at the arch crown, and determining the load distribution among the arch beams based on the condition that the radial displacements at the intersection points of each layer of arch rings and the crown beam are identical； Furthermore, the radial load distributed to the arch ring is evenly distributed from the crown of the arch to its ends; it is assumed that the stress conditions in the beam systems on both sides of the arch crown are the same as those in the arch crown beam itself. After load distribution, the stress in the rear arch is calculated using the pure arch method, while the stress in the beam is calculated as that of a cantilever beam.
The basic principle of the crown beam method is to divide the arch dam into a series of arch systems, considering only one cantilever beam at the arch crown, and determining the load distribution among the arch beams based on the condition that the radial displacements at the intersection points of each layer of arch rings and the crown beam are identical； Furthermore, the radial load distributed to the arch ring is evenly distributed from the crown of the arch to its ends. It is assumed that the stress conditions in the beam systems on both sides of the arch crown are the same as those in the arch crown beam itself. After the load distribution, the arch’s stresses are calculated using the pure arch method, while the stresses in the beams are calculated using the cantilever beam method.
The basic principle of the arch crown beam method is to divide the arch dam into a series of arch systems, considering only one cantilever beam at the arch crown. The load distribution among the arch beams is determined based on the condition that the radial displacements at the intersection points of each layer of arch rings and the arch crown beam are identical. The radial load assigned to each arch ring is distributed evenly from the arch crown to the arch ends, and it is assumed that the stress conditions in the beam systems on both sides of the arch crown beam are the same as those of the arch crown beam itself. After load distribution, the stresses in the arch are calculated using the pure arch method, while the stresses in the beams are calculated as those of a cantilever beam
The basic principle of the arch crown beam method is to divide the arch dam into a series of arch systems, considering only one cantilever beam at the arch crown. The load distribution among the arch beams is determined based on the condition that the radial displacements at the intersection points of each layer of arch rings and the arch crown beam are identical. The radial load assigned to each arch ring is distributed evenly from the arch crown to the arch ends, and it is assumed that the stress conditions in the beam systems on both sides of the arch crown beam are the same as those of the arch crown beam itself. After load distribution, the stress in the arch is calculated using the pure arch method, while the stress in the beam is calculated as that of a cantilever beam.
Theoretical basis: The displacement coordination equations for arches and beams are used to calculate the loads borne by each of them. Advantages: It is a simplified version of the arch beam load distribution method. It uses a cantilever beam at the crown of the arch as a representative element, along with several horizontal arches as calculation units for load distribution, and then calculates the stresses in the crown beam and each arch ring. This approach reduces the amount of computational work required compared to the traditional arch beam load distribution method. The arch beam load-sharing method can be used for the preliminary stress calculation of arch dams in roughly symmetric and relatively narrow river valleys. It can also be used for dam stress calculations during the feasibility study phase for medium and low arch dams.
The crown beam method is a preliminary approach for calculating the load distribution and stresses in arches, based on the principle that the central cantilever beam at the arch crown and several layers of horizontal arches must deform at the same point. This method can be further divided into those based on consistent radial deformation and those based on consistent vertical torsional deformation. It is usually used for preliminary calculations when the river valley is symmetrical. The corresponding multi-arch beam method is the most widely used approach in the design of medium and large arch dams. This method involves dividing the arch dam into several computational elements – horizontal arch systems and vertical cantilever beam systems. The external loads as well as the internal forces at the cut surfaces are applied as loads to the members of these elements, and the displacements and stresses of both the arch and beam systems are calculated separately.