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Dr Ana M. Ruiz-Teran Longitudinal schemes for bridges Introduction

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Longitudinal schemes for bridges. Bridge types: Beams Trusses Portal frames Arch bridges Cable-stayed bridges Suspension bridges

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There is a certain range of spans lengths for every single bridge type It is not possible to establish a limit for every particular bridge type The cost of a particular solution depends on many other parameters (materials, technical requirements, construction procedure, etc) The most economic solution depends on the specific conditions of every single case

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Dr Ana M. Ruiz-Teran Longitudinal schemes for bridges. Part 1: Beams

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Beam bridges are supported in two or more sections. They are able to resist the actions acting on them and transmit them to the foundations. The Bending and Torsion Responses due to vertical loading are not coupled in straight beams The span for bending response is determined as the spacing between support sections that are able to transmit vertical reactions (all of them). The span for torsion response is determined as the spacing between support sections that are able to transmit couples (two bearings per section; deck and piers linked by a fixed connection, etc) The connection between piers and deck is pinned in the longitudinal direction. The longitudinal stiffness of the piers does not affect the response of the deck under vertical loading. The longitudinal stiffness of the piers affect the response under horizontal loading

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In curved bridges, the bending and torsional resistance mechanisms are coupled

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In skewed bridges, the bending and torsional resistance mechanisms are coupled

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The deck has an axial response under imposed longitudinal deformations (due to prestressing, time-dependent effects, temperature, etc) due to the stiffness of the bearing-pier-foundation system The stiffness K should be obtained at bearing level

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Location of the neutral point:

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In bridges with variable depth the Resal effect (shear load resisted by normal stresses) must be taken into consideration Bridges with independent spans. Advantages: (1) Easier analysis, (2) lack of internal forces in the case of a support settlement. Disadvantages: (1) a single structural response mechanism available, (2) lack of continuity in rotations at the support sections, (3) larger bending moments, (4) larger deck depths Continuous bridges with balanced end-spans Location of joints. Compromise solution. Advantages: (1) Eliminate global internal forces due to temperature changes, (2) Reduction on bearing movements when including several joints. Disadvantages: (1) High cost, (2) Traffic disturbance, (3) maintenance, (4) durability

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Dr Ana M. Ruiz-Teran Longitudinal schemes for bridges. Part 2: Trusses

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Model with pin-jointed connections for preliminary analyses and with rigid- and semi-rigid- connections for detailed analyses The neutral axes of all members meeting at one joint should intersect at a single point in order to about induced bending moments

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Dr Ana M. Ruiz-Teran Longitudinal schemes for bridges. Part 3: Portal frames

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In portal frames, there is a link between the piers and the deck in order (1) to reduce the bending moments at mid-span (either to reduce the deck depth or to increase the span range for a certain depth/span ratio) and (2) to share the external bending moment due to permanent and live load between the support and mid-span sections Consequences: (1) the piers are working also under bending, (2) an horizontal reaction is transmitted to the foundations How can this effect being promoted? (1) Designing a fix connection between the piers and the foundation, (2) Increasing the flexural stiffness of the piers, (3) reducing the height of the piers The deck shortening due to imposed longitudinal deformations (due to prestressing, time-dependent effects, temperature, etc) reduces the horizontal reaction and the portal-frame action

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Effect of the horizontal stiffness of the soil in the bending moments in the deck:

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Dr Ana M. Ruiz-Teran Longitudinal schemes for bridges. Part 4: Arches

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Arches are designed with their shape in order to work mainly under compression, avoiding most of the bending In permanent state, the bending moments can be almost cancelled. This is not the case under live load of imposed deformations (temperature, time- dependent effects, etc.)

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Anti-funicular shape of a certain loading (neglecting axial deformations)

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The larger the axial deformation, the smaller the horizontal thrust

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REFERENCES: CHEN, W. F. AND DUAN L. 2003. Bridge Engineering. CRC Press LLC HAMBLY, E.C. 1991. Bridge Deck Behaviour. Spon Press. PARKE G, HEWSON N. 2008. ICE manual of bridge engineering. ICE. MANTEROLA, J. BRIDGES. (6 Volumes, in Spanish). ETSICCP, Madrid

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