Prestress Loss Distributions along Simply Supported Pretensioned Concrete Beams

ABSTRACT: The prestressing forces in prestressed tendons undergo a process of reduction over a period of time. A common assumption is that prestress loss is constantly distributed throughout the span of a simply supported pretensioned concrete beam. The purpose of this work is to investigate the accuracy of this assumption. The types of prestressed concrete beams investigated in this work include the following three typical types of tendon profile: (I) straight strands, (II) single-point depressed, and (III) two-point depressed. The major findings derived from this work are: (1) The total prestress loss is not constantly distributed throughout the span of a simply supported pretensioned concrete beam with any of the three types of tendon profiles, (2) The variation of prestress loss along the span of a pretensioned beam caused by elastic shortening of concrete or creep of concrete is much more significant than that caused by shrinkage of concrete or relaxation of tendons, and (3) The type of tendon profile in a simply supported pretensioned concrete beam has significant effects on the pattern of prestress loss distribution along the beam

Partial-Span Live Loading Effects on the Design of Multi-Story Multi-Bay Steel Moment Frames

Abstract: A critical live load pattern is the live load pattern which will produce the maximum axial force and/or bending moment in a structural member under consideration. Structural engineers commonly select the critical live load pattern from full-span live load patterns rather than partial-span live load patterns. In order to identify the most critical live load pattern, a three-story, two-bay steel moment frame design example is presented in this paper. In this design example, both first-order and second-order analyses are used for the determination of the required strength of the columns, while the effective length method is used for the determination of the design strength of the columns. The results of the example indicate that the effects caused by partial-span live load patterns are more critical than those caused by full-span live load patterns, not only in the computation of the required strength of the structural members, but also in the calculation of the maximum lateral displacement of the entire frame

Shear Lag Factors for Tension Angles with Unequal-Length Longitudinal Welds

When a tension load is transmitted to some, but not all of the cross-sectional elements of a tension member, the tensile force is not uniformly distributed over the cross-sectional area of the tension member. The non-uniform stress distribution in the tension member is commonly referred to as the out-of-plane shear lag effect. The unequal-length longitudinal welds and the in-plane shear lag effect, however, are not addressed by the current American Institute of Steel Construction (AISC) Specification for the determination of the shear lag factors for tension members other than plates and Hollow Structural Sections (HSS). The purpose of this work is to propose a procedure for the computation of shear lag factors accounting for combined in-plane and out-of-plane shear lag effects on unequal-length longitudinal welded angles. The finite element method using three-dimensional solid elements and nonlinear static analyses accounting for combined material and geometric nonlinearities are conducted in this work to verify the accuracy of the proposed procedure

FOOTING FIXITY EFFECT ON PIER DEFLECTION

The rotational restraint coefficient at the top of a pier and the rotational restraint coefficient at the bottom of the pier (that is, the degree of fixity in the foundation of the pier) are used to determine the effective length factor of the pier. Moreover, the effective length factor of a pier is used to determine the slenderness ratio of the pier, while the degree of fixity in the foundation of a pier is used to perform the first-order elastic analysis in order to compute the pier deflection. Finally, the slenderness ratio of the pier is used to determine if the effect of slenderness shall be considered in the design of the pier, while the magnitude of the pier deflection resulting from the first-order analysis is used to determine if the second-order force effect (the p-∆ effect) shall be considered in the design of the pier. The computations of the slenderness ratio and the deflection of a pier, however, have conventionally been carried out by assuming that the base of the pier is rigidly fixed to the footing, and the footing in turn, is rigidly fixed to the ground. Other degrees of footing fixity have been neglected by the conventional approach. In this paper, two examples are demonstrated for the slenderness ratio computation and the first-order deflection analysis for bridge piers with various degrees of footing fixity (including footings anchored on rock, footings not anchored on rock, footings on soil, and footings on multiple rows of end-bearing piles) recommended by the AASHTO LRFD Bridge Design Specifications. The results from the examples indicate that the degree of footing fixity should not be neglected since it significantly affects the magnitude of the slenderness ratio and the deflection of the pier

CAMBER IN PRETENSIONED BRIDGE I-GIRDER IMMEDIATELY AFTER PRESTRESS TRANSFER

Deflection control is an important design criterion for the serviceability of pretensioned concrete bridges. Upward cambers due to prestressing forces can be utilized to offset downward deflections due to gravity loads in order to control cracks and/or to produce desired cambers. The traditional hand-calculated approach simplifies the computation of pretensioned concrete girders by: (1) assuming that the prestressing force acting at the midspan of a girder remains constant along the entire span of the girder, (2) neglecting the p-δ effect on the girder due to the axial compression force in the girder, and (3) using the gross concrete section of the girder to compute the moment of inertia of the girder. The purpose of this work is to investigate the accuracy of the hand-calculated approach for the computation of cambers due to prestressing forces. The type of prestressed concrete girder investigated in this work is a pretensioned I-girder with a combination of straight strands and harped strands. The major findings derived from this work are: (1) the variation (non-uniformity) among prestressing forces acting along the tendons has no significant effect on the deflection of the girder, (2) the traditional hand-calculated approach neglecting the P-δ effect may result in considerably smaller girder deflections, and (3) the traditional hand-calculated approach using the moment of inertia of the gross concrete section (neglecting the additional stiffness contributed by tendons) may result in considerably larger girder deflections

POST-TENSIONED BOX GIRDER BRIDGE An Analysis Approach using Equivalent Loads

Continuous-span, cast-in-place box girders have been popular in modern bridge construction. Secondary moments due to prestressing in continuous-span, post-tensioned girders, however, have significantly complicated the structural analysis and design of the girders. The equivalent load method is a commonly used method in the analysis of continuous-span, post-tensioned concrete girders since the method reduces the analysis of a prestressed structure to that of a nonprestressed structure in which the consideration of secondary moments is not required. The basic concept of the equivalent load method is that the effects of prestressing are replaced by equivalent loads produced by the prestressed tendon along the span of the structure. The approximate equivalent load method significantly simplifies the procedure for the computation of equivalent loads for post-tensioned concrete girders with parabolic tendons and therefore has commonly been used by structural engineers. In this paper, three examples of simply-supported, posttensioned concrete girders with various combinations of locations of the centroid of tendons (c.g.s.) and the centroid of concrete (c.g.c.) are demonstrated to verify the accuracy of the approximate equivalent load method. Finally, an example of the analysis of a bridge composed of a continuous-span, post-tensioned concrete box girder superstructure and a concrete pier is also demonstrated using the approximate equivalent load method. Inconstant cross sections (inconstant c.g.c, lines) near the pier of the bridge are considered in this example