**Theoretical Modeling**

**Chapter 4**

**Provisional chapter**

**Mechanical Performance of Simple Supported Concrete**

**Mechanical Performance of Simple Supported** 

**Concrete Beam-Cable Composite Element with** 

DOI: 10.5772/intechopen.76517

**Beam-Cable Composite Element with External Prestress**

A new reinforcement technology of external prestress based on stretch tilted belly poles has been presented. Taking simply supported beam, which is reinforced by three titled belly poles, as a research object to establish a model of reinforced simply supported beam. Relationship expressions about deflection and internal force increment of external cable or about load and deflection have been deduced. Finite element model is established by ABAQUS. The influence of structure performance of reinforced simply supported beam with cable section, cable sag and initial internal force value was investigated. Three tests are carried out to testify the results of theoretical analysis and numerical simulation. The results show that the redistributions of internal force and sectional stress have occurred, and the stiffness, crack load, ultimate load, and structure ductility are all improved with the increase of three design parameters. For example, the crack load, ultimate load, and structure ductility have increased, respectively, by 24%~40%, 15%~42%, and 14%~40%. High initial internal force, small section, and big cable sag should be avoided, because the probability of brittle failure of structure will increase. The analytical result shows that the reliability of internal increment expression of external cable and carrying capacity

**Keywords:** concrete structure, simply supported beam, external prestress, tilted belly

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Teng Wang, Yanmei Ding, Wangchun Zhang and

Teng Wang, Yanmei Ding, Wangchun Zhang and

expression can be used in the engineering practice.

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.76517

**External Prestress**

Yu Song

Yu Song

**Abstract**

poles, test

**Chapter 4 Provisional chapter**

#### **Mechanical Performance of Simple Supported Concrete Beam-Cable Composite Element with External Prestress Mechanical Performance of Simple Supported Concrete Beam-Cable Composite Element with External Prestress**

DOI: 10.5772/intechopen.76517

Teng Wang, Yanmei Ding, Wangchun Zhang and Yu Song Teng Wang, Yanmei Ding, Wangchun Zhang and Yu Song

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.76517

#### **Abstract**

A new reinforcement technology of external prestress based on stretch tilted belly poles has been presented. Taking simply supported beam, which is reinforced by three titled belly poles, as a research object to establish a model of reinforced simply supported beam. Relationship expressions about deflection and internal force increment of external cable or about load and deflection have been deduced. Finite element model is established by ABAQUS. The influence of structure performance of reinforced simply supported beam with cable section, cable sag and initial internal force value was investigated. Three tests are carried out to testify the results of theoretical analysis and numerical simulation. The results show that the redistributions of internal force and sectional stress have occurred, and the stiffness, crack load, ultimate load, and structure ductility are all improved with the increase of three design parameters. For example, the crack load, ultimate load, and structure ductility have increased, respectively, by 24%~40%, 15%~42%, and 14%~40%. High initial internal force, small section, and big cable sag should be avoided, because the probability of brittle failure of structure will increase. The analytical result shows that the reliability of internal increment expression of external cable and carrying capacity expression can be used in the engineering practice.

**Keywords:** concrete structure, simply supported beam, external prestress, tilted belly poles, test

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### **1. Introduction**

External prestressing is a technique originally developed for reinforcing bridge structures and now has applications in architectural structures [1]. It has gone through three stages of development. In the early stage, external tendons were installed with curvature at the bottom and sides of a beam and held by deviators. Prestressing forces were applied by transverse tensioning. In the second stage, external tendons were installed with curvature only at the vertical sides of a beam, and prestressing forces were applied by a tensioning jack. Multiple weaknesses have been identified in this tensioning technique during practical applications. First, prestressing forces had to be applied to an independent working surface, but the working surface was usually obstructed by columns. Second, the friction between a deviator and an external tendon could weaken the effects of prestressing forces. To avoid the aforementioned problem with working surface, external tendons were usually continuously and axially installed along the full length of a beam. However, this would complicate the stress states of the columns and beam-column joints and thereby undermine the structure's seismic performance [2]. To overcome these disadvantages, retractable web members were introduced to apply prestressing forces in the later stage. Web members can be installed vertically or diagonally, and DWMs are an improvement on vertical web members (patent number: ZL 03134360.0). In DWM prestressing, external tendons are anchored to the upper parts of both beam sides, and retractable DWMs are used to stretch the tendons, which then transfer the prestressing forces to the beam. Compared to the two earlier external prestressing techniques, DWM prestressing has two main advantages: (1) The way in which the prestressing force is applied allows for easier and safer construction and enhances the effects of prestressing forces; (2) As external tendons are not continuously installed along the full beam length and do not span any column, the installation process will neither cause mechanical disturbance to the floor, columns, and other vertical elements nor occupy the space required to reinforce vertical elements; (3) external tendons running through beam ends can increase the shear strength of beam ends [3, 4].

deflection on tendon force were analyzed. Then the pattern of variation in the RC beam's structural performance was obtained. The findings of the study are expected to provide a design basis for practical application of this technique and theoretical support for research on

Mechanical Performance of Simple Supported Concrete Beam-Cable Composite Element...

http://dx.doi.org/10.5772/intechopen.76517

81

**1.** An external tendon is an ideally flexible material subjected only to tension, and it deforms

**2.** The web members have infinite stiffness and do not stretch or shrink during beam deformation. They are always perpendicular to the tangents at the connections between web members and tendons. The effect of dead load of web members on tendons is ignored; **3.** The slip between external tendons and web members during beam deformation is negligible and so is the friction between tendons and beam-end anchorage and between web members and beam-bottom anchorage. The shear deformation of the beam, together with

**4.** The load applied to an external tendon by the three DWMs can be treated as a uniformly

**Figure 1** shows the curves describing deformation of an external tendon in a SSB reinforced

the deformation of a tendon under a uniformly distributed load provided in [9]. The solid line,

, is a broken line for a tendon stabilized by three web members; it is a polygon incised in L1

According to Song Yu [9], the shape function for a tendon under a uniformly distributed load

<sup>2</sup> <sup>+</sup> (*<sup>x</sup>* <sup>−</sup> \_\_*<sup>l</sup>*

2 ( *l* <sup>2</sup> + 8 *f* 2 \_\_\_\_\_ 16*f* )

where *l* and *f* are the tendon span and sag, respectively, after application of the initial pre-

2) 2 \_\_\_\_\_\_\_\_

<sup>2</sup> − 8 *f* <sup>2</sup> \_\_\_\_\_ 16*f* ) 2

\_\_\_\_\_\_\_\_

( *l* <sup>2</sup> + 8 *f* 2 \_\_\_\_\_ 16*f* )

shown in the figure is the elliptic curve describing

<sup>2</sup> = 1 (1)

.

the mechanical behavior of a fixed-end beam after reinforcement.

only elastically throughout its deformation process;

The theoretical analysis was based on the following fundamental assumptions:

its secondary effect, has only negligibly small effects on RC beam.

**2. Theoretical analysis**

**2.1. Increment in tendon stress**

*2.1.1. Fundamental assumptions*

distributed load.

has the following form:

stressing force.

L2

*2.1.2. Computing model of tendon*

by DWM prestressing. The dotted line L1

*2.1.3. Solving for external tendon force*

(*<sup>y</sup>* <sup>−</sup> *<sup>l</sup>*

At present, stress increments in external tendons can be calculated mainly by the reduction factor method, regression analysis of section reinforcement ratio, deformation analysis, and so on. However, there is a lack of unified standard and the standard parameter values for an external tendon in the stiffness of a beam is infinitely great an ultimate state differ between standards from different countries [5–8]. Based on the assumption of infinite beam stiffness, a study [9] examined the force distribution in an external tendon that was subjected to a uniformly distributed load applied by DWM, with the increase in tendon length being used as the parameter. The relationship between tendon extension and load was derived. When DWM external prestressing is applied to a simply supported beam (SSB), the beam does not have infinite stiffness and tends to deform under the prestressing force [10, 11]. The load on tendons applied by web members was not uniformly distributed. Therefore, the mechanical behavior of a beam reinforced by this technique remains unknown. For this reason, the present study investigated the behavior of a SSB reinforced by external prestressing with three DWMs using a combination of theoretical derivation, numerical analysis, and experimental verification. Three variables, including initial tendon force, tendon cross-sectional area, and initial tendon sag, were considered and the influences of beam-end rotation and beam deflection on tendon force were analyzed. Then the pattern of variation in the RC beam's structural performance was obtained. The findings of the study are expected to provide a design basis for practical application of this technique and theoretical support for research on the mechanical behavior of a fixed-end beam after reinforcement.
