- Article
- Open Access

# Growth of Time-Dependent Strain in Reinforced Cement Concrete and Pre-stressed Concrete Flexural Members

- Swarup Rn. Debbarma
^{1}Email author and - Showmen Saha
^{2}

**6**:8

https://doi.org/10.1007/s40069-012-0008-x

© The Author(s) 2012

**Received:**13 February 2012**Accepted:**22 May 2012**Published:**1 July 2012

## Abstract

This paper presents the differences in growth of time-dependent strain values in reinforced cement concrete (RCC) and pre-stressed concrete (PSC) flexural members through experiment. It was observed that at any particular age, the time-dependent strain values were less in RCC beams than in PSC beams of identical size and grade of concrete. Variables considered in the study were percentage area of reinforcement, span of members for RCC beams and eccentricity of applied pre-stress force for PSC beams. In RCC beams the time-dependent strain values increases with reduction in percentage area of reinforcement and in PSC beams eccentricity directly influences the growth of time-dependent strain. With increase in age, a non-uniform strain develops across the depth of beams which influence the growth of concave curvature in RCC beams and convex curvature in PSC beams. The experimentally obtained strain values were compared with predicted strain values of similar size and grade of plane concrete (PC) beam using ACI 318 Model Code and found more than RCC beams but less than PSC beams.

## Keywords

- time-dependent strain
- creep
- shrinkage
- pre-stress concrete
- reinforced concrete
- flexural member

## 1 Introduction

In reinforced and pre-stressed concrete structures the growth of time dependent effects due to creep and shrinkage is complicated and depends upon, presence of steel reinforcement and/or pre-stressing steel, amount of pre-stress force, inherent non-elastic properties of concrete the construction stages of concrete, the continuous re-distribution of stress and the effects of external restraints and supports. Under restrain conditions, shrinkage is always associated with creep which relieves the stresses induced by shrinkage. In general, shrinkage and creep are taken into account of long-term deformation and pre-stress loss analysis of concrete structure (Zamblauskaite et al. 2005). Considering long term effect, shrinkage and creep may significantly reduce crack resistance and increase deformation of reinforced concrete structures subjected to short term loading (Bischoff 2001; Sato et al. 2007).

Shrinkage of an isolated plain concrete member would merely shorten it without causing camber (Gribniak et al. 2007). Reinforcement embedded in a concrete member provides restrain to growth of shrinkage strain leading to compressive stress in reinforcement and tensile stress in concrete. If reinforcement is not placed symmetrically along the cross-section, the strain due to shrinkage of concrete causes non-uniform stress and strain distribution within the height of the section. The maximum tensile stress appears in the extreme concrete fiber, close to the larger concentration of reinforcement area. Zuanfeng et al. (2011) presented a formula to determine the influence coefficients of steels on creep and shrinkage of RCC specimen which was found to be a good agreement between calculated values and measured field data. Gribniak et al. (2008) investigated numerically the influence of shrinkage on behavior of reinforced concrete beams and compared with test data reported in literature.

Objective of this paper is to present the experimental findings of time-dependent strain growth in reinforced and pre-stressed concrete beams. In reinforced concrete beams, the influence of percentage area of reinforcements and its span, in growth of time-dependent strain were investigated. The influence of pre-stress force and its eccentricity in growth of time-dependent strain in pre-stressed concrete beams were investigated and presented. The experimental values were compared with predicted strain values for plane concrete beam using prediction model code for same size of beam. The growth of non-uniform strain across the depth of the experimental beams and its effects in change of beam axis profile is also presented in this paper.

## 2 Experimental Program

Ten numbers of laboratory scale concrete beams were designed and constructed for the experiment. Out of ten, six were reinforced cement concrete (RCC) beams and other four were reinforced pre-stressed concrete (PSC) beams. All the beams were of identical cross sectional dimensions, with similar grade of concrete. The variables were percentage area of reinforcement in tension zone, span, and age of concrete for RCC beams. The influence of pre-stress force in the growth of time-dependent strain was investigated in PSC beams with two different eccentricity (*e*) of applied pre-stress force from its centrodial axis. Vibrating Wire (V.W) strain gauges were embedded in length direction at mid span along the upper and bottom layer of reinforcement of each beam to monitor the growth of strain at regular interval of days. For every identical beam specimens the results were almost same, so average values were considered for analysis and presented in this paper. The growth of time dependent strain in plane concrete (PC) beam of similar cross-sectional area, span, and grade of concrete was determined using prediction model code ACI 318 using Midas Civil software for comparison.

### 2.1 Materials

^{3}was 35.3 MPa. Modulus of elasticity of concrete was 29.7 GPa and flexural strength was 4.16 MPa. The types of reinforcing materials used in both the test beams were 8 mm diameter high yield strength deformed bars conforming to IS:1786, grade Fe415. chemical composition of Fe415 steel bars are shown in Table 2. Modulus of elasticity of steel was 200 kN/mm

^{2}, bulk density 7,860 kg/m

^{3}, yield stress 415 MPa, ultimate tensile strength 485 MPa and 14.5 % elongation.

Mix proportion of concrete in kg/m^{3}.

Cement | Water | Sand | 15 mm aggregate | 10 mm aggregate |
---|---|---|---|---|

400 | 172 | 635 | 619 | 564 |

Chemical composition of Fe415 bars.

Elements | C | Mg | S | P |
---|---|---|---|---|

Max. % by weight | 0.30 | 0.60 | 0.06 | 0.06 |

High tensile steel of diameter 4 mm, conforming to IS:1343, having characteristic strength 1,750 N/mm^{2} was used as a pre-stressing wires. The pre-stress force of 17 KN was imposed on PSC beams through three nos of pre-stressing wires of 4 mm diameter at an eccentricity of 75 and 175 mm from the top fiber of the PSC beams.

### 2.2 Experimental Beams, Testing Apparatus and Procedure

Identity and parameters of RCC beams.

Identity | No. of sample | Span (mm) | % Area of A | % Area of A |
---|---|---|---|---|

B1Fe1 | 02 | 1,000 | 0.32 | 0.48 |

B1Fe2 | 02 | 1,000 | 0.32 | 0.64 |

B2Fe2 | 02 | 2,000 | 0.32 | 0.64 |

Identity and parameters of PSC beams.

Identity | No. of sample | Span (mm) | % Area of (A | % Area of (A | e (mm) |
---|---|---|---|---|---|

PSTFe2 | 02 | 2,000 | 0.32 | 0.64 | 25 |

PSBFe2 | 02 | 2,000 | 0.32 | 0.64 | 125 |

## 3 Test Results and Discussion

Development of time-dependent strain in RCC and PSC experimental beams, up to concrete age of 300 days and 150 days, respectively, are presented and discussed in this paper. In RCC beam the load was self weight of the beam and in PSC beam the load was self weight plus axial pre-stress force.

### 3.1 Effect of Percentage Area of Reinforcement

_{st}). It was observed that with increase in age of concrete, the growth of strain increases in both the beams, having some difference between them. At any particular age of concrete, the beams with lesser percentage area of reinforcement in tension zone exhibits more growth of strain than in beams with more percentage area of reinforcement. At 300 days age of concrete the growth of average time-dependent strain in beams B1Fe2 was 21 % less than in beams B1Fe1, due to presence of 0.16 % more area of steel reinforcement.

### 3.2 Effect of Span of Flexural Members

### 3.3 Effect of Ambient Temperature and Humidity

### 3.4 Effect of Pre-stress in Growth of Time-Dependent Strain

The strain values obtained at particular age, from sections along top and bottom layer of reinforcements were averaged for comparison between RCC and PSC beams. It was observed that, in PSC beams the pre-stress force of 450 N/mm^{2} applied at constant eccentricity of 125 mm below centrodial axis, increases growth of time-dependent strain by 73 % than in RCC beams at 150 days age of concrete.

### 3.5 Effect of Eccentricity of Pre-stress Force in Growth of Time-Dependent Strain

### 3.6 Growth of Non-uniform Strain Across the Depth of Beam

_{sc}), caused growth of more strain. Development of this non-uniform strain across its depth, under freely supported condition will influence the deformation in concave curvature of beam axis which further increases with increase in its age, as shown in Fig. 12a. In PSC beams, growths of time-dependent strain were observed more in section below than in section above centrodial axis. The axial pre-stress force applied in section below centrodial axis causes, growth of more strain than in section above centrodial axis. This developed non-uniform strain across its depth and under freely supported condition and will results in convex curvature of beam axis, which further increases with increase in its age, as shown in Fig. 12b.

## 4 Predicted Time-Dependent Strain in Plane Concrete (PC) Beam

^{2}and length 2,000 mm (same as experimental beam) was determined using MIDAS Civil software. The model code used for prediction of shrinkage and creep strain was ACI 318 (ACI, 2005) along its length up to 1,000 days age of concrete, and shown in Fig. 13. Creep strain was determined for sustained load due to self weight only. The growth of strain in plane concrete beam was uniform across its depth without any restrain or influence of reinforcement or pre-stress force. This will causes no change in the curvature of beam axis with increase in its age (Table 5).

Strain values in RCC and PSC beams at different age of concrete.

Sl. No | Age of conc | Strain growth test beam B2Fe2 | Strain growth test beam PSBFe2 | ||||
---|---|---|---|---|---|---|---|

Above N.A (×E−4) | Below N.A (×E−4) | Difference in strain | Above N.A (×E−4) | Below N.A (×E−4) | Difference in strain | ||

1 | 100 | 2.61 | 1.81 | 0.80 | 4.89 | 5.43 | 0.54 |

2 | 150 | 2.89 | 2.07 | 0.82 | 4.10 | 4.50 | 0.40 |

3 | 300 | 4.64 | 3.27 | 0.87 |

Predicted time-dependent strain values.

Shrinkage strain | Creep strain | Total strain |
---|---|---|

4.33 × E−4 | −5.85 × E−6 | 4.27 × E−4 |

### 4.1 Comparison of Strain Growth in RCC, PSC, and PC Beams

In RCC beams of 2.0 m span, by providing 1.01 % area of steel reinforcement, the reduction in growth of time-dependent strain was 12.9 % in comparison to PC beam at 300 days age of concrete. In PSC beams of 2.0 m span, with applied pre-stress force of 450 N/mm^{2} at eccentricity of 125 mm below centrodial axis, increased the growth of time-dependent strain by 10 % in comparison to PC beam and 62 % in comparison to RCC beam at 150 days age of concrete.

This will also affects the occurrence of ultimate shrinkage and creep strain values of concrete. In PSC members the occurrence of creep and shrinkage of concrete and losses of pre-stress force are inter-related. The two ends of the pre-stressing tendons in PSC beam constantly move towards each other because of creep and shrinkage of concrete, thereby reducing the tensile stress in the tendon and increasing the growth of creep and shrinkage strain.

## 5 Conclusion

Designing of any important RCC or PSC flexural structures like bridge girders etc., the time-dependent effects should not only govern by the properties of concrete in use and environmental conditions but it also governed by the percentage area of reinforcement present in the section, its span, and eccentricity of applied pre-stress force. In RCC members the growth of time-dependent strain increases with increase in its span and decreases on increase in percentage area of reinforcement. In PSC members, the increase in eccentricity of pre-stress force increases the growth of time-dependent strain. Presence of reinforcement and pre-stress force in concrete flexural members develops non-uniform strain across its depth, which influences growth of sagging deflections in RCC flexural members and hogging deflections in PSC flexural members. The ultimate creep and shrinkage strain values for any particular grade of concrete will be different, depending upon its use weather in RCC or in PSC. Hence, before construction of any important flexural concrete structures, to ascertain its long-term performance a similar single unit mock model is required to be made and monitored for its time-dependent strain growth. The ultimate strain value obtained from the mock model is required to be considered for design calculations of original structure.

## Declarations

### Acknowledgments

This is to acknowledge that, the research findings are based on the granted Project No. OLP 096312, fund by CSIR-Central Mechanical Engineering Research Institute, Durgapur.

## Authors’ Affiliations

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## Copyright

This article is published under license to BioMed Central Ltd. **Open Access** This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.