1. Design of Reinforced Concrete Deep Beams for Different Loading and
Support Restraints.
Reference Number: RP 9/91
Collaborators: Emeritus Professor Kong Fung Kew
Approved Project Cost: S$179,000
Duration: July 91 to December 1994
SYNOPSIS
The Applied Research Project is chiefly concerned with the Design of Single-span, Medium-to-High Strength Concrete Deep Beams. In this context, medium-to-high strength concrete refers to compressive cylinder strength f'c >= 40 MPa (6000 psi). Although the beams are single-span, there are a few parameters, which can influence the shear strength. Thus, the research program consists of three series of specimens to study the governing parameters:
Series I- specimens with effective span-depth and shear span-depth variations
Series II- specimens with different main steel contents
Series III- specimens with different web reinforcements
Series I specimens
Nineteen singly reinforced deep beams with main steel percentage p= 1.23% were tested for seven shear span-depth ratios a/d and for four effective span-depth ratios le/d. It is found that the shear span-depth ratio a/d has a significant influence on the ultimate strength but only a marginal influence on the diagonal cracking strength. On the other hand, the effective span-depth ratio le/d has only a marginal influence on the failure loads. Thus, in the subsequent two series, the parameter le/d was omitted in the investigation.
Series II specimens
The influence of main steel content on shear strength was studied with two groups of 7 beams each, reinforced with p= 2.58% and 4.08% respectively. From the test results, it is clear that with high strength concrete deep beams, the influence of the percentage of main steel on shear strength is more significant at the low end of a/d ratios, say a/d <= 1.0. The minimum required web reinforcement for high strength concrete beams should also be increased accordingly.
Series III specimens
The eighteen specimens were organized into three sub-groups of 6 each, on the basis of shear span-to-overall-depth ratios a/h = 0.75, 1.00 and 1.50. In each sub-group, they were provided with five different arrangements of web reinforcement, the sixth beam being the control specimen without any web reinforcement. In this manner, the influence of vertical and horizontal web reinforcements on shear strength could be investigated. The study shows that appropriate web reinforcements could increase the shear strength of deep beams by 1.5 to 3 folds.
In addition to the 51 test data, 182 published deep beam test results were compiled and compared with code predictions based on Hsu-Mau's softened truss model, Zsutty's formula, the ACI code, the Canadian CSA Code and the UK CIRIA Guide 2. The specimens were broadly classified into three concrete strength categories (Table 6.1-6.3); the first category comprised 133 low strength concrete beams with f'c < 40 MPa (6000 psi), the second category had 32 medium strength concrete beams with 40 MPa <= f'c <= 55 MPa (6000 psi <= f'c <= 8000 psi) and the last category of 68 high strength concrete beams had f'c > 55 MPa (8000 psi). The comparisons reported in this paper will provide an added assurance to designers that the deep beam provisions in the ACI Code, though essentially based on test results of concrete strengths of less than 40 MPa (6000 psi), will ensure safe designs for high strength concrete deep beams. The Canadian Code, essentially a strut-and-tie approach, gives reasonable accuracy while the CIRIA Guide equation yields considerable scatter, as the latter was calibrated on low-strength-concrete deep beams. A slight modification of the CIRIA equation is proposed, which gives the most consistent shear strength predictions among the shear design equations considered.
2. Large Prestressed High Strength Concrete Deep Beams
Reference Number: RG64/94
Collaborators: Mr Lu Hai Yun and Mr Tong Kebo
Approved Project Cost: S$99,926
Duration: April 1995 to May 1999
SYNOPSIS
This report comprises 14 chapters, which can be separated into two sections: Part A and Part B. Part A mainly focuses on the general behavior, analysis and design in the shear strength of large reinforced and post-tensioned concrete deep beams. The influence of main steel ratio r, concrete strength fc', shear span-to-overall-height ratio a/h (or shear span-to-effective-depth ratio a/d), overall height h and prestressing force on deep beams are investigated.
Part A was written by Mr Lu Hai Yun for MEng degree and it consists of three test program, as follows:
Study I : A total of 22 high strength concrete deep beams with fc' exceeding 55 MPa is tested to failure. The specimens are divided into four groups based on the main steel ratio r ranging from 2.00, 2.58, 4.08 to 5.80%. Within each group, only one variable is introduced, i.e. a/h ratio (or equivalent a/d). The effect of r and a/h on high-strength-concrete deep beams is described in Chapter 4.
Study II: Tests on 12 medium- and large-sized reinforced deep beams with a/h <=1.0 are conducted. The size h of a typical specimen varies from 500, 1000, 1400 to 1750 mm. The a/h ratio ranges from 0.50, 0.75 to 1.00. The size effect on large reinforced deep beams is presented in Chapter 5.
Study III: Twelve medium- and large-sized post-tensioned deep beams with a/h <= 1.0 are tested. For all specimens, only one prestressing index of 0.28 is involved. The size h of a typical specimen varies from 500, 1000, 1400 to 1750 mm. The a/h ratio ranges from 0.50, 0.75 to 1.00. The size effect on post-tensioned deep beams is also described.
A strut-and-tie model for the shear strength predictions of reinforced and post-tensioned deep beams is also presented. This model is applied to the 46 specimens in the above three studies together with 233 specimens from several published papers, and the predictions are compared with those from the three main design codes: the ACI 318-95 building code, the U.K. CIRIA, and the Canadian building code. Comparisons show that the proposed strut-and-tie model not only provides consistent predictions of the ultimate strength for both reinforced and post-tensioned concrete deep beams, but also reveals the load transfer mechanism inside deep beams.
The studies in Part B (undertaken by Mr Tong Kebo for MEng degree) mainly focus on the strut-and-tie approach to shear strength predictions of deep beams. Both the non-prestressed and prestressed deep beams as well as deep beams with web openings are considered. Different from the strut-and-tie mechanism in Part A, the new strut-and-tie approach is based on the conventional theories of failure, i.e., Mohr-Coulomb's criterion and Kupfer's criterion. Furthermore, the new approach can be derived from first principle as it contains little empiricism.
The new strut-and-tie approach that encompasses non-prestressed deep beams, deep beams with web openings and prestressed deep beams are developed in Chapter 10 through Chapter 12, respectively. All the predictions are verified by experimental results from various sources. The comparison with test results shows that the new approach gives consistently good predictions in the ultimate shear strength of deep beams. Due to limited published literature on the prestressed deep beams, six large prestressed deep I-girders are tested. The six I-girders are divided in two groups with shear-span-to-depth a/d ratios of 0.84 and 1.69, respectively. The partial prestressing ratios are varied as 0, 0.32 and 0.64, respectively. The proposed method gives very consistent predictions for the I-girder; the mean of predictions to test results is 0.80 with a standard deviation of 0.028.
3. Analysis of frame structures in fire
Reference Number: RG 39/96
Collaborators: A/P Fung Tat Ching
Professor George England (Imperial College, UK)
Approved Project Cost: $61,554
Duration: May 1997 to June 2001
SYNOPSIS
This research aims to develop some useful analytical methods for the analysis of steel structures under thermal effects. This could lead to a better understanding of the structural behavior under thermal effects. The successfully developed methods comprise the finite element method, the first- and the second-order elastic-plastic hinge methods, and the Rankine approach. The plastic theorems form the theoretical basis for the development of the elastic-plastic hinge methods and the Rankine approach. For structural analyses incorporating thermal effects, the material model with respect to temperature must be known. This research adopts the mechanical model and the thermal properties of steel at elevated temperatures in Eurocode 3-Part 1.2 (1995).
The proposed finite element model (FEM) comprises the assemblage of co-rotational beam elements in a two-dimensional plane. Both material and geometric nonlinearities are taken into account. A computer program has been developed. Comparison with test and numerical results published in the literature shows good agreement. The proposed FEM provides a practical and economical way to investigate the behavior of steel structures under thermal effects. Additionally, the FEM is used to verify other analytical methods developed in this research.
Three classical plastic theorems, viz. the Lower Bound Theorem, the Upper Bound Theorem and the Uniqueness Theorem, have been successfully extended to frame analysis under thermal effects, with new definitions and mathematical proofs. Stemming from these theorems, the first- and second-order elastic-plastic hinge methods are developed. Both methods employ a step-wise stiffness matrix analysis incorporating the zero-length plastic hinge concept. However, in the first-order approach, undeformed geometry is considered in the element formulation, and thermal stresses are treated as additional external loads acting on the system. On the other hand, in the second-order approach, the second-order effects of instability and thermal stresses are directly incorporated into the element formulation. Two computer programs have been developed for the two respective methods.
The traditional Rankine approach for the analysis under normal conditions has been successfully extended to fire analysis. The proposed Rankine approach allows for the interaction between strength and stability of a steel structure under thermal effects to determine an approximation of the fire resistance of members and frames. Incorporating thermal effects in the analyses, the strength and stability criteria can be determined from the plastic and elastic-buckling analyses, respectively. This approach is applicable for both isolated compression members and framed structures. Verifications with numerical and test results show that the proposed Rankine approach provides consistent and satisfactorily accurate predictions for the fire resistance of steel structures. This suggests that the Rankine approach may serve as a quick tool for fire engineering design.
In this research, the proposed Rankine approach deals with rigid-jointed frames with members subjected to uniform heating. Case studies are also conducted in frames, where only part of the structure is subjected to heating. Once again, the comparison with FEM predictions shows that the Rankine approach gives reasonable predictions of fire resistance of frames. It is noteworthy that in this study, thermal gradients, residual stresses, and lateral torsional and local buckling are not considered. Thus, these shortcomings somewhat restrict the range of application of the Rankine approach and may be considered in the future development.
The performance of frame structures in fire differs from conventional ultimate strength design in that when collapse takes place, it does so under working loads. In many cases, the actual loads will be less than ultimate design values. The project is in joint collaboration with Imperial College of Science and Technology, UK.
4. Size effect on shear strength of concrete structures
Reference Number: RG 39/96
Collaborators: Professor Cheong Hee Kiat
Professor Milija Pavlovic (Imperial College, UK)
Professor Mike Kotsovos (NTUA, Greece)
Approved Project Cost: $139,242
Duration: Jan 2000 - ongoing
SYNOPSIS
It is well known that the shear strength of concrete structures reduces with increasing size. Although this phenomenon is well observed and fairly well documented, up to now, there is no satisfactory explanation for this phenomenological occurrence. We believe the size effect arises because of anomalies in conventional shear design approach. Conventional wisdom has it that the shear stress t is assumed to be uniform across a beam section and is defined by the elastic theory T = V/bd, where b and d are the width and effective depth of beam section, and V is the applied shear force. We believe that such definition actually gives rise to the apparent size effect.
The ultimate aim of the research is to provide reliable and rational design guidelines for consultants to design the shear strength of large reinforced concrete structures. These design guidelines should have theoretical basis, and should be free from empirical factors currently found in all the international codes for shear design. In this manner, a structural engineer can then provide uniform safety margin in the shear design of small and large concrete structures.
This program is on going and aims to achieve the following objectives:
1. From a systematic study on size effect, the phenomenological causes can be unraveled. A consistent theory can then be proposed for the size effect on shear strength.
2. The experimental results will certainly be useful to international code committees as most test data were drawn from small specimens, and extrapolation is required for larger member size.
3. Besides, the two proposed methods (CFP and strut-and-tie) will serve as useful alternatives to current sectional shear design approach, which relies heavily on empirical curve fitting.
Research programs such as that described in the present proposal will help towards clarifying the causes of size effects and, hence, improving both analysis and design methods.
(I) Experimental Program
Four series of beams have been tentatively planned. It should be noted that as the behaviors of tested beams in each series become clearer, specimens in subsequent series might be modified somewhat.
Series 1 (9 rc beams)
Within each group, there will be 3 beams; the 1st beam is designed according to the British and the American Codes, the 2nd beam to CFP method and the 3rd beam to strut-and-tie method. Aiming at a load-carrying capacity corresponding to a flexural mode of failure, all three beams will be tested to failure. The aim of the tests is to assess and compare the flexural design using codes, CFP method and strut-and-tie model.
Series 2 (24 rc beams)
Series 2 is a continuation of Series 1 specimens but on shear design, so as to achieve a full study of the actual size-effect parameter. The aim is to correlate these test results with earlier publication on smaller beams. These beams of 3-D geometrical similarity will enhance user's confidence in the CFP method, which was originally based on smaller beams.
Series 3 (8 rc and 8 pc beams)
In this series, only one shear span-to-depth ratio is studied, say a/d =3.0. The beam width is kept constant while the beam depth and length are increased proportionally to maintain 2-D geometrical similarity. This series of beams will complement beams performed earlier by Assoc Prof Tan.
Series 4 (16 rc beams)
In this series, only one shear span-to-depth ratio is used, say a/d = 3.0. Each series consists of 4 beams.
(II) Analytical program
On the analytical side, two simple approaches (namely, compressive force path method and strut-and-tie method) and one finite element software will be used to analyze the test data.
5. Performance-based design for fire resistance of bare steel structures - BCA project
Reference Number: CRP 01/08/14 and RGM 31/01
Collaborators: A/P Ting Seng Kiong
Asst/P Vassili Novozhilov
Approved Project Cost: S$574,000 (BCA) and S$434,000 (NTU)
Duration: Nov 2001 to Apr 2004
SYNOPSIS
Performance-based design for fire resistance of bare steel structures - BCA project
6. Fire resistance of concrete structures - DSTA project
Reference Number: Still under consideration by DSTA
Collaborators: A/P Tan Teng Hooi
Asst/P Au Siu Kui
Approved Project Cost: S$563,000 (DSTA) and S$426,000 (NTU)
Duration: Apr 2003 to Apr 2008
SYNOPSIS
Fire resistance of concrete structures - DSTA project
7. Material and structural behavior of steel and concrete structures at elevated temperatures
Reference Number:
Principal Investigator: A/P Ting Seng Kiong
Other Collaborators: A/P Tan Teng Hooi
Dr Bill Wong (Monash University)
Approved Project Cost:
Duration: January 2001 - ongoing
SYNOPSIS
In Singapore, the detailed "prescriptive" provisions have controlled fire safety measures of buildings almost entirely. In this "prescriptive" form, the building designers and the regulator enforcing the Regulations are guided by detailed clauses stipulated in the "Code of Practice for Fire Precautions in Buildings". Examples include specified fire resistance in terms of concrete cover for RC structures, or fire protection of exposed steel sections. Although the "prescriptive" approach offers clear guidelines, it does not consider the fire resistance of a framed structure as an integral whole. Besides, it makes no provision for innovation in building.
An alternative approach to achieve fire safety is described as "Performance-Based". Performance-based design provisions offer the flexibility to customize building design using Fire Engineering methods. This approach allows for innovation and cost effectiveness. It actually considers a fire occurrence as a load case. Frame analyses can then be taken for different fire scenarios. Fire Engineering is aimed at achieving uniform fire safety in buildings, not only at the member's level but also at the assembly level. Performance based design approach is driven by the international trend of global harmonization of codes and standards. This relies heavily on the knowledge gained from actual testing and finite element modeling. So far, extensive tests on steel frames at elevated temperatures have been conducted in the U.S.A., the UK, China, Australia, Japan, France, Sweden, Belgium, etc. However, there are relatively fewer publications with regard to the testing and modeling of RC and composite columns under fire conditions. Thus, this research helps to prepare both the academics and the regulatory body for the inevitable move into performance-based design for fire safety.
Essential to the performance-based fire code is the fire resistance of structural elements. The objectives of the research are to understand the actual material and structural behaviour under elevated temperatures simulating the fire conditions. After material testing, experimental tests will be conducted on structural members. From the understanding we derive, we can better model the structural behaviour of steel and concrete members under fire conditions.
Another aspect of the research is on the damage assessment of fire-damaged structures. In the event of fire, considerable damage will be inflicted on the structure. Engineers are often faced with the problem of how and what extent the fire-damaged concrete structures should be re-constructed. Concrete residual strength can be used as a significant indication of the damage sustained during the fire. The understanding of the concrete residual strength can also be applied in the assessment of remaining capacity and performance of the structural members.
8. Strut and tie approach to shear strength of RC walls with openings
Reference Number: RG 36/44
Principal Investigator: Asst Prof Li Bing
Approved Project Cost: $58,000
Duration: May 2000 - ongoing
SYNOPSIS
This project investigates the behavior of walls with openings irregularly distributed and reinforced with small or moderate amounts of steel. The purpose is to formulate a rational procedure for their seismic design using strut and tie models. Professors J. Breen, P. Marti, Schlaich and M.Collins have developed strut and tie models generally applicable for monotonic loading. They have proposed a generalization of the truss analogy for the design of structural concrete, with the consistent application of "strut and tie models" to all regions of a structure. This project attempts to validate this powerful approach for reversed loading case.
Experimental and analytical studies will be conducted on reinforced concrete shear wall specimens. Experimental work includes the setting up of loading frame and the mounting of hydraulic jack to the loading frame. Shear wall specimens will be prepared and tested under lateral cyclic loading applied from the hydraulic jack. Analytical studies include parametric study of shear wall with irregularly openings and analysis of shear wall using strut and tie approach.
9. Design of hybrid structural steel and precast concrete structure
Reference Number: RG 6/97
Principal Investigator: A/P Yip Woon Kwong
Other Collaborators: A/P Ting Seng Kiong
A/P Tan Teng Hooi
Approved Project Cost: $224,600
Duration: Nov 1997 to current
SYNOPSIS
The main objective of this proposed research project is to develop a hybrid form structural steel and precast cocnrete construction technology which is structurally efficient in terms of design and buildability. The proposed research development marries the well-developed technologies in structural steel connections and precast components to evolve a new method in incorporating embedment of partial structural steel sections at the ends of precast components to facilitate their rapid and easy erection on site through the well-established procedures of structural steel connection.
