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International Journal of Civil Engineering and Technology (IJCIET)
Volume 8, Issue 9, September 2017, pp. 486–497, Article ID: IJCIET_08_09_057
Available online at http://http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=8&IType=9
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication Scopus Indexed
PERFORMANCE EVALUATION OF U-BLOCK
LINTEL BEAM ELEMENTS USING FRACTURE
MECHANICS
Aslam Chanda MD
Structural Design Engineer, Shanghvi & Associates Consultants Pvt. Ltd.,
Mumbai, India
Vegiraju Naresh Kumar Varma
Assistant Professor, Gokaraju Rangaraju Institute of Engineering and Technology,
Telangana, India
V. Vasugi
Associate Professor, Structural Engineering Division,
School of Mechanical and Building Sciences, VIT University, Chennai, Tamilnadu, India
ABSTRACT
The strength of block masonry depends upon the strength of blocks and cement
mortar. The strength of any materials inherently related to small flaws which are
invariably present in all structures. This fact is very important in case of block
masonry. Till now it is seen that fracture mechanics theory has not been applied to the
block masonry, in India and abroad. Therefore in the current study which includes the
small flaws in blocks, cement mortar and block masonry is initiated. The propagation
of crack is governed by the stress intensity factor K1c which indicates the ability of a
material to resist crack propagation. Therefore in the present study an effort has been
to investigate Mode-1 critical stress intensity factors of block masonry with the critical
stress intensity factors of block and cement mortar by using laws of mixtures which
already exists in the theory of composites. Among the different specimens adopted
such as centre cracked specimen, single edge crack specimen, double edge cracked
specimen, the most common one has the single edge notched beams in either three
point bending or four point bending. For this investigation experiments were
conducted on blocks, cement mortar and block masonry beams under both three point
and four point bending. Findings: Applications/Improvement: The same kind of study
can be extended to at least different grades of concrete which will help in obtaining a
trend of the variation of fracture energy with compressive strength. The load carrying
capacity of a lintel can be determine by using different diameter of bars within the
minimum and maximum reinforcement as recommended by IS 456-2000[1]. Fracture
energy can also be determined using the other available methods recommended by
RILEM and compared with the fictitious crack model.
Performance Evaluation of U-Block Lintel Beam Elements using Fracture Mechanics
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Key words: U-block beam, Fracture Mechanics, single edge crack propagation, centre
cracked specimen.
Cite this Article: Aslam Chanda MD, Vegiraju Naresh Kumar Varma, V. Vasugi,
Performance Evaluation of U-Block Lintel Beam Elements using Fracture Mechanics.
International Journal of Civil Engineering and Technology, 8(9), 2017, pp. 486–497.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=9
1. INTRODUCTION
Failure of concrete is preceded by formation and growth of cracks. Accordingly, a significant
amount of research has been done to characterize concrete failure using fracture mechanics
parameters. In direct analogy with the compressive strength that forms the basis for the
strength design, fracture energy is a fundamental material parameter in fracture mechanics,
and is defined as the amount of energy required per unit crack propagation. Building codes
specify standard cube tests for the determination of the compressive strength considering its
importance in design for compressive stress. Similarly, standard test methods are necessary in
fracture mechanics design, for the determination of fracture energy. Further, with the
emergence of higher strengths concrete increased strength may not assure safe progression of
critical construction operations, such as removal of formwork after application of pre-
stressing. A parameter based on energy such as fracture energy may provide a better
predictive estimate of failure of concrete, which is visualized to be due to unstable crack
propagation. The most direct way of determining fracture energy is by conducting an axial
tensile test. Unfortunately, it is difficult to perform such direct tensile tests on concrete
specimens. Therefore, indirect test methods such as the three point bend test method are
adopted for concrete. As of today, three methods have been recommended by RILEM [2] as
accepted procedures for the estimation of fracture parameters of concrete, and are employed
by various researchers for fracture energy estimation. The three RILEM [2] procedures are
based on (i) Fictitious crack model ( Hillerborg et al. 1976) [3], (ii) The two parameter
model (Jenq and Shah, 1985) [4] and (iii) The size effect model (Bazant 1987) [5].
The present study is mainly focused on the determination of the fracture energy, which is
very critical in its usage as a material parameter in the analytical model developed using
bilinear softening .This analytical model is used for the moment capacity and minimum
reinforcement evaluation and also for crack width predictions in reinforced concrete beams of
a particular range of sizes. Since the fracture energy value is so dependent on size of beam,
compressive strength of concrete, aggregate size etc., it is necessary to have a realistic
estimate of the fracture energy in relating the proposed theoretical formulation for moment
capacity, crack width prediction and minimum reinforcement to experimental results.
Therefore, the aim of the present investigation is to obtain the complete load deflection curve
of notched plain concrete beams of specific sizes subjected to three point bend test. The load
deflection curve obtained is then used to determine the fracture energy of the plain concrete
beams. The test procedure outlined by RILEM, which is based on the fictitious crack model,
has been employed to determine the fracture energy. The variation of fracture energy with the
beam depth and the grade of concrete are studied.
2. METHODOLOGY AND EXPERIMENTAL PLAN
2.1. Methodology
Fracture energy is the energy dissipated per unit area during the formation of a crack. It is
normally denoted by the symbol Gf . The energy is dissipated within the fracture process zone;
the region in front of a crack tip where the stress decreases as the crack opens. It is the critical
Aslam Chanda MD, Vegiraju Naresh Kumar Varma, V. Vasugi
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value of the strain energy release rate Gc, that is associated with unstable crack extension in
plain concrete. In the current study, fracture energy is determined using a notched beam in a
three point bending as recommended by RILEM [2] and is shown in Figure 1. The deflection
is measured at the center line of the beam along with maximum load.
Figure 1 Schematic of experimental set up to determine fracture energy
Load versus deflection curves are plotted for various notched plain concrete beams tested,
with fracture energy Wo representing the area under the curve, and as indicated in Figure 2.
Figure 2 Schematic of the load deflection curve
Hillerborg (1985) [8] demonstrated that W1 is approximately equal to W2, making the
total energy, W = Wo + 2W1 = Wo + 2 P1 = Wo + m g . This total energy (W) is divided by
the projected area of fracture A as shown in Figure 1 to give the fracture energy (Gf).
2.2. Experimental Plan
The Experiment performed is very critical in accordance to the specimen and Material. The
details of same are discussed below in further points:-
2.2.1. Specimen Details
The series of experimental tests were carried out using universal testing machine which is
screw driven and has a maximum capacity of 600 kN. The beams were cast using single
grade of concrete representing normal strength concrete. The maximum size of the coarse
aggregate and fine aggregate used are 20mm and 4.75mm respectively along with ordinary
Portland cement of 53 grade. The mix design for the grade of concrete is as per IS
10262:2009 [9] for a mean target strength of 20MPa.The proportions arrived for these mixes
were used directly without going for trial mixes as the objective is to have single grade of
Performance Evaluation of U-Block Lintel Beam Elements using Fracture Mechanics
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concrete representing normal strength concrete, Compressive strength was found by
conducting tests on minimum of three cubes of 150 x150 x 150 mm size for each grade of
concrete and averaging it out to obtain the average compressive strength.
Two beam samples each of two different lengths, viz., 1640 mm, & 2080 mm with a
constant width and depth of 200 mm were cast and designated as S200, M200. The un-
reinforced beams are used to determine the fracture energy according to the method specified
in the RILEM draft recommendation (1985) [7]. The beams were supported over cylindrical
rollers at the two extremities – span being four times the depth as shown in Figure 1. The
load was applied at the mid span.
2.2.2. Materials
The maximum size of the coarse aggregate and fine aggregate used are 20mm and 4.75mm
respectively along with ordinary Portland cement of 53 grade. The consistency of the cement
paste is 30%. The initial and final setting times are 81 minutes and 231 minutes respectively.
The fine aggregate used had a specific gravity of 2.66 and fineness modulus of 7.605. The
specific gravity and bulk density of the coarse aggregate are 2.69 and 1674 kg/m3
respectively.
2.2.3. Mix Design
The mix design for the grade of concrete is as per IS 10262:2009 for mean target strength of
20MPa.The details are as shown in Table 1.
Table 1 Mix design detail for concrete of 20 MPa target strength
Details Quantity
Water- cement ratio 0.5
Water (kg/m3) 191.6
Cement (kg/m3) 383
Fine aggregate (kg/m3) 727
Coarse aggregate (kg/m3) 1103
Mix ratio 1:1.89:2.87
2.2.4. Details of U-Block
The U-blocks used in the preparation of specimens are made up of 20MPa grade of concrete
and the weight of each U-block is 21kg.The breadth and depth of U-block is 200mm and
length is 400mm. The maximum size of the coarse aggregate and fine aggregate used are
12mm and 4.75mm respectively along with ordinary Portland cement of 53 grade .The U-
block is shown below in Figure 3.
Figure 3 U-block
Aslam Chanda MD, Vegiraju Naresh Kumar Varma, V. Vasugi
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2.2.5. Specimen Preparation
All the ingredients of the concrete are weight batched as per the mix proportion specified in
Table 1. The ingredients are mixed in a concrete mixer and then poured. The fresh concrete
is poured into the U-blocks using shovels and compacted using a needle vibrator. All the
beams of plain and reinforced concrete are cast on the separate day with a constant width and
depth of 200mm. Cubes of size 150mm x 150mm x150mm were also cast on the same day
simultaneously. These cubes were used to determine the compressive strength. The concrete
cubes were demoulded after twenty four hours and along with the beams are cured in a water
tank until one day prior to testing. The notches are made in the specimen using a diamond
saw cutter one day prior to testing in wet condition. The process of preparation of specimen
is as shown in Figure 4.
Figure 4 Preparation of specimen
2.2.6. Test Apparatus
A universal testing machine was used for conducting the three point bend test on the plain and
reinforced concrete beams of two different sizes. The machine is screw driven and has a
maximum capacity of 600 kN. The machine is interfaced with a printer that prints the load
and the corresponding load point displacement at any stage of loading.
2.2.7. Test Setup
The beams are tested in flexure for three point bend loading arrangement. The beams are
simply supported on the rollers to give the required effective span [6]. The point load at mid
span is applied through a roller. The load and corresponding displacements are directly
recorded through the printer at any stage of loading. The typical testing arrangement for the
three point bend test is shown in Figure 5.
Figure 5 Typical three points bend test arrangement
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2.2.8. Test Procedure
The beam specimen is placed at mid span directly under the load. The beams are loaded at a
constant displacement rate of 0.25mm / minute. The load is noted in kilo-Newton and the
corresponding displacement in millimeters. The fracture energy is then estimated as per the
procedure outlined by RILEM.
Figures 6 to 8 shows step by step sequence in which the test is completed on the beams,
after the application of load on the beam propagation of cracks is observed on the beams as
shown in Figure 7, simultaneously the digital gauge is recording the amount of deflection in
the beam.
Figure 6 Crack Propagation in Specimen
After the application of load, when the load reaches the peak value the specimen fails
suddenly as shown in Figure 7, when the load is applied on the joint which is the weaker part
in a beam the specimen will fail at that joint.
Figure 7 Specimen after failure
Plain concrete beams which are containing only concrete after the failure of the beam can
be seen as shown in Figure 8; where as in case of reinforced concrete beams the same is not
possible because of the reinforcement present in it.
Figure 8 Broken Specimen Containing Plain Concrete
Aslam Chanda MD, Vegiraju Naresh Kumar Varma, V. Vasugi
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2.3. Design of Lintel for Plain Concrete Specimens
For 1m opening:
Effective span=1.342m; Load on lintel=1.8 kN/m
For 1.37m opening:
Effective span=1.725m; Load on lintel= 2.98 kN
2.4. Design of Lintel for Reinforced Concrete Specimen
For 1m opening:
Effective span=1.342m; Load on lintel=1.8 kN/m; 3no of bars of 8 mm dia.
For 1.37m opening:
Effective span=1.725m; Load on lintel= 2.98 kN/m; 3no of bars of 8 mm dia.
3. RESULTS AND DISCUSSION
3.1. Plain Concrete Specimens
The values of load and deflection obtained after testing the specimens are plotted in the form
of graphs for the plain concrete specimens.
Figure 9 Load versus deflection curve for 1.64 m plain concrete specimen 1
Figure 10 Load versus deflection curve for 1.64m plain concrete specimen 2
0
0.5
1
1.5
0 0.1 0.2 0.3 0.4
Load
, kN
Deflection, mm
S1-P
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Figure 11 Load versus deflection curve for 1.64m plain concrete specimen 3
Figure 12 Load versus deflection curve for 2.080m plain concrete specimen 4
Figure 13 Load versus deflection curve for 2.080m plain concrete specimen 5
Figure 14 Load versus deflection curve for 2.08m plain concrete specimen 6
Aslam Chanda MD, Vegiraju Naresh Kumar Varma, V. Vasugi
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Table 2 Fracture Energy obtained for Specimens used
Specimen
number
Specimen ID Beam length,
mm
Fracture energy
Gf, N/m
Average Gf ,N/m
1 S-1 P 1640 75.28
74.98 2 S-2 P 1640 72.29
3 S-3 P 1640 77.37
4 M-1 P 2080 71.89
69.34 5 M-2 P 2080 67.11
6 M-3 P 2080 69.02
4.2. Reinforced Concrete Specimens
The values of load and deflection obtained after testing the specimens are plotted in the form
of graphs for the plain concrete specimens.
Figure 15 Load versus deflection curve for 1.64m reinforced concrete specimen 7
Figure 16 Load versus deflection curve for 1.64m reinforced concrete specimen 8
Figure 17 Load versus deflection curve for 1.64m reinforced concrete specimen 9
Performance Evaluation of U-Block Lintel Beam Elements using Fracture Mechanics
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Figure 18 Load versus deflection curve for 2.080m reinforced concrete specimen 10
Figure 19 Load versus deflection curve for 2.080m reinforced concrete specimen 11
Figure 20 Load versus deflection curve for 2.080m reinforced concrete specimen 12
From the graphs drawn for the reinforced beams and the lintel load calculations, the peak
load and reinforcement required to support the lintel load can be summarized as shown in
Table 3.
Aslam Chanda MD, Vegiraju Naresh Kumar Varma, V. Vasugi
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Table 3 Reinforcement requirements summary
4. CONCLUSIONS
From the tests conducted, the results tabulated and then analyzed, the following conclusion
can be drawn.
Plain concrete filled specimen does not take the lintel load.
By providing 8mm Φ bars and 0.2*0.2m c/s, the load on lintel is 2.98 kN/m.
For U-shaped blocks beam, the resulted peak load 18kN. Hence safe.
By providing bars of lesser diameter the load can be brought down.
As the span of the beam increases, the load carrying capacity of the beam decreases.
By using U-shaped blocks with reinforced concrete fill, the load carrying capacity of lintel
increases significantly.
Fracture energy calculated for plain concrete filled beam is 74.98 N/m and 69.34N/m for
different spans which is less than the regular concrete beams.
REFERENCES
[1] IS 456:2000, Indian Standard, Plain and Reinforced Concrete - Code of Practice is an
Indian Standard code of practice for general structural use of plain and reinforced
concrete. The latest revision of this standard was done in year 2000, reaffirmed 2005.
[2] RILEM Draft Recommendations, TC89-FMT; Fracture Mechanics of Concrete-Test
Methods.
[3] Hillerborg A, Modeer M, Petersson PE. Analysis of Crack formation and Crack Growth in
Concrete by means of fracture Mechanics and finite elements. Cement and Concrete
Research. 1976; 6, 773-782.
Sl.no Description Lintel opening
For 1.00m opening For 1.37m opening
1. Calculated lintel load 1.8 KN 2.98 KN
2. Reinforcement provided for the calculated
lintel load by assuming 200*200 mm c/s of
concrete beam as per IS 456:2000
3-8 mm Φ 3-8 mm Φ
3. Average Peak load obtained from
experiment on a reinforced U-block beam
of 200*200 mm c/s
16.67 KN 11.5 KN
4. Average Peak load obtained from
experiment on a plain U-block beam of
200*200 mm c/s
1.6 KN 1.27 KN
5. Ratio of peak load obtained from
experiment and calculation
1 : 9.26 1 : 3.85
6. Ratio of reinforced and unreinforced U-
block beams obtained from experiment.
1 : 10.41 1 : 9
Performance Evaluation of U-Block Lintel Beam Elements using Fracture Mechanics
http://www.iaeme.com/IJCIET/index.asp 497 [email protected]
[4] Jenq YS and Shah SP. A Fracture Toughness Criterion for Concrete. Engineering Fracture
Mechanics. 1985; 21(5), 1055-1069.
[5] Bazant Z P. Snapback Instability at Crack ligament Tearing and its implication for fracture
Micromechanics. Cement and Concrete Research. 1987; 17, 951-967.
[6] Guinea GV, Planas J, Elices M. Measurements of the fracture energy using three points
bend tests: Part1- Influence of experimental procedures. Materials and Structures. 1992;
25(4): 212-218.
[7] RILEM TCM-85, Determination of the fracture energy of mortar and concrete by means
of three-point bend tests on notched beams. Materials and Structures, 1985. 18(106): p.
287-290.
[8] Hillerborg A. A Modified absorption Theory. Cement and Concrete Research. 1985; 15,
809-816.
[9] IS10262:2009. Concrete Mix Proportioning –Guidelines.
[10] Elwaleed Awad Khidir, Syed Ameer Basha and Hayder M. A. A. Al- Assadi, Analysis of
Stress Corrosion Cracking of X6 5 Oil Pipeline. International Journal of Mechanical
Engineering and Technology, 8(4), 2017, pp. 212–222.
[11] Gurjit Singh, Rajeev Kumar, Dr. Manpreet Singh and Jujhar Singh Detection of Crack
Initiation in The Ball Bearing Using FFT Analysis. International Journal of Mechanical
Engineering and Technology, 8(7), 2017, pp. 1376–1382.
[12] Yehia Abdel Zaher and Yasmin Hefni Abdel Aziz , Effect of Elevated Temperature on RC
Precracked Beams Repaired and Strengthened Using Jackets of Cementitious Materials .
International Journal of Civil Engineering and Technology , 8(5), 2017, pp. 819-831
