Strutandtie model (STM) method evolved as one of the most useful designs for shear critical structures and discontinuity regions (Dregions). It provides widespread applications in the design of deep beams as recommended by many codes. The estimation of bottleshaped strut dimensions, as a main constituent of STM, is essential in design calculations. The application of carbon fibre reinforced polymer (CFRP) as lightweight material with high tensile strength for strengthening Dregions is currently on the increase. However, the CFRPstrengthening of deep beam complicates the dimensions estimation of bottleshaped strut. Therefore, this research aimed to investigate the effect of CFRPstrengthening on the deformation of RC strut in the design of deep beams. Two groups of specimens comprising six unstrengthened and six CFRPstrengthened RC deep beams with the shear span to the effective depth ratios (
Strutandtie model (STM) method evolved as one of the most useful designs for shear critical structures and discontinuity regions (Dregions). It reduces complex states of stress within the Dregion in reinforced concrete (RC) member into a truss comprised of simple and uniaxial stress paths. The concrete stress field in strut, as a main constituent of STM, is usually wider at midlength of the strut than at the ends. Thus, strut generally varies in crosssection along its length. The strut that changes in its width along the length is idealised as a bottleshaped geometry [
The cracking behaviour of bottleshaped strut resembles that of concrete cylinder in a split tensile test. The internal lateral spread of applied compression force results in transverse tension strain in the strut which causes split cracking [
STM method has been used for Dregion analysis in structural elements such as deep beams according to many codes and standards [
Prior research showed that the CFRPstrengthening increased the shear strength of RC deep beams in the range of 24–43% depending on the installation style and fibre direction of CFRP sheet [
There are uncertainties regarding strut dimensioning and deformation while it is subject to load. Width of a strut has been estimated in the previous studies with the assumption that the strut has been stressed to the maximum [
The objective of this research is to investigate the effect of CFRPstrengthening on the deformation of RC strut in deep beam as it affects the failure of strut. The bonding between CFRP sheet and strut disrupts the load trajectories in strut and complicates the estimation of strut dimensions while loading. Hence, this investigation sets the scene for STM of CFRPstrengthened Dregions regarding strut dimensioning.
Tests were performed on two groups of six RC deep beam specimens with and without CFRPstrengthening. Each group of beams had the shear span to the effective depth ratios of 0.75, 1.00, 1.25, 1.50, 1.75, and 2.00. Both groups of beam specimens were identical in every aspect, excluding the condition of strengthening by CFRP sheets. The variables of the investigation were
A typical bottleshaped strut is illustrated in Figure
Strutandtie model of a bottleshaped strut including measurement points.
The CFRP sheet was utilised in the current experiment as an external reinforcement to restrain cracking of RC struts in deep beams. The outline of bottleshaped strut shown in Figure
All the beam specimens were 1840 mm in length, 140 mm in width, and 350 mm in height. Nine deformed steel bars of 16 mm diameter were longitudinally placed in three layers in the bottom of beams as flexural reinforcement. Orthogonal grids of reinforcement with the spacing of 100 mm were provided at two sides of beams using deformed steel bars of 6 mm diameter. The longitudinal steel bars were welded to the two end steel plates to provide adequate anchorage. The end steel plates with 120 mm of height and 10 mm of thickness covered the width of beams fully at both ends of beams. The additional reinforcements (steel cage) using deformed steel bars of 6 mm diameter were placed under the load plates and atop the support plates to prevent local bearing stress. The beams details are indicated in Figure
Beam details for half length: (a) section AA, (b) side view.
Ordinary Portland concrete with 28day cylindrical compressive strength of 37.02 MPa and splitting tensile strength of 3.31 MPa was used to fabricate all the beams. The maximum aggregate size and water to cement ratio were 10 mm and 0.48 in the concrete mix design, respectively. The density of concrete was 2420 kg/
Typical properties of CFRP sheets and epoxy.
Materials  Tensile strength (MPa)  Tensile modulus of elasticity (GPa)  Bond strength (MPa)  Fabric thickness (mm/ply)  Laminate thickness impregnated with resin (mm/ply) 

CFRP sheet  3900  230  —  0.111  0.9 
Epoxy resin  30  4.5  >4  —  — 
Test setup.
All the beams were simply supported over the two steel plates and tested under fourpoint bending configuration. The uniformly increasing load was applied with an increment of 50 kN using a hydraulic actuator with a maximum capacity of 5000 kN. The surface of concrete was carefully rubbed with sand paper before bonding of CFRP sheets. To prepare twopart epoxy resin based on the manufacturer recommendations, the hardener and resin were mixed and stirred for three minutes with a proportion of one to four. After twoweek curing of the beams, the CFRP sheets were installed and covered the shear span of beams at two sides.
The DEMEC discs were installed along and perpendicular to the strut centreline in all the beams with a distance of 200 mm equal to the length of DEMEC bar as shown in Figure
Prior to cracking, the elastic stress field occurred in the Dregion of RC deep beams, which can be quantified with elastic analysis. Cracking occurred in the Dregion as the applied load increased and disrupted the stress field which led to disorientation of the internal load path. The STM method rationally embodies a system of forces which is in equilibrium with a given set of loads. However, CFRPstrengthening disrupted the load trajectories in strut and complicated the disorientation of internal forces. Therefore, the estimation of CFRPstrengthened strut dimensions under loading became inaccurate.
In this experiment, shear failure mode with diagonal crack propagating towards the load plate and support plate was dominant for unstrengthened RC deep beams as expected based on the prior research [
Ultimate shear strength of RC deep beams.




0.75  756.95  905.31 
1.00  709.01  857.89 
1.25  604.08  740.02 
1.50  555.91  691.04 
1.75  403.02  510.01 
2.00  360.02  468.05 
Typical failure of strut in RC deep beams with
The orientation of strut is affected by the ratio of
The cracking and crack widening caused softening behaviour in RC strut which affected strut dimensioning and consequently the strut behaviour under loading. The CFRPstrengthening of RC strut restricted the strut widening compared to the unstrengthened status.
Difference of transverse tensile strains of the unstrengthened and CFRPstrengthened RC struts.
Load (kN)  

100  200  300  400  500  600  700  

0.75  0.0000  (0.0000)  0.0001  0.0001  0.0003  0.0004  0.0006 
1.00  0.0000  (0.0001)  0.0002  0.0003  0.0006  0.0009  0.0018  
1.25  0.0000  (0.0001)  0.0007  0.0009  0.0008  0.0010  —  
1.50  0.0000  (0.0002)  0.0008  0.0009  0.0015  —  —  
1.75  0.0000  (0.0010)  0.0013  0.0023  —  —  —  
2.00  0.0004  (0.0026)  0.0024  —  —  —  — 
Loadtransverse strain curves of unstrengthened and CFRPstrengthened RC struts.
Based on Table
Based on Table
Figure
Based on the experimental results, the value of transverse strain of ordinary RC struts remarkably grew faster than that of CFRPstrengthened RC struts after the amount of loading was higher than approximately 40–60% of ultimate shear strength of ordinary RC deep beams. Hence, the strut widening was remarkably affected by CFRPstrengthening after the applied load was higher than approximately 40–60% of ultimate shear strength of ordinary RC deep beams. The amount of
The value of
Average transverse strains of unstrengthened RC struts for different applied load levels.
Number 






1  0.75  0.0028  0.0032  1.00  1.00 
2  1.00  0.0040  0.0048  1.43  1.50 
3  1.25  0.0063  0.0084  2.25  2.63 
4  1.50  0.0088  0.0128  3.14  4.00 
5  1.75  0.0138  0.0204  4.93  6.38 
6  2.00  0.0176  0.0264  6.29  8.25 
Average transverse strains of CFRPstrengthened RC struts for different applied load levels.
No 






1  0.75  0.0018  0.0025  1.00  1.00 
2  1.00  0.0034  0.0040  1.89  1.60 
3  1.25  0.0044  0.0058  2.42  2.30 
4  1.50  0.0060  0.0080  3.33  3.20 
5  1.75  0.0106  0.0143  5.89  5.72 
6  2.00  0.0138  0.0187  7.67  7.48 
Comparison of average transverse strains of unstrengthened RC struts for different applied load levels.
The values of
Comparison of average transverse strains of CFRPstrengthened RC struts for different applied load levels.
The loadcompressive strain curves consisted of two parts for both ordinary and CFRPstrengthened RC deep beams as shown in Figure
Loadcompressive strain curve of unstrengthened and CFRPstrengthened RC struts.
The effect of CFRPstrengthening on the RC strut shortening was negligible. The curves in Figure
Tests were performed on two sets of six RC deep beam specimens with and without CFRPstrengthening. The objective of the research was to investigate the RC strut deformation regarding its widening and shortening in the design of deep beams. The key variables were shear span to effective depth ratio and applied load level.
In deep beams subjected to load, as the level of widening of strut increases, the compressive strength of strut along its longitudinal axis decreases. Consequently the ultimate shear strength of deep beam decreases. Thus, designer of deep beam must pay attention to the significant effects of
The CFRPstrengthening significantly increased the shear strength of RC deep beams.
Strut deformation in the transverse direction was greater than the direction along the strut centreline for both conditions of with and without CFRPstrengthening.
As the applied load increased the values of transverse strain in both the ordinary and the CFRPstrengthened RC struts increased.
With the same applied load, the transverse strain, and consequently the strut widening in both the ordinary and the CFRPstrengthened RC deep beams with high
With the same applied load, strut widening in ordinary strut increased more than CFRPstrengthened strut as the
The effect of CFRPstrengthening on crack widening restraint increased with the increase of
With the same value of
The value of transverse strain of ordinary RC struts remarkably grew faster than that of CFRPstrengthened RC struts after the amount of loading was higher than approximately 40–60% of ultimate shear strength of ordinary RC deep beams. Therefore, the strut widening was significantly affected by CFRPstrengthening after approximately 40–60% of ultimate shear strength of ordinary RC deep beams.
With the increase of
With the increase of
With the increase of
The increase of strut widening resulted in the increase of strut shortening, and vice versa. The strut shortening was restrained as the CFRP sheet restrained the strut widening. Therefore, the shortening of CFRPstrengthened RC struts was lower than that of ordinary struts.
The average of transverse strain corresponding to 50% and 75% of ultimate shear load
The average of transverse strain corresponding to 75% and 100% of ultimate shear load
The average of transverse tensile strain of ordinary unstrengthened RC strut
The average of transverse tensile strain of CFRPstrengthened RC strut
The difference value between the transverse tensile strains of ordinary unstrengthened and CFRPstrengthened RC strut
The ratio of
The ratio of
The ratio of
The ratio of
Shear span to effective depth ratio
Ultimate shear strength of ordinary unstrengthened RC deep beam from the experiment (kN)
Ultimate shear strength of CFRPstrengthened RC deep beam from the experiment (kN).
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was supported by High Impact Research MoE Grant UM.C/625/1/HIR/MoE/ENG/54 from the Ministry of Education Malaysia. The authors acknowledge Dura Technology S/B for facilitating the experimental work.