- Email: [email protected]
Shear failure of reinforced concrete beams
Shear failure of reinforced concrete beams M. D. Kotsovos hnperial College of Science and Technology, Department o/"Civil Engineering, Imperial College Road, London SW72BU, UK (Received February 1985: revised May 1986)
It has been suggested in a previous work that the causes of shear failure exhibited by reinforced concrete (RC) beams are associated with the stress conditions in the region of the path along which the compressive force is transmitted from support to support. The work described in this paper presents experimental evidence supporting the above concept. The work is based on a comparative study of the behaviour of concrete beams reinforced in compliance with this concept and that of beams reinforced in compliance with current design procedures. Keywords: shear failure, reinforced concrete Codes of practice, such as C P l l 0 , ~ require structural members to be designed so as to exhibit ductile behaviour, since such behaviour gives ample warning of impending collapse. Shear failures, therefore, are undesirable because of their brittle nature which allows little or no such warning. Current shear design procedures are based on the assumption that shear failures occur when the shear capacity of a critical section is exceeded. Thus, the objective of these procedures is to realistically assess the amount of transverse reinforcement required to carry that portion of the shear force in excess of the value which can be sustained by concrete alone. For beams subjected to two-point loading, the critical section is any section situated within the shear span (av) and, therefore, reinforcing this span in compliance with the current strength requirements is generally considered to safeguard against shear failure. It has, however, been argued elsewhere, 2 that the concept of shear capacity of a critical section is insufficient to describe the underlying causes of the observed behaviour of RC beams, Shear failure appears to be associated with the stress conditions in the region of the path along which the compressive force is transmitted from support to support and not with the shear capacity of particular sections. As a result, it has been suggested that compliance with current design procedures, although preventing shear failure, may not be sufficient to provide adequate ductility.-" The present work, therefore, has been aimed at providing experimental evidence to support the above arguments. This evidence has been obtained from tests on 32
Eng. Struct. 1987, Vol. 9, J a n u a r y
RC beams with various arrangements of transverse reinforcement. The beams have been subjected to two-point loading with values of av varying between approximately 1 and 4 times the beam depth. The fundamental causes of shear failure are discussed concisely and this discussion forms the basis of a comparative study of the strength, deformation and failure characteristics exhibited by the beams tested in the programme. An understanding of these causes is essential for the development of new shear design models compatible with the concept of member rather than section design stipulated by the CEB commission IV (Stuttgart meeting, 9 May, 1984).
Causes of shear failure It is generally considered that the behaviour of RC beams without transverse reinforcement is dependent on the value of the shear span to depth (av/d) ratio. For values of a,/d between approximately 1 and 6, such beams are expected to fail in shear before their flexural capacity is attained. For any other value, the beams should attain their flexural capacity. The behaviour of the latter beams has been the subject of previous experimental work. 3 As stated elsewhere, 2 the causes of shear failure are likely to be associated with the stress conditions in the region of the path along which the compressive force is transmitted to the supports after the occurrence of diagonal cracking; an analytical description of these conditions could lead to the formulation of a lower bound criterion for failure. On the basis of this argument, the shear modes of failure exhibited by the beams under 0141-0296/87/01032-07/ $03.00 © 1987Butterworth & Co (Publishers) Ltd
Shear failure o f RC beams: M. D. Kotsovos --'-_s
Path of C .,_
II---
;l 3_
av
Path of C
I
I~1
c
"1
I1
a 4
8 v
d:
-I
Av c
b Figure 1 Path of compressive force, C, and combinations of compressive and tensile, T, forces causing: (a) type 1, av/d< 2-2.5; (b) type 2, av/d> 2-2.5
two-point loading may be broadly classified into two types:
Type 1 This includes modes of failure which occur in beams with avid smaller than a value between approximately 2 and 2.5. Such beams are characterized by a path of compressive force comprising linear portions, within both the shear and middle spans, intersecting each other in the region of the load point (Figure l(a)). It has been argued that, in spite of the high compressive stresses in the region of the load point, diagonal cracking is unlikely to lead to a crushing mode of failure since the multiaxial compressive state of stress which exists there will cause an increase of the local strength. 2 Instead, the diagonal crack should branch near-horizontally towards the compressive zone of the flexure span of the beam in order to by-pass this high strength region. The tensile stress resultant which exists at the tip of the crack branch combined with the compressive stress resultant due to the bending action will reduce the strength capacity of the compressive zone of the flexure span of the beam. It would be the failure of this region, therefore, that would eventually lead to collapse of the beam.
Type 2 This includes the shear modes of failure which occur in beams with avid larger than a value of between approximately 2 and 2.5. Such beams are characterized by a path of compressive force consisting of two linear portions within the shear span, connected in the region of the tip of the diagonal crack (Figure l(b)). This change in the direction of the compressive force generates, for equilibrium purposes, a tensile stress resultant, intersecting the obtuse angle of the linear portions, which is superimposed on the tensile force existing near the tip of the diagonal crack. Failure occurs when the capacity of the region to sustain the combined compression-tension stress field is exceeded.
Figure2 Effectof transverse reinforcement on path of compressive force, C, in shear span of beam with av/d> 2
It should be noted, however, that the presence of shear forces inevitably gives rise, for equilibrium purposes, to an inclined tensile force within the near-horizontal part of the compressive force path adjacent to the load point. There is no experimental evidence to suggest that the above tensile force can cause failure and the reason for this appears to be the triaxial stress conditions which have always been found to exist within the compressive zone. 3 As discussed for the case of RC beams in flexure, 3 the compressive zone in the region of cross-sections including deep web cracks is subjected to a triaxial compressive state of stress. A part of the vertical component of this compressive state of stress counteracts the tensile stresses which develop in the presence of shear forces and, hence, the combined stress conditions remain compressive.
Transverse reinforcement The effect of transverse reinforcement placed within the shear span of the beams is to delay or even prevent a shear mode of failure within this span. Furthermore, for avid > 2, an additional effect may be that the angle between the longitudinal axis of the beam and the portion of the compressive path within the shear span near the load point increases from an initial near-zero value (Figure l(b)) to a considerably larger value (Figure 2). ~ Such behaviour may induce a wedge-like action in the region of the load point which should cause failure of the compressive zone of the flexure span, where the state of stress is essentially uniaxial, rather than the region of the load point where a triaxial compressive state of stress exists. 2,4 It should be noted that such failure is similar to those classified above as type 1 shear failures and may be brittle since it may occur before the full flexural capacity of the beam is exceeded. It would appear, therefore, that although current shear design procedures may guard against diagonal failure of the shear span, they may not necessarily lead to a ductile type of behaviour that gives adequate warning of impending structural collapse.
Experimental programme The present work is concerned with an attempt to obtain experimental verification of the concepts described in the preceding section regarding the causes of shear failure. The work is based on a comparative study of the behaviour of concrete beams reinforced in accordance with these concepts and that of similar beams reinforced in accordance with the code requirements.
Eng. Struct. 1987, Vol. 9, J a n u a r y
33
Shear failure o f RC beams: M. D. Kotsovos 0.8
av/d 0 V
_l
<2
>2
51
51
~" 0.6 I E Z 0.4
I
,,
l
450
I-
:
0.2
t2
0
0 I
Beam
i
A
J
I
1
I
t
10
20
30
40
50
60
Strain (mm rn- 1)
Figure 4 Stress-strain characteristics of tension reinforcement
I
2~3 I
Ii
I(lll I I I Kllllllllil'll 1
I
i
[(ll
• beam A--without transverse reinforcement • beam B--with transverse reinforcement within the shear span only • beam C--with transverse reinforcement throughout beam span • beam D--with transverse reinforcement within the flexure span in the region of the load points only • Beam E--with transverse reinforcement as for beam D, but with additional top longitudinal reinforcement throughout the shear span
.] ~I0
' [
i t,
•
l
I
I,
D
Beams A and B, with av/d = 2.25 and 3. and beam C, in all cases, had top longitudinal reinforcement throughout their length. The transverse reinforcement consisted of closed hoops of 3 mm diameter mild steel with f~ = 250 N mm-2 and spacing (Sv) of approximately 40 turn. The top longitudinal bars used to form the reinforcement cage had characteristics similar to those of the transverse reinforcement. The beams used to investigate type 1 behaviour had two tension bars, whereas those used to investigate type 2 behaviour had three bars. Beams D and E were only used to investigate type I behaviour.
Illl
Figure3 Details of beams tested: dimensions in mm
Table I Details of concrete used in tests
Testing
Proportions by weight Ordinary Portland cement Coarse sand (with 5 mm aggregate) Fine sand Total water Cube strength at time of testing (N mm 2) Age attesting (mortth)
1 2.07 0,89 0.67 45 2
RC beams The beams tested in the programme were under-reinforced, 1000ram long with a 900ram span and 102ram height × 51 mm width cross-section (Figure 3). Details of the concrete mix used are given in Table I. In all cases, the tension reinforcement consisted of 6 mm diameter deformed bars with a yield stress ( f 0 of 570N mm -2. The bars were bent back at the ends of the beams and anchored within the compressive zone. The stressstrain characteristics of the steel bars used are shown in Figure 4. The a,/d ratios investigated were approximately 1.5 (Type 1 behaviour), 2.25 and 3 (type 2 behaviour). Two beams were tested for each a~/d. Depending on the transverse reinforcement, the beams tested were classified as follows (Figure3):
34
E n g . S t r u c t . 1987, V o l . 9, J a n u a r y
Load was applied in increments of approximately 0.5 kN through a hydraulic ram and spreader beam supported by loading plates of 20ram x 51ram placed with the smaller dimension along the length of the beam. Similar plates were used at the supports as shown in Figure 3. At each increment, the load was maintained at a constant value for approximately 15 s in order to measure the load and the deformation response of the beams. The load was measured by using a load cell and the deformation response by displacement transducers (LVDT) measuring the deflection at the tensile face of both the middle and the loaded sections of the beams. The load and deflections were recorded using a Hewlett Packard computer-logger measuring to a sensitivity of _+0.1 N and ±0.0001 ram, respectively. Results
of tests
The main results of the tests, together with information necessary for their interpretation, are given in Tables 2 and 3 and Figures 5-10. Tables 2 and 3 give the Madcarrying capacity of the beams tested in the programme, while Figures 5, 8 and 9 show the failure modes exhibited by the beams with values of av/d of 1.5, 2.25 and 3.0, respectively. Typical load-deflection relationships for
Shear failure o f RC b e a m s : M. D. Kotsovos
Figure 5 Typical mode of failure exhibited by beams without transverse reinforcement with av/d = 1.5
1.0
Table 2 Load-carrying capacity of beams with av/ d = 1.5
' K .
m
Maximum load (kN)
P -I
Maximum load
0.8 oo
x "-
0.6
0
-~ 0.4
Beam
Measured
Calculated*
Measured/ Calculated
A B C D E
35 41.5 41.5 40 26
40.8 40.8 43 40.8 43
0.86 1.02 0.97 0.98 0.61
* Corresponding to flexural capacity
~
0.2
0 .J
0
0
I
I
5
10
1
Table 3 Load-carrying capacity of beams with a v / d > 2
I
15
20
25
Maximum load (kN)
Deflection (ram)
Figure 6 Load-deflection relationships of beams B, C, D with av/d= 1.5: (--) beam B; ( - - - ) beam C; (- - -) beam D
Maximum load
Measured/
av/d
Measured
Calculated*
Calculated
21.4 16.4
41 30
0.52 0.55
40 30
41 30
0.98
43 31
41 30
1.05 1.04
Beam A 2.25 3
Path of C
Beam B ~ - J
Cc
2.25 3
£
Beam C 2.25 3
[4
av
P-IV
1
* Corresponding to flexural capacity
Cs
C
Discussion o f results
Beams with a,/ d < 2
Figure 7 Effect of top longitudinal reinforcement on path of compressive force, C, within shear span: Cs is the compressive force transmitted by compression reinforcement and Cc the path of C in the absence of top reinforcement
the beams tested are shown in Figures 6 and 10 where, for comparison purposes, the load is expressed in a form normalized with respect to the maximum load sustained by the beams calculated on the basis of the beam fiexural capacity. Finally, Figure 7 indicates the effect of top longitudinal reinforcement on the path of the compressive force within the shear span.
On the basis of the concept of 'shear capacity of a critical section', beams A and D must have a similar load-carrying capacity, since their shear span is without transverse reinforcement, and yet, Table 2 indicates that beam D has a load-carrying capacity significantly larger than that of beam A. Furthermore, the load-carrying capacity of beam D is essentially equal to that of beams B and C, for which the shear span is reinforced in compliance with the code design provisions. The above behaviour indicates that transverse reinforcement placed within the flexure span in the region of load points can be as effective as transverse reinforcement placed within the shear span. Since the shear force within the flexure span is zero, the failure of the beams cannot be associated with the concept of 'shear capacity of a critical section'.
E n g . S t r u c t . 1987, V o l . 9, J a n u a r y
35
Shear failure o f RC beams: M. D. Kotsovos
I-igure 8 Modes of failure exhibited by beams with av/d= 2.25: from top to bottom, beams A, B, C, respectively
Figure 9 Modes of failure exhibited by beams with av/d= 3: from top to bottom, beams A, B, C, respectively
The failure mode shown in Figure _5 indicates that, as discussed in a previous section, the cause of the beam failure is associated with the fact that the diagonal crack, which forms at an earlier load, does not penetrate into the region of the load point and cause crushing of this region as is generally considered. 5 Instead, it by-passes the region of the load point and causes failure of the compressive zone of the flexure span. Placing transverse reinforcement within the flexure span prevents the extension of the diagonal cracks and leads to a significant increase of the load-carrying capacity. Similarly, placing transverse reinforcement within the shear span also prevents the extension of the diagonal crack and, thus, has a similar effect on the load-carrying capacity. Furthermore, placing transverse reinforcement throughout the beam span ha~¢he additional effect of significantly improving ductility (Figure 6). The above results described regarding transverse reinforcement on the load-carrying capacity and ductility
36
Eng. Struct. 1987, Vol. 9, J a n u a r y
of RC beams with av/d< 2 are compatible with those predicted by finite element analysis in a previous work. ~' It is interesting to note in Table 2 that the presence of top longitudinal reinforcement within the shear span of beams without transverse reinforcement (beam E) causes a significant reduction of load-carrying capacity. The cause of such behaviour appears to be associated with the shape of the path along which the compressive force is transmitted from support to support. For beams with av/d < 2 and without compression reinforcement, the portion of this path within the shear span is linear
(Figure 1 (a)).2 The presence of top longitudinal reinforcement changes the shape of the path from linear to curvilinear, since a portion of the compressive force is transmitted by the top longitudinal reinforcement (Figure 7). Such a shape of path gives rise to tensile stresses in the orthogonal direction which lead to failure at an earlier load stage. Failure occurs within the shear span and, as a
Shear failure o f RC beams: M. D. Kotsovos
1.0 0.8
av/d= 2.25
O
E E
0.6
"10
0.4
E x
Softening branch Yes
O _J
x No
0.2
0
I
0
5
I
10
|
I
I
15
20
25
Deflection (mm)
1.0 0.8 0
E
av/d = 3
0.6
0.4 0 _.1
°'ii 0
Figure 10 avid>2
I
I
1
I
I
5
10
15
20
25
Deflection (mm) Load-deflection relationships of beams B, C with
result, in contrast to the behaviour of beams without top longitudinal reinforcement, placing transverse reinforcement only within the flexure span is ineffective.
Beams with av/d > 2 Figures 8 and 9 show the effect of transverse reinforcement on the failure mode of beams with avid equal to 2.25 and 3, respectively. As expected, the beams without transverse reinforcement suffered a diagonal failure of their shear span. Placing transverse reinforcement only within the shear span delayed the occurrence of diagonal cracking in all eases. Collapse occurred due to failure of the compressive zone of the flexure span in the region of the load point. This mode of failure is similar to those observed in previous investigations of the behaviour of reinforced7'8 and prestressed 9 concrete beams. The occurrence within the middle span of inclined web cracks and horizontal cracks along the tension reinforcement is a post-failure phenomenon which is not typical of a bending failure. Figures 8 and 9 indicate that a characteristic feature of the above mode of failure is the absence of significant flexural cracking. Such behaviour may be considered
to indicate that the collapse occurred before the beams attained their flexural capacity. In contrast to this behaviour, the beams with transverse reinforcement throughout their length collapsed after they had suffered considerable flexural cracking. This behaviour is considered to be the cause of the considerably larger ductility exhibited by the beams with transverse reinforcement throughout their length (Figure 10). Furthermore, it should be noted that, while these beams are also characterized by a gradually descending post-peak load deflection relationship, those with transverse reinforcement only within the shear span suffered a complete and immediate loss of load-carrying capacity as soon as a peak level was attained. This supports the argument that placing transverse reinforcement within the shear span only may be inadequate for providing sufficient ductility.2 Since the nominal reinforcement specified by current codes of practice may be inadequate to safeguard against the failure of the compressive zone experienced by the beams tested in this programme, it is recommended that the reinforcement of the shear span be extended by at least a length equal to the beam depth d beyond this span. In addition to the considerable improvement in ductility, Figure 10 indicates that transverse reinforcement throughout the beam length also resulted in a small but finite increase of the load-carrying capacity of the beams. This increase appears unlikely to be due to an enhancement of the compressive strength of concrete caused by the confining effect of the transverse reinforcement. This is because the transverse reinforcement spacing is significantly larger than the depth of the compressive zone and it has been suggested that such spacing cannot lead to an increase of the concrete strength. ~° Instead, it is considered that the amount of transverse reinforcement used merely reduced the detrimental effect of transverse tensile stresses on the load-carrying capacity of the compressive zone. As shown in previous work, 3 significant tensile stresses invariably develop within the compressive zone of the flexure span when the beam is subjected to load levels approaching its loadcarrying capacity.
Conclusions • For avid < 2, the load-carrying capacity and deformational characteristics of RC beams with transverse reinforcement within the flexure span are similar to those of beams with transverse reinforcement within the shear span. • The above behaviour is compatible with the concept that the causes of shear failure are associated with the stress conditions in the region of the path along which the compressive force is transmitted from support to support and not with the shear capacity of critical sections. • For a given av/d < 2, the presence of top longitudinal reinforcement appears to considerably reduce the load-carrying capacity of RC beams without transverse reinforcement. This is considered to occur because the presence of such reinforcement transforms the shape of the path of compressive force into a shape that characterizes a beam with a larger avid. The shape of this path, therefore, appears to be the underlying cause of the dependence of the beam behaviour on a,./d.
Eng. Struct. 1987, Vol. 9, January
37
Shear failure of RC beams: M. D. Kotsovos
• Transverse reinforcement within the shear span only does not necessarily result in adequate ductility. Extending this reinforcement within the flexure span improves ductility considerably.
Acknowledgements The author wishes to thank Messrs. A. Papamakarios and S. Pavlou who carried out the experiments and Dr M. Pavlovic who reviewed the paper and made valuable comments.
References I
2
38
'Code of practice for the structural use of concrete', CP110: part 1, 'Design, materials and workmanship', British Standards Institution, London, 1972, 154 Kotsovos, M. D. 'Mechanisms of shear failure', Mag. Concr. Res., 1983, 35 (123), 9%106.
Eng. Struct. 1987, Vol. 9, January
3
Kots{}v{}s, M. D. 'A iundanlcntal cxplanali{m {}1 Ihc I}uhaxiotu of reinforced concrete beams in flexure based ,}n tl]~.t pr{}pcrtie~ of c{>nerctc under multiaxial slrcss', Malt'r. ~'lt'litl., R I I , K M . 198,2, 15 {9{11,529-537 4 Bobrowski, J. 'Origins {}l satcty in concrete s m t c t u r c s , l'h.D. The.~is, University of Surrey, June 1982, 276 5 Allen. A. H. 'Reinforced concrete design to ('PI IO---simply explained'. Cement and Coner. Assoc., 1974, S6 6 Kotsovos, M. D. 'Behaviour of reinforced concrete beams with shear span to depth ratios between I and 2.52 A ( ' I .l., l'roc., 1984, V81 (3}, 279-286 7 Leonhardt, F. and Walther, R. q ' h c Stuttgart shear tests, 196,1', Translation No, 111, Cement and Concr. Assoc. Library, 134 8 A S C E - A C I Task Committee 426 on Shear and Diagonal Tension o1 the Committee on Masonry and Reinforced Concrete of the Structural Division. 'The shear strength of reinforced concrete members', J. Struct. Div. A S C E . , 1973, 99 {ST6), 1091-1189 9 Pinto, P. E. and Chalzona, R. 'Espericnzc sul c o m p o r t a m e n t o a taglio precompressc a cavi post-tesi', Universita degli Studi di R o m a , Facolta di Architettura, Instituto di Scienza e Tecnica della Construzioni, R o m e , 1971, Publ. 29, 124 1{1 lyengar, S. R., Desayi, P. and Reddy. K, N, 'Stress-strain characteristics of concrete confined in steal binders', Mag. ('oncr, Res.. 197(/, 22 (72), 173-184
It has been suggested in a previous work that the causes of shear failure exhibited by reinforced concrete (RC) beams are associated with the stress conditions in the region of the path along which the compressive force is transmitted from support to support. The work described in this paper presents experimental evidence supporting the above concept. The work is based on a comparative study of the behaviour of concrete beams reinforced in compliance with this concept and that of beams reinforced in compliance with current design procedures. Keywords: shear failure, reinforced concrete Codes of practice, such as C P l l 0 , ~ require structural members to be designed so as to exhibit ductile behaviour, since such behaviour gives ample warning of impending collapse. Shear failures, therefore, are undesirable because of their brittle nature which allows little or no such warning. Current shear design procedures are based on the assumption that shear failures occur when the shear capacity of a critical section is exceeded. Thus, the objective of these procedures is to realistically assess the amount of transverse reinforcement required to carry that portion of the shear force in excess of the value which can be sustained by concrete alone. For beams subjected to two-point loading, the critical section is any section situated within the shear span (av) and, therefore, reinforcing this span in compliance with the current strength requirements is generally considered to safeguard against shear failure. It has, however, been argued elsewhere, 2 that the concept of shear capacity of a critical section is insufficient to describe the underlying causes of the observed behaviour of RC beams, Shear failure appears to be associated with the stress conditions in the region of the path along which the compressive force is transmitted from support to support and not with the shear capacity of particular sections. As a result, it has been suggested that compliance with current design procedures, although preventing shear failure, may not be sufficient to provide adequate ductility.-" The present work, therefore, has been aimed at providing experimental evidence to support the above arguments. This evidence has been obtained from tests on 32
Eng. Struct. 1987, Vol. 9, J a n u a r y
RC beams with various arrangements of transverse reinforcement. The beams have been subjected to two-point loading with values of av varying between approximately 1 and 4 times the beam depth. The fundamental causes of shear failure are discussed concisely and this discussion forms the basis of a comparative study of the strength, deformation and failure characteristics exhibited by the beams tested in the programme. An understanding of these causes is essential for the development of new shear design models compatible with the concept of member rather than section design stipulated by the CEB commission IV (Stuttgart meeting, 9 May, 1984).
Causes of shear failure It is generally considered that the behaviour of RC beams without transverse reinforcement is dependent on the value of the shear span to depth (av/d) ratio. For values of a,/d between approximately 1 and 6, such beams are expected to fail in shear before their flexural capacity is attained. For any other value, the beams should attain their flexural capacity. The behaviour of the latter beams has been the subject of previous experimental work. 3 As stated elsewhere, 2 the causes of shear failure are likely to be associated with the stress conditions in the region of the path along which the compressive force is transmitted to the supports after the occurrence of diagonal cracking; an analytical description of these conditions could lead to the formulation of a lower bound criterion for failure. On the basis of this argument, the shear modes of failure exhibited by the beams under 0141-0296/87/01032-07/ $03.00 © 1987Butterworth & Co (Publishers) Ltd
Shear failure o f RC beams: M. D. Kotsovos --'-_s
Path of C .,_
II---
;l 3_
av
Path of C
I
I~1
c
"1
I1
a 4
8 v
d:
-I
Av c
b Figure 1 Path of compressive force, C, and combinations of compressive and tensile, T, forces causing: (a) type 1, av/d< 2-2.5; (b) type 2, av/d> 2-2.5
two-point loading may be broadly classified into two types:
Type 1 This includes modes of failure which occur in beams with avid smaller than a value between approximately 2 and 2.5. Such beams are characterized by a path of compressive force comprising linear portions, within both the shear and middle spans, intersecting each other in the region of the load point (Figure l(a)). It has been argued that, in spite of the high compressive stresses in the region of the load point, diagonal cracking is unlikely to lead to a crushing mode of failure since the multiaxial compressive state of stress which exists there will cause an increase of the local strength. 2 Instead, the diagonal crack should branch near-horizontally towards the compressive zone of the flexure span of the beam in order to by-pass this high strength region. The tensile stress resultant which exists at the tip of the crack branch combined with the compressive stress resultant due to the bending action will reduce the strength capacity of the compressive zone of the flexure span of the beam. It would be the failure of this region, therefore, that would eventually lead to collapse of the beam.
Type 2 This includes the shear modes of failure which occur in beams with avid larger than a value of between approximately 2 and 2.5. Such beams are characterized by a path of compressive force consisting of two linear portions within the shear span, connected in the region of the tip of the diagonal crack (Figure l(b)). This change in the direction of the compressive force generates, for equilibrium purposes, a tensile stress resultant, intersecting the obtuse angle of the linear portions, which is superimposed on the tensile force existing near the tip of the diagonal crack. Failure occurs when the capacity of the region to sustain the combined compression-tension stress field is exceeded.
Figure2 Effectof transverse reinforcement on path of compressive force, C, in shear span of beam with av/d> 2
It should be noted, however, that the presence of shear forces inevitably gives rise, for equilibrium purposes, to an inclined tensile force within the near-horizontal part of the compressive force path adjacent to the load point. There is no experimental evidence to suggest that the above tensile force can cause failure and the reason for this appears to be the triaxial stress conditions which have always been found to exist within the compressive zone. 3 As discussed for the case of RC beams in flexure, 3 the compressive zone in the region of cross-sections including deep web cracks is subjected to a triaxial compressive state of stress. A part of the vertical component of this compressive state of stress counteracts the tensile stresses which develop in the presence of shear forces and, hence, the combined stress conditions remain compressive.
Transverse reinforcement The effect of transverse reinforcement placed within the shear span of the beams is to delay or even prevent a shear mode of failure within this span. Furthermore, for avid > 2, an additional effect may be that the angle between the longitudinal axis of the beam and the portion of the compressive path within the shear span near the load point increases from an initial near-zero value (Figure l(b)) to a considerably larger value (Figure 2). ~ Such behaviour may induce a wedge-like action in the region of the load point which should cause failure of the compressive zone of the flexure span, where the state of stress is essentially uniaxial, rather than the region of the load point where a triaxial compressive state of stress exists. 2,4 It should be noted that such failure is similar to those classified above as type 1 shear failures and may be brittle since it may occur before the full flexural capacity of the beam is exceeded. It would appear, therefore, that although current shear design procedures may guard against diagonal failure of the shear span, they may not necessarily lead to a ductile type of behaviour that gives adequate warning of impending structural collapse.
Experimental programme The present work is concerned with an attempt to obtain experimental verification of the concepts described in the preceding section regarding the causes of shear failure. The work is based on a comparative study of the behaviour of concrete beams reinforced in accordance with these concepts and that of similar beams reinforced in accordance with the code requirements.
Eng. Struct. 1987, Vol. 9, J a n u a r y
33
Shear failure o f RC beams: M. D. Kotsovos 0.8
av/d 0 V
_l
<2
>2
51
51
~" 0.6 I E Z 0.4
I
,,
l
450
I-
:
0.2
t2
0
0 I
Beam
i
A
J
I
1
I
t
10
20
30
40
50
60
Strain (mm rn- 1)
Figure 4 Stress-strain characteristics of tension reinforcement
I
2~3 I
Ii
I(lll I I I Kllllllllil'll 1
I
i
[(ll
• beam A--without transverse reinforcement • beam B--with transverse reinforcement within the shear span only • beam C--with transverse reinforcement throughout beam span • beam D--with transverse reinforcement within the flexure span in the region of the load points only • Beam E--with transverse reinforcement as for beam D, but with additional top longitudinal reinforcement throughout the shear span
.] ~I0
' [
i t,
•
l
I
I,
D
Beams A and B, with av/d = 2.25 and 3. and beam C, in all cases, had top longitudinal reinforcement throughout their length. The transverse reinforcement consisted of closed hoops of 3 mm diameter mild steel with f~ = 250 N mm-2 and spacing (Sv) of approximately 40 turn. The top longitudinal bars used to form the reinforcement cage had characteristics similar to those of the transverse reinforcement. The beams used to investigate type 1 behaviour had two tension bars, whereas those used to investigate type 2 behaviour had three bars. Beams D and E were only used to investigate type I behaviour.
Illl
Figure3 Details of beams tested: dimensions in mm
Table I Details of concrete used in tests
Testing
Proportions by weight Ordinary Portland cement Coarse sand (with 5 mm aggregate) Fine sand Total water Cube strength at time of testing (N mm 2) Age attesting (mortth)
1 2.07 0,89 0.67 45 2
RC beams The beams tested in the programme were under-reinforced, 1000ram long with a 900ram span and 102ram height × 51 mm width cross-section (Figure 3). Details of the concrete mix used are given in Table I. In all cases, the tension reinforcement consisted of 6 mm diameter deformed bars with a yield stress ( f 0 of 570N mm -2. The bars were bent back at the ends of the beams and anchored within the compressive zone. The stressstrain characteristics of the steel bars used are shown in Figure 4. The a,/d ratios investigated were approximately 1.5 (Type 1 behaviour), 2.25 and 3 (type 2 behaviour). Two beams were tested for each a~/d. Depending on the transverse reinforcement, the beams tested were classified as follows (Figure3):
34
E n g . S t r u c t . 1987, V o l . 9, J a n u a r y
Load was applied in increments of approximately 0.5 kN through a hydraulic ram and spreader beam supported by loading plates of 20ram x 51ram placed with the smaller dimension along the length of the beam. Similar plates were used at the supports as shown in Figure 3. At each increment, the load was maintained at a constant value for approximately 15 s in order to measure the load and the deformation response of the beams. The load was measured by using a load cell and the deformation response by displacement transducers (LVDT) measuring the deflection at the tensile face of both the middle and the loaded sections of the beams. The load and deflections were recorded using a Hewlett Packard computer-logger measuring to a sensitivity of _+0.1 N and ±0.0001 ram, respectively. Results
of tests
The main results of the tests, together with information necessary for their interpretation, are given in Tables 2 and 3 and Figures 5-10. Tables 2 and 3 give the Madcarrying capacity of the beams tested in the programme, while Figures 5, 8 and 9 show the failure modes exhibited by the beams with values of av/d of 1.5, 2.25 and 3.0, respectively. Typical load-deflection relationships for
Shear failure o f RC b e a m s : M. D. Kotsovos
Figure 5 Typical mode of failure exhibited by beams without transverse reinforcement with av/d = 1.5
1.0
Table 2 Load-carrying capacity of beams with av/ d = 1.5
' K .
m
Maximum load (kN)
P -I
Maximum load
0.8 oo
x "-
0.6
0
-~ 0.4
Beam
Measured
Calculated*
Measured/ Calculated
A B C D E
35 41.5 41.5 40 26
40.8 40.8 43 40.8 43
0.86 1.02 0.97 0.98 0.61
* Corresponding to flexural capacity
~
0.2
0 .J
0
0
I
I
5
10
1
Table 3 Load-carrying capacity of beams with a v / d > 2
I
15
20
25
Maximum load (kN)
Deflection (ram)
Figure 6 Load-deflection relationships of beams B, C, D with av/d= 1.5: (--) beam B; ( - - - ) beam C; (- - -) beam D
Maximum load
Measured/
av/d
Measured
Calculated*
Calculated
21.4 16.4
41 30
0.52 0.55
40 30
41 30
0.98
43 31
41 30
1.05 1.04
Beam A 2.25 3
Path of C
Beam B ~ - J
Cc
2.25 3
£
Beam C 2.25 3
[4
av
P-IV
1
* Corresponding to flexural capacity
Cs
C
Discussion o f results
Beams with a,/ d < 2
Figure 7 Effect of top longitudinal reinforcement on path of compressive force, C, within shear span: Cs is the compressive force transmitted by compression reinforcement and Cc the path of C in the absence of top reinforcement
the beams tested are shown in Figures 6 and 10 where, for comparison purposes, the load is expressed in a form normalized with respect to the maximum load sustained by the beams calculated on the basis of the beam fiexural capacity. Finally, Figure 7 indicates the effect of top longitudinal reinforcement on the path of the compressive force within the shear span.
On the basis of the concept of 'shear capacity of a critical section', beams A and D must have a similar load-carrying capacity, since their shear span is without transverse reinforcement, and yet, Table 2 indicates that beam D has a load-carrying capacity significantly larger than that of beam A. Furthermore, the load-carrying capacity of beam D is essentially equal to that of beams B and C, for which the shear span is reinforced in compliance with the code design provisions. The above behaviour indicates that transverse reinforcement placed within the flexure span in the region of load points can be as effective as transverse reinforcement placed within the shear span. Since the shear force within the flexure span is zero, the failure of the beams cannot be associated with the concept of 'shear capacity of a critical section'.
E n g . S t r u c t . 1987, V o l . 9, J a n u a r y
35
Shear failure o f RC beams: M. D. Kotsovos
I-igure 8 Modes of failure exhibited by beams with av/d= 2.25: from top to bottom, beams A, B, C, respectively
Figure 9 Modes of failure exhibited by beams with av/d= 3: from top to bottom, beams A, B, C, respectively
The failure mode shown in Figure _5 indicates that, as discussed in a previous section, the cause of the beam failure is associated with the fact that the diagonal crack, which forms at an earlier load, does not penetrate into the region of the load point and cause crushing of this region as is generally considered. 5 Instead, it by-passes the region of the load point and causes failure of the compressive zone of the flexure span. Placing transverse reinforcement within the flexure span prevents the extension of the diagonal cracks and leads to a significant increase of the load-carrying capacity. Similarly, placing transverse reinforcement within the shear span also prevents the extension of the diagonal crack and, thus, has a similar effect on the load-carrying capacity. Furthermore, placing transverse reinforcement throughout the beam span ha~¢he additional effect of significantly improving ductility (Figure 6). The above results described regarding transverse reinforcement on the load-carrying capacity and ductility
36
Eng. Struct. 1987, Vol. 9, J a n u a r y
of RC beams with av/d< 2 are compatible with those predicted by finite element analysis in a previous work. ~' It is interesting to note in Table 2 that the presence of top longitudinal reinforcement within the shear span of beams without transverse reinforcement (beam E) causes a significant reduction of load-carrying capacity. The cause of such behaviour appears to be associated with the shape of the path along which the compressive force is transmitted from support to support. For beams with av/d < 2 and without compression reinforcement, the portion of this path within the shear span is linear
(Figure 1 (a)).2 The presence of top longitudinal reinforcement changes the shape of the path from linear to curvilinear, since a portion of the compressive force is transmitted by the top longitudinal reinforcement (Figure 7). Such a shape of path gives rise to tensile stresses in the orthogonal direction which lead to failure at an earlier load stage. Failure occurs within the shear span and, as a
Shear failure o f RC beams: M. D. Kotsovos
1.0 0.8
av/d= 2.25
O
E E
0.6
"10
0.4
E x
Softening branch Yes
O _J
x No
0.2
0
I
0
5
I
10
|
I
I
15
20
25
Deflection (mm)
1.0 0.8 0
E
av/d = 3
0.6
0.4 0 _.1
°'ii 0
Figure 10 avid>2
I
I
1
I
I
5
10
15
20
25
Deflection (mm) Load-deflection relationships of beams B, C with
result, in contrast to the behaviour of beams without top longitudinal reinforcement, placing transverse reinforcement only within the flexure span is ineffective.
Beams with av/d > 2 Figures 8 and 9 show the effect of transverse reinforcement on the failure mode of beams with avid equal to 2.25 and 3, respectively. As expected, the beams without transverse reinforcement suffered a diagonal failure of their shear span. Placing transverse reinforcement only within the shear span delayed the occurrence of diagonal cracking in all eases. Collapse occurred due to failure of the compressive zone of the flexure span in the region of the load point. This mode of failure is similar to those observed in previous investigations of the behaviour of reinforced7'8 and prestressed 9 concrete beams. The occurrence within the middle span of inclined web cracks and horizontal cracks along the tension reinforcement is a post-failure phenomenon which is not typical of a bending failure. Figures 8 and 9 indicate that a characteristic feature of the above mode of failure is the absence of significant flexural cracking. Such behaviour may be considered
to indicate that the collapse occurred before the beams attained their flexural capacity. In contrast to this behaviour, the beams with transverse reinforcement throughout their length collapsed after they had suffered considerable flexural cracking. This behaviour is considered to be the cause of the considerably larger ductility exhibited by the beams with transverse reinforcement throughout their length (Figure 10). Furthermore, it should be noted that, while these beams are also characterized by a gradually descending post-peak load deflection relationship, those with transverse reinforcement only within the shear span suffered a complete and immediate loss of load-carrying capacity as soon as a peak level was attained. This supports the argument that placing transverse reinforcement within the shear span only may be inadequate for providing sufficient ductility.2 Since the nominal reinforcement specified by current codes of practice may be inadequate to safeguard against the failure of the compressive zone experienced by the beams tested in this programme, it is recommended that the reinforcement of the shear span be extended by at least a length equal to the beam depth d beyond this span. In addition to the considerable improvement in ductility, Figure 10 indicates that transverse reinforcement throughout the beam length also resulted in a small but finite increase of the load-carrying capacity of the beams. This increase appears unlikely to be due to an enhancement of the compressive strength of concrete caused by the confining effect of the transverse reinforcement. This is because the transverse reinforcement spacing is significantly larger than the depth of the compressive zone and it has been suggested that such spacing cannot lead to an increase of the concrete strength. ~° Instead, it is considered that the amount of transverse reinforcement used merely reduced the detrimental effect of transverse tensile stresses on the load-carrying capacity of the compressive zone. As shown in previous work, 3 significant tensile stresses invariably develop within the compressive zone of the flexure span when the beam is subjected to load levels approaching its loadcarrying capacity.
Conclusions • For avid < 2, the load-carrying capacity and deformational characteristics of RC beams with transverse reinforcement within the flexure span are similar to those of beams with transverse reinforcement within the shear span. • The above behaviour is compatible with the concept that the causes of shear failure are associated with the stress conditions in the region of the path along which the compressive force is transmitted from support to support and not with the shear capacity of critical sections. • For a given av/d < 2, the presence of top longitudinal reinforcement appears to considerably reduce the load-carrying capacity of RC beams without transverse reinforcement. This is considered to occur because the presence of such reinforcement transforms the shape of the path of compressive force into a shape that characterizes a beam with a larger avid. The shape of this path, therefore, appears to be the underlying cause of the dependence of the beam behaviour on a,./d.
Eng. Struct. 1987, Vol. 9, January
37
Shear failure of RC beams: M. D. Kotsovos
• Transverse reinforcement within the shear span only does not necessarily result in adequate ductility. Extending this reinforcement within the flexure span improves ductility considerably.
Acknowledgements The author wishes to thank Messrs. A. Papamakarios and S. Pavlou who carried out the experiments and Dr M. Pavlovic who reviewed the paper and made valuable comments.
References I
2
38
'Code of practice for the structural use of concrete', CP110: part 1, 'Design, materials and workmanship', British Standards Institution, London, 1972, 154 Kotsovos, M. D. 'Mechanisms of shear failure', Mag. Concr. Res., 1983, 35 (123), 9%106.
Eng. Struct. 1987, Vol. 9, January
3
Kots{}v{}s, M. D. 'A iundanlcntal cxplanali{m {}1 Ihc I}uhaxiotu of reinforced concrete beams in flexure based ,}n tl]~.t pr{}pcrtie~ of c{>nerctc under multiaxial slrcss', Malt'r. ~'lt'litl., R I I , K M . 198,2, 15 {9{11,529-537 4 Bobrowski, J. 'Origins {}l satcty in concrete s m t c t u r c s , l'h.D. The.~is, University of Surrey, June 1982, 276 5 Allen. A. H. 'Reinforced concrete design to ('PI IO---simply explained'. Cement and Coner. Assoc., 1974, S6 6 Kotsovos, M. D. 'Behaviour of reinforced concrete beams with shear span to depth ratios between I and 2.52 A ( ' I .l., l'roc., 1984, V81 (3}, 279-286 7 Leonhardt, F. and Walther, R. q ' h c Stuttgart shear tests, 196,1', Translation No, 111, Cement and Concr. Assoc. Library, 134 8 A S C E - A C I Task Committee 426 on Shear and Diagonal Tension o1 the Committee on Masonry and Reinforced Concrete of the Structural Division. 'The shear strength of reinforced concrete members', J. Struct. Div. A S C E . , 1973, 99 {ST6), 1091-1189 9 Pinto, P. E. and Chalzona, R. 'Espericnzc sul c o m p o r t a m e n t o a taglio precompressc a cavi post-tesi', Universita degli Studi di R o m a , Facolta di Architettura, Instituto di Scienza e Tecnica della Construzioni, R o m e , 1971, Publ. 29, 124 1{1 lyengar, S. R., Desayi, P. and Reddy. K, N, 'Stress-strain characteristics of concrete confined in steal binders', Mag. ('oncr, Res.. 197(/, 22 (72), 173-184