Design and Detailing of Structural Concrete Using Strut-and-tie Models
Strut and Tie Modelling of Reinforced Concrete Deep Beams
Abstract and Figures
Numerical analysis of the performance of reinforced concrete (RC) deep beam subjected to static and fixed-point pulsating loading at the midpoint has been investigated. Three-dimensional nonlinear finite element model using the Strut and Tie approach was adopted. The damage level under the influence of the applied fixed pulsating loading is higher than the static applied loading, hence early crack was observed because of the stepwise loading in the form of vibration. Although the Strut and Tie approach gave a good estimation of the resistance capacity of the beam, the beam undergo high shear damage when subjected to these two types of loading. Material strength properties, applied loadings and cross-sections adopted are some of the factors that affect the performance of the deep beam.
Beam dimension and strut and tie layout A beam of 1m, a width of 400mm and the total length of 2.4 m were adopted. The beam self-weight is calculated as part of the applied load, the solution for the Strut and tie (STM) is given as; The reaction regarding Figure 3, í µí± í µí°´=µí°´= í µí± í µí°µ = 1000 í µí±˜í µí± The shear span to depth ratio of this beam is less than 2, therefore, the beam is considered as the disturbed region (D region). Since the beam is symmetrical, the developed STM layout in Figure 3 consists of the strut in compression and the tie in tension. The width of the bearing plate is assumed as 200 mm, the upper nodes are usually located at a distance, c, equal one-quarter of the width of the bearing plate. Which is 50 mm. hence, the distance is assumed as 50mm. The length of the diagonal strut C1 is;
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Al-Nahrain Journal for Engineering Sciences NJES 23 (3)306-312 , 2020
http://doi.org/10.29194/NJES.23030306
NJES is an open access Journal with ISSN 2521- 9154 and eISSN 2521-9162
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
306
Strut and Tie Modelling of Reinforced Concrete Deep Beams Under
Static and Fixed Pulsating Loading
Ajibola Ibrahim Quadri
Authors affiliations:
1) Department of Civil
Engineering, The Federal
University of, Akure-Nigeria.
dgeneral1201@gmail.com
Paper History:
Received: 22nd April 2020
Revised: 29th June 2020
Accepted: 14th Aug. 2020
Abstract
Numerical analysis of the performance of reinforced concrete (RC)
deep beam subjected to static and fixed-point pulsating loading at the
midpoint has been investigated. Three-dimensional nonlinear finite element
model using the Strut and Tie approach was adopted. The damage level
under the influence of the applied fixed pulsating loading is higher than the
static applied loading, hence early crack was observed because of the
stepwise loading in the form of vibration. Although the Strut and Tie
approach gave a good estimation of the resistance capacity of the beam, the
beam undergo high shear damage when subjected to the se two types of
loading. Material strength properties, applied loadings and cross-sections
adopted are some of the factors that affect the performance of the deep
beam.
Keywords: Deep Beam, Fixed Pulsating Load, Static Load, Strut and Tie Model
1. Introduction
Reinforced concrete (RC) structures are subjected
to various deterioration such as concrete spalling,
cracks, large deformation, rebars rupture, and
collapse during their service time. This is caused by
environmental and man-made factors; aging of the
structures, reinforcing bar corrosion, earthquakes,
blasts, overloading, etc. [1]. The behavior of some RC
members is dominant under shear failure while some
experienced flexural failure or bending. Some parts of
RC structures are overestimated with certain accuracy
during design, while other parts are designed using
the rules of thumb or based on experience. However,
all parts of structures are important and must be
treated accurately because of the nonlinear behavior
of concrete [2]. When the span-to-overall depth ratio
of a beam (l/d) equal to 4 or less, or the shear span-
to-overall depth ratio of a beam (a/d) is equal or less
than two, the beam is termed a deep beam. It is often
loaded at the face and supported at the opposite face.
Deep beams are qualified by having a shear span-
depth ratio (a/d) relatively small Figure 1, [3] thus,
their behavior is dominant under shear rather than
flexure and their capacity depends on the mode of
application of load and supports condition. Many
investigations have been conducted on the behavior
of a simply supported RC deep beam under static
loading [3,4], however, some RC deep beams are
under the influence of pulsating loading such as the
vibrating machine. Their behaviors are different when
compared to the static loading [5].
Figure (1): Common types of struts and tie
1.1 Research Significance
Deflection of RC deep beam under static loading
is always apparent and allows users to evacuate
before the total failure, however, little or no warning
is given under the pulsating types of loading. Due to
the heterogeneous constituents of concrete, load
stress generated under pulsating load is always lower
than that of the static stress capacity, thus, crack
initiation to propagation may not be apparent before
failure. By using the structs-and-ties approach, the
bond behavior of the RC beam can easily be analyzed
under continuum model. The results of the past
NJES 23 (3)306-312 , 2020
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307
experimental investigations show that the bond-zone
response of RC structure is highly nonlinear and
always affected by the stress-strain state of the
structure [5]. Hence, strut and tie approach is
proposed to model the bond strength in the RC deep
beam
2. Struct s and Ties Consideration
The truss analogy was introduced by Ritter [6],
and Morsch [7] more than a century ago, to show the
emergence of internal stresses in a cracked beam,
which is the basis for the design of concrete beams.
This method was improved and extended to be struts
and ties by Leonhardt [8], Rusch [9] and Kupfer [10].
Thereafter, Collins and Mitchell, [ 11] further
investigated the deformation of the truss model and
came up with a refined approach for shear and
torsion. Demerdash, [12 ] considered a nonlinear
finite element approach to design the behavior of
deep beam, it was reported that cracking patterns,
deflections, failure mode, and stress-strain
distributions, cannot be determined with the strut-
and-tie model.
Strut and Tie models (STM) are one of the
approaches to describe stress growth and distribution
developed in a continuum structural field. The action
of external loading resulting in flexure, shear,
compression, torsion is initially borne by the material
constituents in the microscopic level, the overall
effect is visible as a failure because once the material
is completely in the plastic region, relatively low
additional resistance to increase loading is exhibited.
Strut and Tie models are basically a truss
analogy that essentially depends on the limit analysis
of the lower bound theorem of collapsed load [13]. In
this case, only the equilibrium and the yield criterion
are satisfied with stress generalization. Hence, in
reinforced concrete structures, members subjected to
compression termed as Struts are the concrete. The
strut transfers stresses from node to other nodes and
may be reinforced as structural elements or a typical
wall. While the members in tension consist of the
steel reinforcement are the Ties that transfer tensile
stresses to the nodes. On many cases, transverse
reinforcement is provided to prevent the splitting of
the RC caused by transverse tension due to the high
compressive stress generated by the struts. The shape
of the strut depends upon the stress path from which
the strut emerges, and details of any tension joined to
the tie, [14]. Struct are classified into three as shown
in Figure 1, Prismatic structs are mainly adopted to
model the compressive stress block of a beam
member. When the section at the end of the strut is
well defined but the rest of the struct is not confined
to a specific portion of the member, Bottle-shaped
strut is adopted to model the section, Compression
fan strut emerges when stresses flow from a large
source to a smaller source.
ACI 318R-19 [1 5] has been adopted for the
analysis of the strut and tie model in this study. The
strength of concrete in compression depends on the
multi-ax ial state of stress and the disturbance from
reinforcement and cracks. The effective compressive
strength of the concrete strut is given in Eq. 1 as;
(1)
is the cylindrical concrete compressive
strength and
for the cube concrete
compressive strength. is the effective factor for
concrete strut which accounts for the stress
conditions, geometry and the crack angle surrounding
the strut. The values of for various conditions
adopted for this investigation according to the ACI
318R-19, [15] is presented in Table 1. The tie cross
section area, , is taken as constant along its length
and is obtained from the tie force and the yield stress
of the steel, . The nominal strength of a tie Ft is
expressed in Eq. 2 as;
(2)
Table (1). Strut and Node Efficiency Factor
According to ACI 318M-11
Strut and Node Efficiency
Struts with uniform cross-section
over its length
Bottle-shaped strut with
reinforcement
Bottle-shaped strut without
reinforcement
Struts in the tension member
The compressive strength of concrete at the
nodal zone depends on the tensile straining from tie
intersection, confinement provided by compressive
forces and the confinement by the transverse
reinforcement. To distinguish between the
confinement condition and straining for the nodal
zone, Figure 2 presents the node classification.
➢ C-C-C is the nodal zone bounded by
compression strut only,
➢ C-C-T is the nodal zone bounded by
compression struts and a tension tie,
➢ C-T-T is the nodal zone bounded by a
compression strut and two tension ties, and
➢ T-T-T is the nodal zone bounded by tension
ties only.
Figure (2): Nodes Classification
The effective compressive strength of concrete in
a nodal zone,
is given in Eq. 3 as;
(3)
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308
is the effectiveness strength factor of a nodal zone
as given in Table 1.
The nominal compressive strength of a nodal zone,
is given in Eq. 4 as;
(4)
is the minimum of the area of the nodal zone
where the force acts.
3. A numerical scheme for the beam
verification
To determine the reinforcement for the simply
supported deep beam in Figure 3, an assumed
factored load of 2000kN was used, a concrete
cylindrical strength, , steel yield stress
Figure (3): Beam dimension and strut and tie layout
A beam of 1m, a width of 400mm and the total
length of 2.4 m were adopted. The beam self-weight
is calculated as part of the applied load, the solution
for the Strut and tie (STM) is given as;
The reaction regarding Figure 3,
The shear span to depth ratio of this beam is less
than 2, therefore, the beam is considered as the
disturbed region (D region). Since the beam is
symmetrical, the developed STM layout in Figure 3
consists of the strut in compression and the tie in
tension. The width of the bearing plate is assumed as
200 mm, the upper nodes are usually located at a
distance, c, equal one-quarter of the width of the
bearing plate. Which is 50 mm. hence, the distance is
assumed as 50mm.
The length of the diagonal strut C1 is;
The force in strut
The force in
The angle between and T,
3.1 Effective concrete design strength of
struts and nodes
The effect of concrete design strength of the
struts and nodes are calculated using the cylindrical
concrete compressive strength as given in Eqs. 1 and
3 respectively.
The strut strength for the inclined strut by
adopting for the bottle-shaped is;
The strut strength for the inclined strut by
adopting for the prismatic shape is;
The effective design strength of the node using
the cylindrical compressive strength for various nodes
classification and adopting equivalent in Table 1,
can be calculated as;
At A, the node component is C-C-T thus,
At B, the node is C-C-C,
The bearing stress generated from node B is given as
For the section at the interface between strut C 2
and the node, the design strength should be the
smaller of the node strength and the strut strength,
both of which are the same in the case of 25.5 MPa.
The required width of strut C2 is calculated as
The difference between the assumed width of
C2 =100 mm and the required width is on the safe
side and is not significant, there is no need for
dimension modification.
NJES 23 (3)306-312 , 2020
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309
The required width for the strut C1 is calculated
as;
(5)
The corresponding stress is given as;
(6)
The stress generated at node A is given as
3.2 Required Reinforcement
Since the strut joining nodes A and B has a
bottle-shaped stress field, transverse reinforcement of
the strut is required to resist a total force.
Strut C1 requires transverse reinforcement as;
The total required reinforcement perpendicular
to the strut is;
The total length of C1 is calculated as 1204.16
mm, hence the required transverse reinforcement is
, hence, a 10 mm
diameter bar of 100 mm spacing is provided.
Tie T:
The reinforcement required to resist the force of this
tie is;
hence, is provided.
4. Finite Element Model and Loading
Three-dimensional nonlinear finite element model
of the RC deep beam was adopted, the option is to
present the hexagonal behavior of the nodes in an
element. The meshing of the individual RC element
has been achieved with the Concrete Model of 3-
Dimension software package which allows the
simulation of nonlinear response of concrete
structures, the software allows the two materials
(concrete and steel) to have a common node with a
common element bonded together. The beam
supports are made of elastic material which is simply
supported. Figure 4 shows the model of the deep
beam with the calculated reinforcing bar detailing.
The model ensures proper bonding between the
reinforcement and the concrete.
Table 2 shows the material strength properties of
the concrete, reinforcement and the elastic support.
Two kinds of loads; a static load at the top of the
beam, was applied on each node with its magnitude
calculated, and a pulsating load (this was applied by
loading and unloading on each beam) as shown in
Figure 4. The pulsating load was step-wisely applied
on the nodes with the loading and unloading within
0.003 seconds, by adopting 5 time-step.
Numerical FEM investigation of the of the beam
was carried out with the help of the Concrete Model
of 3-Dimension. The beam was discretized into 894
elements, each element has the same dimension, and
1420 nodes.
Figure (4): 3-dimensional FE model of Deep beam with rebar detailing
Table (2). Material Strength and Properties
Concrete Compressive
strength (MPa)
Strain softening
coefficient
4.1. Cracks Delineation
The crack formed in the deep beam was
evaluated in terms of the localized principal stresses
and strains generated in the discretized critical
element along the flexural cracks as expressed in Eqs.
7 and 8. Localized damage was evaluated using the
combined stress-strain effect from the reinforced
concrete element of the deep beam. Once the load
reaches the ultimate value, the maximum yield strain
is simultaneously reached hence further loading does
not have an impact on the failure of the beam.
NJES 23 (3)306-312 , 2020
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310
(7)
(8)
➢ and are the diagonal tensile stress and the
strain of in the reinforced concrete beam,
➢ and are the normal stress and strain,
➢ and are the orthogonal stress and strain
to the corresponding normal stress and strain
➢ and are the shear stress and strain caused by
the shear force along the corresponding normal
and orthogonal stress-strain.
5. Global Damage Mode of the Deep
beam
The failure mode of a deep beam is characterized
by a deep inclined crack that appears to form within
the shear span that does not depend on the flexural
cracks. The cracks are initiated at the bottom of the
beam near the support and propagate towards the
face of the beam, Figure 5, this is cumulated with the
compressive damage by the applied load at the region
of the point load. The global damage forming a tied
arch action. Such behavior has been linked to result
from the stresses sustained by the tension bar
transferred to crack concrete through bond effect at
the ultimate state.
Figure (5): Damage Mode of Deep Beam
Figure 6 shows the principal strain of the damage
mode of the beam when subjected to static load (left)
and fixed-point pulsating load (right) at the midpoint.
Concrete crack was initiated at an applied static load
of about 350 kN at the bottom face of the beam
close to the supports, while crack initiation for the
fixed pulsating loads was around 195 kN equivalent
to about 55 percent of the static load. Propagation of
the cracks flows diagonally across the beam up to the
compression zone forming a bottle-shape. Flexural
crack was formed when the fixed pulsating load was
applied as shown at the underside of the beam, this is
due to the stepwise application of the pulsating load.
Tension bar rupture leads to the rupture of the
reinforcement at the compression zone in Figure 6
(right). Due to prolong loading, cracks of concrete
were formed across all the stirrups and fracture
occurred at least in the first two stirrups close to the
supports. Rupture of stirrup close to the right
support
occurred at around a hundred thousand
(100,000) cycles under the fixed pulsating loading
accounting for a low strain less than 2000μ and total
failure of the beam occurred at over 500,000 cycles.
Figure 7 shows the analytical response of the deep
beam under the static and fixed-point pulsating load
with the maximum capacity of 3360 kN and 3390 kN
respectively which shows the same agreement. This
increase to about 60% of the ultimate force, the
curves exhibit an initial elastic relationship, with
deviation from linearity at around 300 kN and 150
kN for the static and pulsating forces that correspond
to the crack initiation phase. Crack propagation is
symptomatic of increasing loading until the
nonlinearity causes the variation in failure. Quasi-
brittle failure of the concrete in both cases of the
applied load is formed. Strain softening increases in
the fixed pulsating case with larger deflection
compared with the static case.
NJES 23 (3)306-312 , 2020
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311
Figure (6): The principal strain of the Damage Mode of the Deep beam (a) Static point load (left) (b) Fixed-point
Pulsating load (right).
Figure (7): Load-Deflection Response of the beam Figure (8): stress-strain comparison of the static and
the under pulsating loading Static and Fixed Pulsating Load.
The softening properties of the stress-strain
relation adopted in the constitutive model are mesh
dependent which is defined by the finite element of
the beam model; thus, similar meshes are used and
are adjusted to eliminate the inconsistency in the
fracture energy. The strain-softening coefficient in
the plain concrete is considerably higher than the
reinforced concrete element so that damage is
delimitated by the total global failure of the material
(see Table 2).
Figure 8 shows the stress-strain comparison of
the static and the pulsating loads. A localized crack of
the tensile element pickup as shown by a white
rectangle was analyzed as discussed in section 4.1.
there is an agreement between the static and the
pulsating loading up to the proportional limit before
deviation at stress over 250 MPa corresponding to
strain 1600μ. There is an increase in strain at constant
stress between the two curves after their
corresponding yield strain before the failure of the
static load. At the constant stress, the fixed pulsating
load undergoes unloading and further reloading
forming a loop around 7000μ strain which leads to
loss of energy. Total failure formed by the curves is
elasto-plastic fracturing.
6. Conclusion
Behavior of deep beam subjected to static and
fixed pulsating load has been numerically analyzed
using the strut and tie approach, the following
conclusions are therefore reached.
1. The strut and tie model is efficient in calculating
the various stresses generated in the beam, and
hence reasonable estimate of the load carrying
capacity of the analyzed reinforced concrete deep
beam.
2. The 3-dimensional FE analysis of the normal
strength concrete analyzed yielded an accurate
anticipated response as deep beams are
susceptible to shear damage. The shear failure
occurred near the support and propagated up to
the compression zone. Concrete crushing was
observed at the loaded point in case of the
applied fixed pulsating load, this occurred
immediately before the shear crack grows towards
the compression zone at about 500 thousand
cycles.
3. The level of damage is higher under fixed
pulsating loading when compared with static
loading even at lower stress because of the
stepwise loading of the beam, and as the concrete
stress increases, the crack strength also increases.
7. References
[1] Lateef, H.T., Ibrahim, A.Q., "Human Error
Uncertainties for Structural Detailing in Reinforced
Concrete Buildings" . Proceeding of School of
0
500
1000
1500
2000
2500
3000
3500
4000
0 0.5 1 1.5 2
Force (kN)
Deflection (mm)
Static Force
Pulsating Force
0
50
100
150
200
250
300
350
02000 4000 6000 8000 10000
Shear Stress (MPa)
Shear Strain (µ)
Static stress
Pulsating stress
NJES 23 (3)306-312 , 2020
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Engineering and Engineering Technology FUTA. pp.
766- 779. August 2108.
[2] Ajibola, Q. I. (2019). "Reliability Appraisal of
Nominal Eccentricity of Short Reinforced Concrete
Column Designed to BS 8110 and Eurocode (EN:2)-
Ultimate Limit State on Fatigue ". Reliability
Engineering and Resilience.
https://doi.org/10.22115/rer.2019.197264.1013 .
[3] Abdul-Razzaq, K. S., Jalil, A. M. & Jebur, S. F.
Behaviour of reinforced concrete deep beams in
previous studies. IOP Conf. Ser.: Mater. Sci. Eng.
518, 022065 (2019).
[4] Saleem Abdul-Razzaq, K. & Farhan Jebur, S.
Suggesting alternatives for reinforced concrete deep
beams by reinforcing struts and ties. MATEC Web
Conf. 120, 01004 (2017).
[5] Zhi-Q. L., H., Zhao, H and Zhongguo J. M., Kim,
T.H., Cheon, J.H., Shin., H.M., "Evaluation of
behavior and strength of prestressed concrete deep
beams using nonlinear analysis". Computers and
Concrete 9, 63– 79.
[6] Ritter, W., "Die bauweise hennebique
(hennebiques construction method)." Schweizerische
Bauzeitung (Zurich), 33(7), 59-61. 1899
[7] Mörsch, E., "Concrete Steel Construction (Der
Eisenbetonbau). English Translation of the 3rd
German Edition." McGraw-Hill Book Co., New
York. 1909.
[8] Leonhardt, F., "Reducting the shear reinforcement
in reinforced concrete beams and slabs". Magazine
Concrete Research: 17(53): p187.December 1965,
[9] Rusch, H., "Researches toward a general flexural
theory for structural concrete." Journal of ACI, 57(7),
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[10] Kupfer, H., "Erweiterung der Möhrsch'schen
Fachwerkanalogie mit Hilfe des Prinzips vom
Minimum der Formänderungsarbeit (Expansion of
Mörsch's truss analogy by application of the principle
of minimum strain energy)". CEB Bulletin: 40: Paris.
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[11] Collins M. P. and Mitchell, D. "A rational
approach for shear design-The 1984 Canadian code
provisions, "ACI Journal 1986, 83(6), pp 925-933.
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[12 ] Demerdash, W. E., El -Metwally, S. E., El -
Zoughiby, M. E., and Ghaleb, A. A., "Strut-And-Tie
Model and 3-D Nonlinear Finite Element Analysis
for The Prediction of The Behavior of RC Shallow
and Deep Beams with Openings," p. 21. 2014.
[13] Chen, W. F, and El-Metwally, S. E,
"Understanding Structural Engineering from Theory
to Practice". CRC Press, New York. 2011.
[14] Schlaich J., and Schafer, K., "Design and
Detailing of Structural Concrete Using Strut-and- Tie
Models". The Structural Engineering., V.69, No. 6,
pp 113-125. 1991.
[15 ] ACI Committee 318-19 Building Code
Requirements for Structural Concrete and
Commentary.American Concrete Institute, 2019.
ResearchGate has not been able to resolve any citations for this publication.
This paper studied reinforcing struts and ties in deep beams based on the Strut-and-Tie Model (STM) of ACI 318M-14. The study contained testing 9 simply supported specimens, divided into 3 groups. The difference between the groups was the loading type which was 2-concentrated forces, 1-concentrated force and uniformly distributed load. Each group contained three specimens; the first specimens in each group were conventional deep beams as references which had a length of 1400 mm, a height of 400 mm and a width of 150 mm. The second specimens were the same as references in dimensions, but with removing shoulders. In addition, only the paths of struts & ties of STM were reinforced in the second specimens as compression and tension members, respectively. The third specimens were the frames that took their dimensions from STM of ACI 318M-14. From the experimental work, it is found that the proposed frames were good alternatives for the references despite the small loss in ultimate capacity. However, these proposed frames already carried loads greater than the factored design loads of STM. In comparison with the references, these proposed frames provided 41-51% reduction in weight, 4-27% reduction in cost besides providing front side area about 46-55%.
The Strut-and-Tie Model, STM, has been widely applied for the design of non-flexural and deep members in reinforced concrete structures. In this paper, strut-and-tie models for selected (shallow and deep) beams with openings, have been suggested based on the available experimental results of; crack patterns, modes of failure, and internal stresses trajectors obtained from elastic finite element analysis. The proposed STM approach is, then, applied to one group of simple shallow beams and one group of simple deep beams tested experimentally. In addition, a three-dimensional nonlinear finite element analysis using ANSYS 12.0 computer program has been employed for two selected (shallow and deep) beams which were analyzed using the STM method. Some of the important factors affecting the behavior of reinforced concrete beams (named: concrete compressive and tensile strength, span to depth ratio, shear span to depth ratio, physical and mechanical properties of horizontal, vertical web reinforcement and main steel, loading position, opening dimensions and location) are investigated throughout a parametric study with the aid of the nonlinear finite element analysis. With such analysis, results of cracking patterns, deflections, failure mode and strain and stress distributions, that cannot be determined using the strut-and-tie model, are obtained. A comparison of the finite element results with test results and STM results has been carried out.
- Michael P. Collins
-
![Denis Mitchell]()
The 1984 Canadian Concrete Code contains new shear design provisions that are believed to be more rational and more general than the shear regulations of the 1983 ACI Building Code. This paper summarizes the new shear design procedures and illustrates their use by means of design examples.
-
![Tae-Hoon Kim]()
- Ju-Hyun Cheon
- H.M. Shin
The purpose of this study is to evaluate the behavior and strength of prestressed concrete deep beams using nonlinear analysis. By using a sophisticated nonlinear finite element analysis program, the accuracy and objectivity of the assessment process can be enhanced. A computer program, the RCAHEST (Reinforced Concrete Analysis in Higher Evaluation System Technology), was used for the analysis of reinforced concrete structures. Tensile, compressive and shear models of cracked concrete and models of reinforcing and prestressing steel were used to account for the material nonlinearity of prestressed concrete. The smeared crack approach was incorporated. A bonded or unbonded prestressing bar element is used based on the finite element method, which can represent the interaction between the prestressing bars and concrete of a prestressed concrete member. The proposed numerical method for the evaluation of behavior and strength of prestressed concrete deep beams is verified by comparing its results with reliable experimental results.
- J. Schlaich
So-called 'details' are as important for a structure's behaviour and safety as the standard problems of design which are covered in the Codes. A unified design concept which covers also the details consistently for all types of concrete structure is described in this paper. It is based on strut-and-tie models, including the truss model for beams as a special case. After the principles of the method and the modelling process are explained, simplified rules are proposed for dimensioning all the individual members of the model and their nodes. Some examples show the application of the method and demonstrate, also, its use for the improvement of the conceptual design of details.
Reliability Appraisal of Nominal Eccentricity of Short Reinforced Concrete Column Designed to BS 8110 and Eurocode (EN:2)-Ultimate Limit State on Fatigue
- Q I Ajibola
Ajibola, Q. I. (2019). "Reliability Appraisal of Nominal Eccentricity of Short Reinforced Concrete Column Designed to BS 8110 and Eurocode (EN:2)-Ultimate Limit State on Fatigue". Reliability Engineering and Resilience. https://doi.org/10.22115/rer.2019.197264.1013.
Behaviour of reinforced concrete deep beams in previous studies
- K S Abdul-Razzaq
- A M Jalil
- S F Jebur
Abdul-Razzaq, K. S., Jalil, A. M. & Jebur, S. F. Behaviour of reinforced concrete deep beams in previous studies. IOP Conf. Ser.: Mater. Sci. Eng. 518, 022065 (2019).
Design and Detailing of Structural Concrete Using Strut-and-tie Models
Source: https://www.researchgate.net/publication/346230175_Strut_and_Tie_Modelling_of_Reinforced_Concrete_Deep_Beams
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