 Open Access
 Total Downloads : 206
 Authors : Khattab Saleem Abdul – Razzaq, Alaa Hussein Abed, Hayder Ihsan Ali
 Paper ID : IJERTV5IS050171
 Volume & Issue : Volume 05, Issue 05 (May 2016)
 Published (First Online): 12052016
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Parameters Affecting Load Capacity of Reinforced SelfCompacted Concrete Deep Beams
Khattab Saleem Abdul – Razzaq1 1 Civil Engineering Department, College of Engineering/
Diyala University, Iraq
Alaa Hussein Abed2
2 Civil Engineering Department, College of Engineering Nahrain University, Iraq
Hayder Ihsan Ali3
3 M.Sc. Student
Civil Engineering Department, College of Engineering Nahrain University, Iraq
Abstract : This paper studies the behavior of self compacted concrete (SCC) deep beam and the parameters affecting the ultimate capacity. Eighteen specimens represented by ANSYS 11 program to study the effect of several variables like the percentage of shear span to effective depth ratio (a/d), areas of the web openings, web openings shape, concrete compressive strength (f'c), horizontal stirrups and vertical stirrups on the ultimate capacity of SCC deep beams. The finite element model uses Solid65 to model the SCC deep beams and link180 to model steel reinforcement. All beams are simply supported and tested under two concentrated point loads. All beams have the same dimensions and reinforcement. They have an overall length of 1200 mm, a height of 440 mm and a width of 110 mm. Conclusions showed that reducing the shear span to effective depth ratio (a/d) from 1.2 to 0.8 leads to an increase in ultimate capacity by 20%. The deep beams ultimate capacity increases by 9% after reducing the size of the square opening by 30.5%. The circular openings are recommended more than other web openings shape.
Keywords: – Deep Beams, Shear Span To Effective Depth Ratio (A/D), Web Openings, SelfCompacted Concrete, Horizontal And Vertical Reinforcement, Finite Element.

INTRODUCTION
Deep beams are recognized by comparatively small values of spantodepth ratio. As per code provisions given by American Concrete Institute (ACI 31811) a beam shall be considered as deep beam when the ratio of effective span to overall depth ratio is less than 4.0 or regions with concentrated loads within twice the member depth from the face of the support. Pipes and ducts that intersect structural beams are necessary to accommodate essential services like water supply, sewage, airconditioning, electricity, telephone, and computer network. Usually, the depth of ducts or pipes varies from a couple of centimeters to half a meter. In this paper, the ANSYS 11 finite element program is used to simulate the behavior of selfcompacted reinforced concrete deep beams. The finite element model uses a Solid65 and link180 to model reinforced selfcompacting concrete deep beams.

ANALYTICAL MODEL

Element Types, Real Constants, Material Properties, and Parameters
Characters of the finite elements types were used in modeling the eighteen SCC deep beams and studied by ANSYS program were summarized in Table (1). Each element type in this model has been used to represent a specified constituent of beams.
The real constants need the geometrical properties of the used elements such as crosssectional area, thickness and values of the interface elements. While the material properties need the behavior and characteristics of the constitutive materials depending on mechanical tests such as yield stress, modulus of elasticity, Poisson`s ratio and stress strain relationship.
However, each of the specified types of finite elements had a number of fundamental parameters that are identified in the element library of ANSYS. Values of those element parameters are necessary for similar representation of each test beam as they are used in estimating the elements real constants and material properties. Their numerical values are shown in Table (2).
Table (1): Characteristics and identifications of the selected ANSYS finite element types representative of the main components for all beams
Beam components
Selected element from ANSYS library
Element characteristics
SelfCompacting Concrete
SOLID65
8node Brick Element
(3 Translation DOF per node)
1Reinforcing bars (main, horizontal and vertical stirrups)
2Connector Studs outside interface.
LINK180
2node Discrete Element (3 Translation DOF per node)
Steel Bearing Plate of loading
SOLID45
8node Brick Element
(3 Translation DOF per node)
Table (2): Parameters identifications and numerical values for element types of the present ANSYS model for all beams
Element
Parameter
Definition
Value
Solid65
f'C
Ultimate compressive strength(MPa)
40
ft
Ultimate tensile strength(MPa)
3.9
o
Open shear transfer coefficient
0.15
c
Close shear transfer coefficient
0.85
Ec
Youngs modulus of Elasticity (MPa)
30000
Poissons ratio
0.2
definition of strainstress relationship for concrete (SOLID 65)
Stress (MPa)
0
12
25.63
34.57
40
40
Strain
0
0.0004
0.00098
0.0015
0.00269
0.0035
Link180
Parameter
Definition
Value
Ab
Cross sectional area (mm2)
Steel reinforcing stirrups Ã˜4
13.2
Steel reinforcing main bar Ã˜16
203.655
Fy
Yield strength(MPa) for Ã˜4
Steel reinforcing stirrups Ã˜4
442
Steel reinforcing main bar Ã˜16
614
Es & Et
Modulus of elasticity &strain hardening modulus (MPa)
Es
Steel reinforcing stirrups Ã˜4
205000
Et
Steel hardening Ã˜4
6150
Es
Steel reinforcing main bar Ã˜16
215000
Et
Steel hardening Ã˜16
6450
Poissons ratio
Steel reinforcing bars
0.3
Solid45 (for all tested beams)
Modulus of elasticity (MPa)(assumed)
200000
Poissons ratio
0.3

Modeling and Meshing of the ConcreteMedia and the Bearing Plates
The initial step of modeling includes formation of blocks of the concrete and steel bearing plate volumes. Concrete and steel bearing plate volumes were formed by identifying keypoints of one side edge of the concrete block and the steel bearing plate, then creating lines between these keypoints to establish the areas and volumes that are created by extruding these areas.
After identifying the volumes, finite element analysis needs meshing of the model. Whereby, the model was divided into a number of small elements, to obtain good consequences. The use of a rectangular mesh is recommended to secure good results from the element Solid65. Therefore, rectangular meshing was applied in the present model. The volume sweep command was used to mesh the bearing plate at load points and support regions for deep beam by Solid45 element. This correctly sets the length and width of elements in the bearing plates to be compatible with nodes and elements in the concrete portions of the model. The meshing of concrete and bearing plates at load points and support regions for solid deep beam DB1 are shown in Fig. (1).
Figure (1): Finite element mesh used for concrete and bearing plate of deep beam reference (DB1)

Modeling of Steel Reinforcing Bars
For all alignments of the steel reinforcing bars, LINK180 element was used as shown in Fig. (2) for beam DB1. In spite of volumes meshing for concrete and while volumetric and real meshings are used for the concrete media and the steel plate, respectively, no meshing for LINK180 elements representing the reinforcing steel bars was needed because individual elements were introduced in the model through the nodes created by volumetric meshing of the concrete media.
Figure (2): ANSYS modeling of reinforcing steel bars for beam DB1 (reference)

Loads and Boundary Conditions
The left support was put as hinge support by constraining a single line of bearing plate nodes along the width of the beam soffit in the x and ydirections (i.e Ux =Uy=0), and the right hinge support was put as roller by constraining the ydirection (Uy=0), see Fig. (3).
The external loads were distributed on the single line of the bearing plate nodes across the width of the top surface of the beam, see Fig. (4).
Figure (3): Boundary conditions for simple supports beam DB1

Analysis Type
Figure (4): External loads for beam DB1
The finite element model for this analysis is a simple beam under transverse loading. For the purposes of this model, the Static analysis type is utilized. The Restart command is utilized to restart an analysis after the initial run or load step has been completed. The use of the restart option will be detailed in the analysis portion of the discussion. The Soln Controls command dictates the use of a linear or nonlinear solution for the finite element model. Typical commands utilized in a nonlinear static analysis are shown in Table (3).
Table (3): Commands used to Control Nonlinear Analysis
In the particular case considered in this work the analysis is small displacement and static. The time at the end of the load step refers to the ending load per load step. The sub steps are set to indicate load increments used for this analysis. The commands used to control the solver and output are shown in Table (4).
Table (4): Commands Used to Control Output
All these values are set to ANSYS defaults. The commands used for the nonlinear algorithm and convergence criteria are shown in Table (5). All values for the nonlinear algorithm are set to defaults.
Table (5): Nonlinear Algorithm and Convergence Criteria Parameters
The values for the convergence criteria are set to defaults except for the tolerances. The tolerances displacement is set as 5 times the default values. Table (6) shows the commands used for the advanced nonlinear settings.
Table (6): Advanced Nonlinear Control Settings Used
The program behavior upon nonconvergence for this analysis was set such that the program will terminate but not exit. The rest of the commands were set to defaults.


DETAILS OF BEAM SPECIMENS FOR THE ANALYSIS
Eighteen simply supported reinforced SCC deep beams have the same dimensions and reinforcement. They have an overall length of 1200 mm, a height of 440 mm and a width of 110 mm. All specimens are designed to fail in shear see Fig. (5). The amount of flexural bottom reinforcement for all tested beams is 216 mm (=0.0132 where is the flexural reinforcement ratio). The amount of shear reinforcement for the tested beams is 4 mm @100mm. The beams are tested with an overall clear span (Ln) of 1000 mm under two point symmetric loading which results in a ratio of clear span (Ln) to overall depth (h) equals to (Ln/h=2.3) which is less than 4 [ACI Committee 318M318RM, 2011]. The locations of openings if they exist are at the center of the inclined struts. All these specimens have the same geometry and flexural reinforcement as shown in Fig (5).

PARAMETRIC STUDY
The parametric study presented here consists of analyzing eighteen deep beams which have been modeled using ANSYS numerical program. The parameters considered in this numerical study are: shear span (a) / effective depth (d) = (a/d), openings size, openings shape, concrete compressive strength (f'c) and the effect of the horizontal and vertical stirrups. The variables of the testing program specimens and the summary of test results of all specimens are shown in Table (7).
Table (7): Testing variables considered and testing results.

Effect of Concrete Compressive Strength (f'c):
Load P (kN)
Load P (kN)
Four grades of concrete compressive strength have been used, (Group 1, see Table(7)). It can be noted that the increase in the value of the compressive strength (fc') from 25 MPa to 40 MPa leads to increase the ultimate capacity by 52% and increase the midspan displacement by 63%. The load midspan displacement response for Group 1 are shown in Fig. (6).
700
600
500
400
300 DB1
DB2
200 DB3
100 DB4
0
0 2 4 6 8 10 12 14 16
Displacement (mm)
700
600
500
400
300 DB1
DB2
200 DB3
100 DB4
0
0 2 4 6 8 10 12 14 16
Displacement (mm)
Figure (6): Loadmidspan deflection for Group 1

Effect of openings size:
Load P (kN)
Load P (kN)
To study the effect of web opening size on the ultimate capacity of deep beams, three beams with different square web openings size were provided, (Group 2, see Table(7)). It was noted that the decrease in opening area from 3600 mm2 to 2500 mm2 and then to 1600 mm2 leads to increase in the ultimate capacity by 4% and 5% respectively. The load midspan displacement response for Group 2 are shown in Fig. (7).
700
600
500
400
300
200
100
0
DB5
DB6 DB7
700
600
500
400
300
200
100
0
DB5
DB6 DB7
0 2 4
6
Displacement (mm)
10
12
0 2 4
6
Displacement (mm)
10
12
8
8

Effect of openings shape:
Figure (7): Loadmidspan deflection for Group 2
Load P (kN)
Load P (kN)
Five different shapes of web openings with the same size and location were used in this study, (Group 3, see Table (7)). The locations of openings are in the centers of the inclined struts. All these beam specimens had same geometry, reinforcement, web openings size and tested under two point loads. It is noted that the minimum loss in ultimate capacity (Pu) takes place when the circular openings were used. Where, it is about 18.5%. The load midspan displacement response for Group 3 are shown in Fig. (7).
600
500
400
300
100
0
DB5
DB8 DB9 DB10
600
500
400
300
200
100
0
DB5
DB8 DB9 DB10
0 2 4
6 8 10
12
0 2 4
6 8 10
12
Displacement (mm)
Displacement (mm)
Figure (8): Loadmidspan deflection for Group 3

The effect of using the horizontal and vertical reinforcement:
Four beam specimens are tested to study the effect of using horizontal and vertical stirrups, (Group 4, see Table (7)). It can be noted that the increase in both horizontal and vertical web reinforcement ratios vh and v from 0.0% to 0. 0.0132% leads to increase the failure load by about 44% and also increase the corresponding displacement by about 75%. The load midspan displacement response for Group 4 are shown in Fig. (9).
700
600
500
400
300
200
100
0
DB1
DB12 DB13 DB14
0 2 4 6 8 10 12 14 16
700
600
500
400
300
200
100
0
DB1
DB12 DB13 DB14
0 2 4 6 8 10 12 14 16
Displacement (mm)
Displacement (mm)
Load P (kN)
Load P (kN)
Figure (9): Loadmidspan deflection for Group 4

The effect of shearspan to effective depth ratio (a/d):
The shear failure is mainly dependent on a/d ratio. To study the effect of this important parameter, six beams specimens were analyzed by ANSYS and divided in two Groups according to existing web opening. Group 5 have three solid deep beams with a/d=0.8, 1 and 1.2, respectively and Group 6 have three deep beams having square web openings with a/d=0.8, 1 and 1.2, respectively. The numerical results of ultimate capacity (Pu) and the corresponding midspan deflection (f) for specimens are shown in Fig (10) and Fig (11). It can be observed that when reducing the shear span to effective depth ratio (a/d) from 1.2 to
Load P (kN)
Load P (kN)
0.8 leads to an increase in ultimate capacity by 20%.
700
600
500
400
300
200
100
0
DB1
DB15 DB16
0 2 4 6 8 10 12 14
16
700
600
500
400
300
200
100
0
DB1
DB15 DB16
0 2 4 6 8 10 12 14
16
Displacement (mm)
Displacement (mm)
Load P (kN)
Load P (kN)
Figure (10): Loadmidspan deflection for Group 5
600
500
400
300
200
100
0
DB5
DB17 DB18
600
500
400
300
200
100
0
DB5
DB17 DB18
0 2 4
Displ 6 ement
8 mm)
10
12
14
0 2 4
Displ 6 ement
8 mm)
10
12
14
ac
ac
(
(
Figure (11): Loadmidspan deflection for Group 6


CONCLUSIONS Based on the numerical study, following conclusions are arrived at.

The ultimate loads of deep beams with or without web openings increase when the a/d ratio decreases.

The concrete compressive strength significantly affects the capacity of SCC deep beams.

The increase in both longitudinal and transverse reinforcement ratios leads to an increase in the ultimate load of SCC deep beams

The circular openings make the less decrease in the ultimate capacity of solid deep when compared with rhombus, square, vertical rectangular and horizontal rectangular openings.

The decrease in the web openings size leads to increase the ultimate capacity of SCC deep beams.
REFERENCES

ACI Committee 318M318RM, 2011, Building Code Requirements for Structural Concrete and Commentary, American Concrete Institute, Farmington Hills, Michigan, pp. 503.

ANSYS Manual, Version 11, 2007.

Fafitis, A., and Won, Y. H., Nonlinear Finite Element Analysis of Deep Beams, Journal of Structural Engineering, Vol. 120, No. 4, April, 1994, pp. 12021220.

Mansur M. A. and KiangHwee Tan., "Concrete beams with openings: analysis and design", B. Raton, Florida, CRC Press LLC, 1999, 220 pp.