Analysis of Deep Beam Using Cast Software and Compression of Analytical Strain with Experimental Strain Results

Table of contents

1. Introduction

trut-and-tie modeling (STM) is an approach used to design discontinuity regions (D-regions) in reinforced and prestressed concrete structures. A STM reduces complex states of stress within a D-region of a reinforced concrete deep beam into a truss comprised of simple, uniaxial stress paths. Each uniaxial stress path is considered a member of the STM. Members of the STM subjected to tensile stresses are called ties and represent the location where reinforcement should be placed. STM members subjected to compression are called struts. The intersection points of struts and ties are called nodes. Knowing the forces acting on the boundaries of the STM, the forces in each of the truss members can be determined using basic truss theory. Strain obtained analytical by software was compared with strain recorded experimentally. II. Computer Aided Strut-And-Tie (Cast) Analysis

A research programme was recently conducted to advance the STM for overcoming the aforementioned challenges. In addition to making the design and analysis process using the STM more efficient and transparent, the research aimed to extend the basic use of the STM from a design tool to an analysis tool that can be used for evaluating member behavior and E-mails : [email protected], [email protected], [email protected] there by making it possible to evaluate/validate/extend design code provisions (e.g. dimensioning rules and stress limits) of deep beam. By using a computer-based STM tool called CAST (computer aided strut-and-tie) was developed by Tjhin and Kuchma at the University of Illinois at Urbana-Champaign (2002). This tool is the subject of this paper. CAST facilitates the instruction activities for analysis of reinforced concrete deep beam by STM. This paper considers D-regions that can be reasonably assumed as plane (two-dimensional) structures with uniform thickness and the state of stress is predominantly plane (plane stress condition). Two point loading acting on the D-regions is limited to static monotonic, but can be extended to account for the degradation effects of repeated loading. Only strut-andtie models that consist of unreinforced struts and nonprestressed reinforcement ties are considered. The primary failure modes of the D-regions are the yielding of ties, crushing of struts or nodal zones and diagonal splitting of struts. Failures due to reinforcement anchorage and local lateral buckling are not considered.

2. III. Analytical Modeling Of RC Deep Beam

The strut-and-tie model was analyzed using CAST software. Experimental and analytical deep beam model was having 0.7 m length, 0.4 m depth and 0.15 m thick. The materials properties obtained from material tests will used for concrete and reinforcing steel in the models. By doing so, the strength reduction factor ? was set to unity. The supports where modeled as a vertical reaction on the left support and a vertical and horizontal reaction on the right support The software's capacity prediction feature was used to estimate the capacity using the provided steel reinforcement, concrete struts and nodal zones.

Additionally, the software has a feature that allows analysis of the nodes to ensure that geometry and stress limits are not exceeded. The estimated capacity according to CAST, the failure would occur by yielding of the diagonal tie. This is desirable in STM because it allows the member to fail in a ductile manner as the reinforcing bars yield first before failure, as opposed to brittle failure of the concrete strut. Since equilibrium of the truss with the boundary forces must be satisfied (step 2) and stresses everywhere must be below the limits (step 3 and 4), one can see that the Strut-and-Tie Method is a lower-bound (static or equilibrium) method of limit analysis.

3. Experimental Work

In experimental investigation of deep beam we have taken same size of deep beam of total length 700 mm, depth 400 mm and width 150 mm. Which were casted in concrete technology labarotaty and curring was carried out for 28 days. M25 gread of concrete were used for deep beam. For application of load we have used 1000 kN capacity hydraulic heavy testing machine. To measure deflection dial gauge where placed at central position of bottom of deep beam. to measure strain along mid span we have used strain gauge at equally spacing from top to bottom. Analytical strain obtained By using cast software are tabulated in table 2.

In above table 1, shows experimental strain at mid span of deep beam at definite incremental loading at various depth to understand the nature of strain.

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Figure 1.
are illustrated using the design example of a deep beam. 1. Define the boundaries of the D-Region and determine the boundary forces (the ultimate design forces) from the imposed local and sectional forces. Boundary forces include the concentrated and distributed forces acting on the D-Region boundaries. Boundary forces can also come from sectional forces (moment, shear, and axial load) at the interface of D-and B-Regions. Body forces include those resulted from D-Region self-weight or the reaction forces of any members framing into the D-Region. 2. Sketch a Strut-and-Tie Model and solve for the truss member forces. 3. Select the ordinary reinforcing steel and prestressing steel that are necessary to provide the required Tie capacity and ensure that they are properly anchored in the Nodal Zones. 4. Evaluate the dimensions of the Struts and Nodes such that the capacity of all Struts and Nodes is sufficient to carry the truss member forces. 5. Provide distributed reinforcement to ensure ductile behavior of the D-Region.
Figure 2. Figure 1 :
1Figure 1 : Forces in members by CAST analysis Above figure shows the forces in strut and tie developed in deep beam using CAST software similarly strain and stress are obtained in graphical as well as tabulated form.V.
Figure 3. Figure 2 :
2Figure 2 : Test setup for Deep beam
Figure 4. Figure 3 :
3Figure 3 : Strain measurement of deep beamTable1: Experimental Strain (in mm) Load 100 kN 200 kN 300 kN 400kN 440 kN Depth 150 0.00008 0.00011 0.00022 0.00029 0.00032 100 0.00006 0.00011 0.00026 0.00036 0.00045 50 0.00009 0.00023 0.00052 0.00096 0.00121 0 0.00014 0.00035 0.00072 0.00140 0.00165 -50 0.00005 0.00019 0.00038 0.00080 0.00092 -100 -0.00001 -0.00001 -0.00002 0.00000 0.00000 -150 -0.00009 -0.00015 -0.00035 -0.00038 -0.00039

Appendix A

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Date: 2012-01-15