STRUT AND TIE MODEL FOR PILE CAP REPORT

Phương pháp thiết kế đài cọc bê tông cốt thép theo phương pháp giàn ảo (strut and tie model) theo tiêu chuẩn châu âu EC và Hoa Kỳ ACI. Tính toán cấu kiện bê tông cốt thép theo mô hình giàn ảo theo các tiêu chuẩn nước ngoài

UNIVERSITY OF TRANSPORT Strut and tie model for design of reinforced concrete pile caps Nguyen Thanh Trung Pham Hong Thai Faculty of Civil Engineering HCMC UNIVERSITY OF TRANSPORT Ho Chi Minh City, August 2016 MINISTRY OF TRANSPORT HO CHI MINH CITY UNIVERSITY OF TRANSPORT FACULTY OF CIVIL ENGINEERING Strut and tie model for design of reinforced concrete pile caps Supervisor: Research student: Pham Tien Cuong, Ph.D Nguyen Thanh Trung Pham Hong Thai Ho Chi Minh City, August 2016 Abstract During country modernlizing and developing time, construction industry has developed maturely Many impressive structures have built among the country, as a result, the theory of design of concrete structures has a lot of changes in order to gain a more accurate and effective design TCVN 5574-2012-the structural concrete design standard is the main guide for engineers in Viet Nam, in which the calculation is mostly based on sectional approach This approach is derived from Bernoulli hypothesis that is suitable only for B-region Normally, engineers will apply this design approach for the whole structure which includes both B and D-region In this case, the calculation may not appropriate to the members behaviors Stocky pile caps with high thickness under concentrated load are kind of members that are entirely in D-region which is not well treated by design code International building codes such as Eurocode (EC2), American building code (ACI 318), etc, now present an exact method for design of reinforced concrete in D-region called strut and tie model The model is based on the lower bound theorem of plasticity that ensures the structure is safe under ultimate loading and it also gives the designer a better look of structural behavior Bridge engineers in Viet Nam are also familiar to this method through 22TCN 272-02 but the application of this method in building-pile caps design is still limited Therefore, the main objective of this work is to make a guide of using strut and tie model for design of pile cap with instruction from ACI 318-11 which may take more advantages than traditional bending theory Key words: pile caps, strut and tie model, nodal zone Table of Contents 1.1 History of strut and tie model and specifications 1.2 Definition of B and D-regions 1.3 Lower bound theorem of plasticity 1.4 Design procedure using strut and tie model 1.5 Development of strut and tie model 1.5.1 Strut 1.5.2 Tie 1.5.3 Node and nodal zone 1.6 Constructing strut and tie model 11 1.6.1 Elastic analysis approach 12 1.6.2 Load path approach 12 1.6.3 Standard model 13 1.6.4 Notices on modelling strut and tie model 13 1.7 Analyzing model and ACI provisions 16 1.7.1 Analyzing model 16 1.7.2 ACI provisions for strut and tie model 18 21 2.1 Working mechanism 21 2.1.1 Direct arch action 22 2.1.2 Truss action 22 2.2 Traditional approach 22 2.3 Strut and tie approach 23 2.3.1 Boundary conditions 23 2.3.2 Development of strut and tie model for pile caps 25 2.3.3 Reinforcement and anchorage 27 2.4 Comparison 28 A 30 A.1 Synopsis 30 A.2 Example 1: Two piles – pile cap 30 A.2.1 Pile cap geometry 30 A.2.2 Design calculations 31 A.3 Example 2: Four piles – pile cap 35 A.3.1 Pile cap geometry 35 A.3.2 Design calculations 35 List of figures Figure 1.1 – St.Venant’s principle (Brown et al, 2006) Figure 1.2 – Bernoulli’s hypothesis Figure 1.3: B and D-regions on structures Figure 1.4 – Design flowchart using STM Figure 1.5 – Prismatic strut Figure 1.6 – Bottle shape strut Figure 1.7 – Fan shape strut Figure 1.8 – CCC node Figure 1.9 – CCC node in pile caps Figure 1.10 – CCT node Figure 1.11 – CTT node Figure 1.12 – Hydrostatic nodal zone 10 Figure 1.13 – Non-hydrostatic nodal zone 10 Figure 1.14 – Extended nodal zone at a CCT node 11 Figure 1.15 – Good and poor STM model for pile caps 11 Figure 1.16 – Stress trajectories in deep element 12 Figure 1.17 – Load path approach on deep beam [7] 13 Figure 1.18 – Singular and general model of a 16 piles – pile cap [5] 13 Figure 1.19 – Angle between strut and tie 14 Figure 1.20 – Idealized prismatic strut 15 Figure 1.21 – Resolve struts together 15 Figure 1.22 – Nodal zone geometry 16 Figure 1.23 – Optimizing the height of model 16 Figure 1.24 – Loading condition on the interface of B and D-regions 17 Figure 1.25 – Statically determinate and statically indeterminate model 17 Figure 1.26 – Internally statically indeterminate model 18 Figure 1.27 – Development of anchored length 20 Figure 2.1 – Direct arch and truss action mechanism of shear transfer 21 Figure 2.2 – Provisions of ACI code for strain, stress and rectangular stress diagram 22 Figure 2.3 – Simple modelling of pile cap 22 Figure 2.4 – Moment and shear diagram (neglecting pile cap self-weight) 23 Figure 2.5 – Comparison of simplified analysis and FE analysis 24 Figure 2.6 – Position of applied forces by elastic distribution 24 Figure 2.7 – Position of applied forces at ultimate limit state 25 Figure 2.8 – Vertical position of ties and nodes at the bottom and top face 26 Figure 2.9 – Reinforcement layouts in pile caps 27 Figure 2.10 – Combination of square bunched and grid reinforcement layout 28 Figure A.1 – Plan view of the pile cap 31 Figure A.2 – Analyzing the pile cap for ultimate limit state 32 Figure A.3 – Stress distribution from finite element analysis 32 Figure A.4 – Stress distribution from finite element analysis 35 Figure A.5 – Analyzing the pile cap for ultimate limit state 37 List of tables Table 1.1 – Values of  s for strut strength 19 Table 1.2 – Values of  n for nodal zone strength 19 Table 2.1 – Comparison of FE analysis and simplified analysis 24 Table A.1 – Piles reaction force 35 List of notations a Depth of equivalent rectangular stress block Acs Cross sectional area at one end of the strut Anz The smaller of section through the nodal zone As' Area of compression reinforcement Ats Area of non-prestress reinforcement f ce Effective compressive strength of the concrete strut or nodal zone f c Specific compressive strength of concrete f se Effective stress in prestressing steel (after allowance for all prestress losses) f py Specified yield strength of prestressing steel f p Increase in stress in prestressing steel Fu Factored force acting in strut, tie, bearing area, or nodal zone in a strut and tie model; Fn Nominal capacity of strut, tie, or nodal zone; Fns Nominal strength of concrete strut Fnn Nominal strength of nodal zone Fnt Nominal strength of ties Mn Nominal flexural strength at section Mu Factored moment at section Vn Nominal shear strength Vu Factored shear force at section z Overall height of strut and tie model n Factor to account for the effect of the anchorage or ties on the effective compressive strength of a nodal zone s Factor to account for the effect of cracking and confining reinforcement of the effective compressive strength of the concrete in a strut 1 Factor relating depth of equivalent rectangular compressive stress block to neutral axis depth  Strength reduction factor Chapter 2: Strut and tie model for pile caps Top of footing Centroid of steel a 1 c/2 h/8 center of stress block Figure 2.8 – Vertical position of ties and nodes at the bottom and top face For the case of nodes located directly beneath the column, the position of these nodes relative to the top surface of the footing is an uncertainty From result of many older researches, potential nodal positions are discussed below i) Nodes are located at the top surface of the footing This position is raised by some researchers such as Adebar and Zhou in 1996 However, if it is the case, the effective triaxial confinement of these notdes could not be guaranteed This position also results in a large overall depth of the model which may potentially underestimate the amount of reinforcement ii) Nodes are located at center of rectangular stress block The pile cap is an exceedingly deep member which subjects to loads in a proximity area Therefore, the entire pile cap is expected to exhibit complex D region behavior that is in no way related to flexural member’s behavior iii) Nodes are located at h/8 from the top face This recommendation comes from the research of the flexural compression zone of an elastic column at a beam-column joint made by Paulay and Priestley in 1992 that the height of compression stress block is equal to h/4 Considering the nature of pile caps, application of this suggestion may be improper iv) Nodes coincide with top reinforcement The top mat of steel is necessary to resist shrinkage and temperature effects In some cases, where tensile ties exist near the top surface of pile caps, this position would be truly accepted For the model without ties at the top face, there is no fundamental reason why the nodal locations must coincide with the reinforcement Although there is a high level of uncertainty regarding the nodal locations, Widianto and Bayrak state that “it is believed that the final design outcome is not very sensitive to the exact location of the nodal zone underneath the column” [1] HCMC University of Transport 26 Chapter 2: Strut and tie model for pile caps 2.3.3 Reinforcement and anchorage 2.3.3.1 Reinforcement arrangement As usual, engineers often spread the flexural reinforcement uniformly over the pile cap as described in Grid layout (a) Square bunched layout (b) Cross bunched layout (c) Figure 2.9a This arrangement is mostly created for the simplicity of practical construction and the missing of design technique and experience However, many researchers have shown that by using square bunched reinforcement over the supports can increase the average ultimate failure load up to 20% [5] This advantage is not applied to cross bunched reinforcement layout which is shown in Figure 2.9c Grid layout (a) Square bunched layout (b) Cross bunched layout (c) Figure 2.9 – Reinforcement layouts in pile caps The reasons for the increment in ultimate capacity of pile cap with square bunched reinforcement can be explained as follows:  The natural load path is formed from the column down to the piles where tensile stress concentrates over piles-line This shows a fact that middle reinforced bars in grid pattern will be less efficient than the reinforcement over piles which causes a reduction of strength as from test results HCMC University of Transport 27 Chapter 2: Strut and tie model for pile caps  In square bunched layout, there are many reinforced steel bars crossing each other over piles which results in a better confinement at nodal zone, an enhancement of the strength of struts and also guaranties the anchorage thus increase the ultimate strength However, if designers intend to use square bunched reinforcement only, at service stage, excessive cracking may occur and special attention should be pay for crack control There are some more reasons which cause the use of square bunched layout become unrealistic such as difficulties in construction, reducing the effective height, etc Therefore, specialists recommend the application of combination of both square bunched and uniform grid layout as shown in Figure 2.10 This method possess the valuable advantages of the two layouts while increases strength and reduces cracking The maximum bars spacing in this case should rely on code provisions for crack control Figure 2.10 – Combination of square bunched and grid reinforcement layout 2.3.3.2 Anchorage 2.4 Comparison This section provides the comparison of the two approaches: traditional-sectional method and strut and tie model Since the use of stirrup and other materials is not affected, the comparison is mostly pay attention on the amount of flexural reinforcement resulting from two methods More detail of the calculation should be referred to appendix A Table 2.2 – Comparison of result from two design methods Design method Strut and tie model Traditional approach Disparity HCMC University of Transport Area of reinforcement (mm2) Example Example 319.1 362.65 12% 28 Chapter 2: Strut and tie model for pile caps HCMC University of Transport 29 APPENDIX A DESIGN CALCULATIONS A.1 Synopsis The design of pile caps are presented in two examples Each example performs the design with one unit load case by two methods Three dimensional strut and tie model is attempted to be built for the case of piles-pile cap since the use of a set of two dimensional model may oversimplify the rather complex stress distribution within the footing and can lead to unconservative specified amounts of reinforcement A.2 Example 1: Two piles – pile cap A.2.1 Pile cap geometry The considering 800mm thick pile cap is shown in Figure A.1 which is 500mm wide and 1250mm long It supports a 300mm square column and is in turn supported by two precast concrete pile, each 250mm square The pile cap is subjected to the ultimate axial load from the super structure of 769.3kN and the moment of 12.6kNm Concrete grade B20 and reinforcement grade AIII (comply with Vietnamese design standard [2]) are supposed to be used for the pile cap Material properties are given below, more detail of properties conversion from TCVN 5574-2012 [2] to ACI 318-14 [3] should be referred to other publications Concrete grade B20: compressive strength, f c  16 MPa Reinforcement grade AIII: yield strength, f y  390 MPa HCMC University of Transport 30 Appendix A: Design Calculations 769.3 kN 12.6 kNm 125 250 500 250 125 125 250 300 500 800 300 500 250 125 Figure A.1 – Side and plan view of the pile cap A.2.2 Design calculations A.2.2.1 Reaction forces The precise estimation of piles reaction force are very complicated due to lots of affected factors as mentioned in section 2.3.1.1 Therefore, in this design example, the simplest method which assumed the pile cap is rigid is used Calculations are shown in equations below 769.3 12.6  0.375   P1   0.3752  0.375  367.9 kN   Mx N  P  n i  12.6  0.375 n  P  769.3  xi  401.5 kN  2  i 1 0.375   0.375    In equations above, structural self-weight of the pile cap is supposed to be small compared to the ultimate load from the super structure and thus, is neglected However, this is not always the case In some large and thick pile cap, neglecting pile cap loading could lead to an unconservative design A.2.2.2 Sectional approach The pile cap is analyzed by assumptions given in section 2.2 This the most common method for estimating maximum moment and shear at critical section The calculation of some needed variables are also performed HCMC University of Transport 31 Appendix A: Design Calculations 500 M=90.3 kNm 401.5 kN 225 Figure A.2 – Analyzing the pile cap for ultimate limit state Maximum moment M  P2  x2 = 401.5  0.225 = 90.3kNm Effective height d  0.9h 0.9  800 = 720mm = Height of rectangular stress block 2M u  90.32 106 a d   720   20.8 mm 0.85  16  0.9  500 0.85 f c b Amount of reinforcement required Mu 90.32 106 As    362.6 mm2 a 20.8     f y  d   0.9  390   720   2    A.2.2.3 Strut and tie model approach In section 1.6, there are three common ways to develop a strut and tie model including elastic analysis, load path approach and standard model This example is intended to give guideline to construct the model in two methods The following figure demonstrates stress distribution resulted from finite element analysis A CSI FEA software – SAP2000 is used Figure A.3 – Stress distribution from finite element analysis HCMC University of Transport 32 Appendix A: Design Calculations As seen in the analysis, two compression struts are formed from the column down to the piles, the tension tie obviously resists tensile stress at the bottom Therefore, the suitable model should be built close to a triangular form Suppose the bottom reinforcement is 14mm in diameter and the top reinforcement is 12mm Overall height of the model is: z  800  100  12  14  662 mm 769.3 kN 25 662 367.9 kN 112 kN kN B 512 6k N A C 401.5 kN Figure A.4 – Forces in struts and tie Reinforced steel bar of 20mm in diameter are used to enhance strength of the column, then, the lever arm between centroid of compressive reinforcement and tensile reinforcement is b  300   25  20  230mm  Fcomp  FTens  Pu  769.3 kN   Fcomp  439.4 kN   0.23 0.23  FTens   12.6 kNm  FTens  329.8 kN  Fcomp  2  The result of FTens is negative that shows both FTens and FComp are compression a) Calculate reinforcement From the model illustrated above, simple analysis process gives the tensile force in tie BC of 112kN The amount of resisting reinforcement then can be computed as: Fu 112  103 As    319.1mm 0.9 f y 0.9  390 b) Nodal strength check Node B and C which are subjected to compression forces of 367.8kN and 401.5kN respectively are classified as CCT node, thus equation from section 1.7.2.2 with modified factor  n of 0.8 are applied HCMC University of Transport 33 Appendix A: Design Calculations Fnn  Anz f ce where f ce  0.85   n  f c  0.85  0.8  16  10.9 MPa Anz  250  250  62500 mm2   0.75 (clause 9.3.2.2 [3]) Then,  Fn  0.75  62500 10.9 103  510kN  Satisfactory Node A located right under the column is the connection of three concrete struts Concrete confinement and triaxial stress state in this case create a better strength of nodal zone Since value of related factors  n should be taken as 1, concrete effective strength is equal to 13.6MPa Then,  Fn  0.75  90000 13.6 103  918kN  Satisfactory c) Strut strength check The model proposed contains two concrete struts AB and AC However, since the area cross section at nodes are equivalent, the check should only be carried out for strut AC which is subjected to a higher compression force The projection of the strut on the nodal zone, in this case, is in form of a rectangular with two sides as below w s  wt cos  lb sin   214cos68.50  250sin 68.50  329.2 mm 214 mm 32 9.2 mm Extended nodal zone Nodal zone 250 mm The nominal strength of the strut: Fns  f ce Acs where fce   0,85s fc' ;0,85n fc'   0.85  0.75 16  10.2MPa Acs  wsb  329.2  250  82300 mm2 Then,  Fn  0.75  82300 10.2 103  629kN  Fu  512kN  Satisfactory HCMC University of Transport 34 Appendix A: Design Calculations A.3 Example 2: Four piles – pile cap A.3.1 Pile cap geometry The pile cap in the second example is 1800mm thick while two other sides are 5600mm wide It supports a rectangular column of 800 by 1100mm The pile cap is subjected to the ultimate axial load from the super structure of 10289.2kN Bending moment about X and Y axis are 854.5kNm and 1580kNm respectively This loading is totally carried by four bored concrete piles which are 1200mm in diameter Concrete grade B30 with compressive strength of 25 MPa and reinforcement grade AIII are supposed to be used for design and construction of the pile cap Y 1200 400 5600 1200 2400 X 400 2400 1200 800 5600 1100 1200 400 400 Figure A.5 – Stress distribution from finite element analysis A.3.2 Design calculations A.3.2.1 Reaction forces The calculations of piles reaction force are similar to the first example However, since the pile cap considered is subjected to biaxial compression The equation given in section A.2.2.1 should be modified accordingly P N M x yi M y xi  n  n n  yi  xi i 1 i 1 Calculation results are summarized in the table below Table A.1 – Piles reaction force Piles xi xi m HCMC University of Transport m yi yi m m P kN 35 Appendix A: Design Calculations -1.8 1.8 -1.8 1.8 tổng 3.24 3.24 3.24 3.24 12.96 -1.8 -1.8 1.8 1.8 tổng 3.24 3.24 3.24 3.24 12.96 2234.2 2673.1 2471.5 2910.4 A.3.2.2 Sectional approach The design is carried out similar to those in section A.2.2 for both orthogonal directions respectively a) Reinforcement in X direction M  ( P2  P4 )  d  (2673.1  2910.4)  1.25  6979.3 kNm Maximum moment d  0.9h  0.9  1800  1620 mm Effective height Height of rectangular stress block a  d2  2M u  6979.3  106  16202   40.7 mm 0.85  25  0.9  5600 0.85 f c b Amount of reinforcement required Mu 6979.3  106 As    12430.4 mm2 a 40.7     f y  d   0.9  390  1620   2    b) Reinforcement in Y direction M  ( P3  P4 )  d  (2471.5  2910.4)  1.4  7534.6 kNm Maximum moment d  0.9h  0.9  1800  1620 mm Effective height Height of rectangular stress block 2M u  7534.6  106 a d   1620   44 mm 0.85  25  0.9  5600 0.85 f c b Amount of reinforcement required Mu 7534.6  106 As    13433.2 mm2 a 44     f y  d   0.9  390  1620   2    HCMC University of Transport 36 Appendix A: Design Calculations 1250 Y I II II 1400 X I Figure A.6 – Analyzing the pile cap for ultimate limit state A.3.2.3 Strut and tie model approach In section 1.6, there are three common ways to develop a strut and tie model including elastic analysis, load path approach and standard model This example is intended to give guideline to construct the model in two methods The following figure demonstrates stress distribution resulted from finite element analysis A CSI FEA software – SAP2000 is used As seen in the analysis, two compression struts are formed from the column down to the piles, the tension tie obviously resists tensile stress at the bottom Therefore, the suitable model should be built close to a triangular form Since the column is subjected to biaxial compression, it is more complicated to determine the position of the neutral axis Xác định tải trọng tác dụng lên mô hình giàn ảo Do cột bị uốn nén hai phương, ta quy đổi moment từ hai phương phương M u  M x2  M y2  854.52  15802  1796.2 kN m Nu  10289.2kN Ta phân lực tác dụng vào cột Phương trình trục trung hòa tiết diện chân cột M N M 10289.2 854.5 1580    x y y x  y x0 0.8  1.13 A Ix Iy 0.8  1.1 1.1 0.8 12 12 y HCMC University of Transport 37 Appendix A: Design Calculations Suppose that the use of 14mm steel bar is applied for the bottom reinforcement while on the top, reinforcement of 12mm in diameter is used The overall height of the model is computed as distance between the bottom and the top reinforcement, explanation of this choice should be referred to section 2.3.2 h  800  100  12  14  662 mm  Fcomp  FTens  Pu  769.3 kN   0.23 0.23  FTens   12.6 kN m  Fcomp  2   Fcomp  439.4 kN   FTens  329.8 kN Ta thấy FTens  nên lực lực nén Kiểm tra khả chịu lực giằng BC Lực nén giằng BC giải từ mô hình: Fu  112 kN As  Fu 112 1000   319.1mm2 0.9 f y 0.9  390 Kiểm tra khả chịu lực vùng nút Vùng nút dạng C-C-T gồm nút B nút C Khả chịu lực vùng nút Fu   Fn Fn  Acn f cu f cu  m f c Trong  tra theo bảng (mục 5.7.5 AASHTO LRFD (2010)) HCMC University of Transport 38 Appendix A: Design Calculations HCMC University of Transport 39 References Dean Deschenes and Oguzhan Bayrak Chris Williams, Strut and Tie Model Design Examples for Bridges, 2012 Ministry of Construction, TCVN 5574-2012: Concrete and Reinforced Concrete Structures - Design Standard, 2012 American Concrete Institute, Building Code Requirements for Structural Concrete (ACI 318M-14) and Comentary (ACI 318RM-14), 2014 D.A and Collins Kuchma, M.P., Strut and Tie Model for the Design of Pile Caps: An Experimental Study, 1990 Gautier Chantelot and Alexandre Mathern, Strut and Tie Modelling of Reinforced Concrete Pile Caps, 2010 K.H Reineck, Examples for Design of Structural Concrete with Strut and Tie Models, 2002 Jorg Schlaich, Toward a Consistent Design of Structural Concrete, 1987 HCMC University of Transport 40 [...]... for strength using strut and tie model HCMC University of Transport 4 Chapter 1: Strut and tie model 1.4 Design procedure using strut and tie model The design procedure of strut and tie model can be summarized as the flowchart in Error! Reference source not found below Separate B and D-regions Determine the reaction forces and the boundary conditions Determine a sufficient STM model Determine the forces... singular model of a 16 piles – pile cap subjected to axial load and its general model when considering moment about two axes (a) (b) Figure 1.18 – Singular and general model of a 16 piles – pile cap [5] 1.6.4 Notices on modelling strut and tie model When building a strut and tie model, there are some notices that designer should keep in mind 1.6.4.1 Angle limitation When an inclined compression strut. .. Development of anchored length HCMC University of Transport 20 CHAPTER 2 STRUT AND TIE MODEL FOR PILE CAPS This chapter provides special attention for applying strut and tie model for the design of pile caps which is the main aim of this paper work In order to get a good understanding, basis of working mechanism and traditional approach of pile caps have to be mentioned first 2.1 Working mechanism In a cracked... method for disturbed regions like pile caps is STM which is recommended by researchers and codes as well Aims and limitations This work is done with the main aims of comparing the differences between traditional and STM design method for the design of pile caps and also making a guide for designers when they want to apply STM for pile caps Due to limitation of time and knowledge, the pile caps modeled... conditions Determine a sufficient STM model Determine the forces in members Calculate reinforcement Check struts and nodal zones Provide reinforcement and anchorage Figure 1.4 – Design flowchart using STM HCMC University of Transport 5 Chapter 1: Strut and tie model 1.5 Development of strut and tie model Strut and tie model are apply within D-regions It is a conceptual framework where the stress distribution... other This type of struts is called fan-shape strut Figure 1.7 – Fan shape strut 1.5.2 Tie A tie is an internal member under tension within a strut and tie model Ties may consist of reinforcement, a portion of the concrete that is concentric with and surrounds the axis of the tie and any special detail reinforcement The tie area is defined by the surrounding concrete Although the tensile capacity of the... Chapter 2: Strut and tie model for pile caps 2.1.1 Direct arch action The process of transferring forces from application points to supports without the use of vertical tie are called direct arch action In this action, only compression struts in concrete and tension ties in flexural reinforcement are used to transfer the load 2.1.2 Truss action In a slender beam or a pile cap supported by piles, force may... – Moment and shear diagram (neglecting pile cap self-weight) However, application of deep beam method seems to be limited by the complex of pile cap geometries and loading For instance, when a 4 piles – pile cap is subjected to biaxial compression, reactions from piles are totally different and are also not on the same plane, thus, create difficulties and confusion in design 2.3 Strut and tie approach... can consider pile caps and the superstructure in a single model, they could obtain a more reliable result HCMC University of Transport 1 CHAPTER 1 STRUT AND TIE MODEL 1.1 History of strut and tie model and specifications In 1890’s, German engineer named Wilhelm Ritter introduced the ideal of design concrete beam using truss analogy where reinforcing steel bars would carry tensile forces and concrete... Transport 8 Chapter 1: Strut and tie model Figure 1.10 – CCT node c) CTT node CTT note is the intersection of two tensile forces and one compressive force, it is often located “inside” the STM and classified as smear node Figure 1.11 – CTT node 1.5.3.2 Hydrostatic and non-hydrostatic nodal zone In order to build-up a strut and tie model and proceed the design, the geometries and forces of each components ... structure for strength using strut and tie model HCMC University of Transport Chapter 1: Strut and tie model 1.4 Design procedure using strut and tie model The design procedure of strut and tie model. .. using strut and tie model 1.5 Development of strut and tie model 1.5.1 Strut 1.5.2 Tie 1.5.3 Node and nodal zone 1.6 Constructing strut and tie. .. Provide reinforcement and anchorage Figure 1.4 – Design flowchart using STM HCMC University of Transport Chapter 1: Strut and tie model 1.5 Development of strut and tie model Strut and tie model are