After performing the analysis of truss model, the strength evaluation results of nodal zones (concentrated node) can be checked ‘Nodal Zone (Concentrated Node)’. Concentrated nodes are likely to fracture compared to smeared node, so detailed check is needed. The ‘Nodal Zone (Concentrated Node)’ consists of two graphic windows and one calculation window, showing the element forces at node, shape of nodal zones, and strength evaluation results, respectively.

– Technical Reference

1. Shape of Nodal Zone

The shape of a nodal zone is largely determined by two constraints. The first constraint is that all action lines of struts and ties, as well as any external forces, must coincide. The second one is that the widths and relative angles of the struts and ties determine the nodal zone geometry.

1) The shape of a nodal zone is determined by the intersection of the stress fields that are framed into the nodal zone. The boundary of a nodal zone does not necessarily need to be perpendicular to the strut, tie, or bearing plate. It is assumed, however, as shown in Fig. 1, that there is another stress field which affects only the shape of the nodal zone, by expanding the cross-sectional area of a steel tie to the opposite side of the node.

Fig. 1 General Shape of Nodal Zone

2) When more than three elements are connected to a node, the cross-sections of all elements that are framed into the node, instead of the three representative elements, as shown in Fig. 2(b), need to be considered, as shown in Fig. 2(c).

(a) Forces acting on Node

(b) Nodal Zone Shaped by Representative Elements

(c) Nodal Zone Shaped by All Elements

Fig. 2 Nodal Zone Shaped by Multiple Struts and/or Ties

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– Structural shape

– ESO

– Stress Flow

– Truss, Strut and Tie Model

]]>This example requires two truss analyses to include main tension reinforcements in strut-tie model. The design procedure for this example is as follows.

Step 1 : Construct the strut-tie model excluding elements representing main tension reinforcements according to compressive principal stress flow.

Step 2 : After performing the truss analysis, find the vertical reactions at nodes 1 and 2.

Step 3 : After adding the element representing main tension reinforcements in the strut-tie model, the reactions determined in the above model are loaded.

Step 4 : After performing the analysis of modified strut-tie model, perform strength verification of struts, ties, and nodal zones.

Example File Downloads : Foundation_on_Rock.stm

]]>< E. S. O >

< Stress Flow >

< Truss – STM Model >

]]>**1.1 Introduction**

The strut-tie model design of simply supported deep beams is usually conducted by the determinate strut-tie models representing an arch mechanism shown in Fig. 1-1(a), or a truss mechanism shown in Fig. 1-1(b). The cross-sectional forces of struts and ties in these types of strut-tie models are determined regardless of the stiffness of struts and ties.

(a) Strut-tie model representing arch mechanism

(b) Strut-tie model representing vertical truss mechanism

(c) Strut-tie model representing combined mechanism

Fig. 1-1 Typical strut-tie models for reinforced concrete deep beams

The CSA (2004) and AASHTO LRFD (2014) have suggested a basic concept of a strut-tie model that satisfies equilibrium and constitutive relationships, and they have allowed the design of reinforced concrete deep beams with the strut-tie model shown in Fig. 1-1(a). This has influenced the ACI 318-14 (2014) to allow the same model for the reinforced concrete deep beams with the requirement that the angle between a concrete strut and a tie be greater than 25 degrees. When the requirement on the angle is considered, the strut-tie model shown in Fig. 1-1(a) is used for the beams with a shear span-to-effective depth ratio a/d of less than 1.93 (*a*/*z* ≤ 2.14, *z* = 0.9*d*). In addition, according to the design book of the ACI Subcommittee 445-1 (2002), the reinforced concrete deep beams with a/d of larger than 1.93 can be designed by using the strut-tie model shown in Fig. 1-1(b).

FIB (2010) suggested the determinate and indeterminate strut-tie models of Figs. 1-1(a), 1(b), and 1(c) for reinforced concrete deep beams, representing respectively an arch load transfer mechanism for *a*/*z* ≤ 0.5, a truss load transfer mechanism for *a*/*z* ≥ 2.0, and a combination of arch and truss load transfer mechanisms for 0.5 < *a*/*z* < 2.0. As the strut-tie model in Fig. 1-1(c) is the first-order indeterminate truss structure, a load distribution ratio was proposed to calculate the cross-sectional forces of struts and ties by simply employing the force equilibrium equations at nodes. With the proposed load distribution ratio α, varying linearly as a function of *a*/*z* as shown in Eqn. (1-1), the cross-sectional force of a vertical steel tie *P** _{w}* in the truss mechanism of Fig. 1-1(a) is directly obtained from the following equation:

*α* = *P** _{w}* /

In the following sections, the deep beam introduced in ACI Subcommittee 445-1 (2002) is designed by using the three types of aforementioned strut-tie models. The ACI 318M-14 code and the software **AStrutTie** was used in the design.

**Relative Contents**

**AStrutTie** Design Example – 1. Design of deep beams subjected to concentrated load (1)

**AStrutTie** Design Example – 1. Design of deep beams subjected to concentrated load (2)

**AStrutTie** Design Example – 1. Design of deep beams subjected to concentrated load (3)

**AStrutTie** Design Example – 1. Design of deep beams subjected to concentrated load (4)

Enjoy AStrutTie ESO video!

Email : astruttie@aroad.co.kr

]]>Fig.6 Strut-and-tie models for the deep beam with opening for a volume fraction of 17%, a Classic model, b T&C model

Compare AStrutTie with Fig.6(b)

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SP273-1 Bridge Pier – Hammerhead Bent Cap

**Download : 01BridgePier_bentcap.xlsx**

**Download : 01BridgePier_bentcap.stm**

**Introduction**

Initial modeling is performed using a template.

Below are the inputs.

After initial modeling, modeling of ACI SP273-1 was implemented using the Edit function, define Tie Types, and define Strut Types.

Using Edit Function : stretch, move, copy, paste, mirror, etc

Two load combinations were applied and each modeling was applied.

Below are the Project Information inputs.

Below are the General Properties inputs.

Below are the Area Properties inputs.

< Structural Shape and Loads >

< Modeling 1 >

< Modeling 2 >

< ESO >

< Stress Flow >

**Report Preview**

**Download : 01BridgePier_bentcap.xlsx**

**Download : 01BridgePier_bentcap.stm**

**Reference**

ACI-ASCE Committee 445, *Further Examples for the Design of Structural Concrete with Strut-and-Tie Models; SP-273*, American Concrete Institute, Michigan, USA, 2010.

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**2. Excel File(.xlsx)**

**Download : Deepbeam_SI_EC2.xlsx**

**3. Word File (.rtf)**

**Download : Deepbeam_SI_EC2.rtf**

**Download : Deepbeam_SI_EC2.xlsx**

**Download : Deepbeam_SI_EC2.rtf**

**Relative Contents**

**2. Excel File(.xlsx)**

**Download : Deepbeam_SI_AASHTO.xlsx**

**3. Word File (.rtf)**

**Download : Deepbeam_SI_AASHTO.rtf**

**Download : Deepbeam_SI_AASHTO.xlsx**

**Download : Deepbeam_SI_AASHTO.rtf**

**Relative Contents**