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3. Calculation of the Diagonal Length (R) at the Joint
Let’s verify the safety of the culvert joint.
In the structures we design, where is the section that receives the greatest force?
While forces act on various sections such as the areas where forces are applied and Supports, the joints, where the structure is connected, will experience the greatest forces.
Joints are the areas where two or more components meet and where forces are transmitted. Failure at the joints is a critical part that can lead to the collapse of the entire structure.
Therefore, it is essential to conduct a thorough examination of the joints, and in the case of concrete structures, the design should include measures such as haunches and reinforcement placement to enhance the stiffness of the joints when necessary.
Today, we will explore the evaluation methods for joints in culverts, which are commonly used in various civil engineering projects such as roads and waterways.
1. Overview
In the case of a culvert, the joint between the culvert sections is typically designed with a haunch to ensure greater rigidity. It takes on the following shape.
Figure 1. Culvert Joint
The haunch commonly installed in culverts refers to a “section where the cross-sectional area of the culvert is larger in the region where relatively large bending moments are present at the ends compared to the central portion. It is primarily installed near the support of continuous beams or in the vicinity of the node of Rahmen.” Ultimately, these haunches serve to enhance the stiffness of the joints (intersection points) where loads (moments) are concentrated.
When performing calculations for culvert joints, it is not easy to define the required cross-sections for tensile stress calculations and calculate the diagonal length needed to determine the section under tension due to the installation of haunches.
2. Examination of Joints
The examination of culvert joints follows the KDS 44 90 00: 2021 Road Culvert Structural Design Standards.
First, the usage tensile stress of the joint is calculated, and it is compared with the design tensile strength. If necessary, reinforcement bars are placed after the examination.
When examining the usage tensile stress, the combination loads of the Serviceability Limit State (SLS) are applied. If reinforcement bars are required, the combination loads of the Ultimate Limit State (ULS) are applied according to KDS 14 20 24. The reinforcement bars are calculated using the strut-tie model.
The decision for the placement of reinforcement bars is based on the following conditions:
Usage tensile stress (ft) ≥ Design tensile strength (fctk): Placement of reinforcement bars
Usage tensile stress (ft) < Design tensile strength (fctk): Reinforcement bars are not necessary
Here,
Usage tensile stress (ft): The stress induced in the diagonal direction of the cross-section due to the outermost joint moment caused by the combination load I in the Serviceability Limit State.
Design tensile strength: Fctk = 0.7 x fctm (fctm = 0.3 x (fcm)^(2/3), fcm = fck + Δf)
Here, Δf refers to the reference in KDS 24 14 21, section 3.1.2.1.
The formula for calculating the usage tensile stress of culvert joints is as follows:
When the closing moment acts on the outermost tension bending moment of the culvert joint, the tensile stress is distributed along the diagonal direction of the joint section, as shown in the diagram below:
Considering the stress distribution shown in the diagram, the usage tensile stress of the diagonal section can be approximately calculated as follows:
Calculation of usage tensile stress (ft):
The length of the diagonal R at the joint is defined as shown in the diagram below:
Figure 3. Length of diagnoal R in culvert joints The calculation of the diagonal length at the joint requires a somewhat complex process when performed by an engineer.
3. Calculation of the Diagonal Length (R) at the Joint
The cross-section used for calculating the usage tensile stress is shown in the diagram below. The most important dimension in this case is the length of the diagonal, R, which should be calculated considering the haunch.
Figure 4. Dimensions used for calculating the diagonal length at the culvert joint
The derivation process of the calculation formula for the diagonal length (R) at the culvert joint is as follows:
Derivation of the Diagonal Length (R) at the Joint
Using the derived formula from the above process, the value of the diagonal length (R) required for calculating the usage tensile stress can be determined.
After calculating the value of the diagonal length (R), the tensile stress of the concrete can be calculated according to the proposed method in the design standards. This allows for the examination of the need for reinforcement bars.
4. Conclusion
The joint is one of the most crucial parts in terms of the safety of a structure, as it is a region where loads are concentrated. Therefore, a precise evaluation should be conducted for this section.
Among them, the consideration of the haunch at the culvert joint posed a challenge in terms of evaluation through analytical calculations due to the calculation of the diagonal length of the joint.
While using midas Civil for structural analysis allows for calculations considering various conditions at the joint, we have provided a method in this content to perform a preliminary evaluation through analytical calculations.
In practical design, it is often necessary to reinforce the joint as the usage tensile stress caused by the moments acting on the haunch rarely satisfies the design tensile strength. In such cases, the calculation of reinforcement bars should be performed using a strut-tie model.
In the next content, we will explain the calculation method for reinforcement bars using a strut-tie model for the haunch at the culvert joint.
👉Please fill out the Download Section (Click here) below the Comment Section to download the Calculation Sheet for Culvert Joint Tesile Stress.
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