Hello, Engineers! Today, we will be discussing calculations for reinforced concrete slabs with openings, specifically hollow core slabs.

Hollow core slabs

Hollow core slabs are a popular structural members used in civil, industrial, and transportation projects. The presence of through holes in these structures significantly reduces material costs and, consequently, the weight of the element, making them an economical choice. As designers, this is a crucial factor to consider.

These slabs are typically made of reinforced or prestressed concrete and are used as prefabricated elements. Each slab section is combined with other sections in direction, perpendicular to the span, with the required number of sections selected based on the building's dimensions.

Since multi-cell slabs serve as supporting elements, it is crucial to calculate them accurately.

Why calculate the slab?

The slab is a crucial structural member of any building or structure. Calculating its strength and load-bearing capacity is essential to ensure the safety and stability of the entire structure.

There are various situations where a slab's calculation may be necessary. For instance, when designing a new, custom slab, it's vital to perform calculations. However, even if you are using typical designs such as the 1ПК, 2ПК series, etc., a verification calculation may be necessary under the following circumstances:

• unclear data on the load for which the slab is designed
• designing a building for a load that differs in value or layout from what is specified in the technical documentation
• using slabs manufactured in another country or according to different standards
• assessing the actual condition of an existing structure, and so on
• in any case, neglecting to perform the necessary calculations can lead to structural failures, safety hazards, and increased costs

Utilizing Digital Solutions to Calculate Hollow Core Slabs

In this article, we will highlight the critical importance of checking hollow core slabs for bending moments. Neglecting this calculation can result in potentially disastrous consequences, making it a crucial step in the design process for structures subjected to bending loads.

To aid in this task, we have developed a dedicated digital solution: a ready-to-use text report that operates within the TechEditor environment. This report automates all calculations, including section numbering, formulas, and tables, providing a convenient and standalone document that can be utilized for design work immediately after downloading.

Let's delve into how to work with the report.

Automated Features in the Report

Our report provides automated features for the following elements:

• text styles that maintain the uniform format of repeated text elements
• page numbering to enhance readability
• numbering of sections, figures, tables, and formulas to ensure consistency and ease of navigation
• sources of information to cite references and support the calculations
• table of contents to help readers locate specific sections easily
• mathematical calculations to obtain accurate results efficiently

Title page

The title page of our report is designed to provide a clear overview of the calculation process. It includes essential information such as the project title, the date of the calculation, the client's name, and the engineer's name. We believe that a clear and informative title page can help to enhance the credibility of the report and provide a professional impression to stakeholders.

All pages, except the title page, have their own footer number starting from 1. You can configure the title page's specific properties by going to Project > Page Setup in the menu:

Table of Contents

On the second page, you'll find the table of contents. The paragraph numbers and page numbers are assigned programmatically, but each line of content is added manually. You can use two universal objects in TechEditor to create any numbered sequences and references to them: Label and Reference. These commands are located on the Numbered Sequences toolbar:

To work with numbered sequences, you need to create them in the manager. Each sequence covers one level of numbering. For example, if your report only requires single-level numbering (such as only chapters), then you need to add one numbered sequence.

To add a new sequence, use the Add button in the manager. You can modify existing sequences using the Modify button and delete them using the Delete button. In our report, we have numbered sections, paragraphs, and sub-items. They are referred to as H1, H2, and H3 in the manager, respectively.

Each image, table, formula, and information source in this report also has its own number, and the corresponding sequences have been created for them. In total, this report uses seven independent lists of numbers.

To insert a number in the report, use the New Label command. A dialog box will appear with three fields: Format, Keyword, and Title. The Format field is mandatory and should contain special tags enclosed in curly braces. For example, the {N1} tag means that we want to see the current value of the sequence that is stored in the manager under the number 1. In our case, this is the numbering of sections.

The next section is located a few pages from the current one. You can use the New Label command again, or you can copy the previous label and edit its tag to {N1+}. The plus sign means that one should be added to the current section number. Make sure that this mechanism works (if the data in the report did not update automatically, press F5):

To automate the numbering of the second paragraph in the second section, first, we write the section tag {N1}, then add a dot, and then write the paragraph tag {N2+}. Note that the dot is not a mandatory element here — we only added it because we want to see this symbol as a separator of numbers. In general, this can be any other symbol or symbols. That is, you can format labels as you like (clear syntax is only necessary for tags).

Some labels in this report have the Keyword and Title fields filled in. These fields are used for references. The Keyword field contains unique text, which is then indicated in the reference. The Title field is used for the title and is displayed in the reference if you include the {T} tag in the format. Thus, the table of contents is organized. You can find more information about this in our Knowledge Base.

Input Data

Now let's return to the report. The introductory section provides general information such as a description of the design, the problem statement, calculation assumptions, and input data. The "Input Data" paragraph is particularly important as it sets all the initial parameters for the calculation. Coefficients are assigned simple numerical values, and physical quantities are given corresponding units of measurement.

What You Need to Know About Mathematics in TechEditor

To perform mathematical calculations and display them in the report, TechEditor provides two main elements: Math Object and Math Latex Object. The former is used to insert expressions that don't require a strict scientific presentation, while the latter is used for writing formulas in canonical mathematical notation and displaying intermediate parameter values. By using the Math Latex Object, all calculations performed in the report can be depicted in any form.

It's worth noting that starting from version 3.3, TechEditor supports the following Cyrillic units of measurement: с (second), м (meter), кг (kilogram), Н (Newton), and Па (Pascal). TechEditor 3.3 also supports all multiple and fractional Cyrillic prefixes for SI units of measurement. Therefore, the following units are also acceptable: мм, см, дм, мс, нс, кН, МН, кПа, МПа, and others.

For more information about mathematical calculations in TechEditor, please refer to our Knowledge Base.

ULS Analysis of the Slab

Design Model Description

Let's discuss the design model of the slab. In the vertical plane, the slab functions as a beam that is hinged at the supports. The cross-section of the slab is assumed to be a rectangle, which is a valid assumption if the slab is not subjected to significant concentrated forces that can cause the webs of the slab to collapse due to local compression. In this context, the "webs" refers to the vertical parts of the cross-section formed by the edges of adjacent openings. Since the slab in question is only subjected to surface loads, uniform stress distribution in the cross-sections occurs. The tapered shape of the openings additionally helps to reduce stress concentration.

All calculations in the report are performed using the section method and simplified models of the behavior of reinforced concrete structures. For instance, a bilinear relationship between stress and strain of concrete is used, and a uniform distribution of normal compressive stress in the compressed zone is assumed. The lower part of the slab contains the working reinforcement bars that directly resist tensile forces.

Loads

The slab is subjected to both live and dead loads, including a crowd of people, partitions, floor screed, parquet board, and its own self-weight. First, characteristic values of loads are determined, and then, factored loads are calculated. All calculations, including factor values, are automated. For example, the reliability coefficient for a live load is determined using the following formula:

yfm1:=if{cp1<(2 kPa)}(1.3 1.2)

This textual formula contains a special "if" function that compares the characteristic value of the load "cp1" with 2 kPa, as specified in the design standards. If the load is less than 2 kPa, the function returns the value "1.3", otherwise, it returns the value "1.2". This approach is recommended for all calculations.

Slab strength checking

The third section of the report focuses on verifying the plate's strength under bending moment. This verification is one of the main checks for structures according to the ultimate limit state (ULS).

As we know, the strength of a member is considered to be provided if the bending moment at a certain section does not exceed the resistance moment. The maximum bending moment in the slab is calculated based on the intensity of the distributed load and the beam's length, and the resistance moment is determined by the geometric characteristics of the cross-section and material properties. The final ratio of the moments should not exceed unity.

The report concludes with a list of the information sources used.

Conclusions

The report uses data and recommendations from the following regulatory documents of Ukraine:

1. ДБН В.2.6-98:2009 "Бетонні та залізобетонні конструкції. Основні положення". Конструкції будинків і споруд / К.: Мінрегіонбуд України, 2011. - 71 с.
2. ДБН В.1.2-2:2006 "Навантаження і впливи. Норми проектування". Система забезпечення надійності та безпеки будівельних об'єктів / К.: Мінбуд України, 2006. - 75 с.
3. ДСТУ 3760:2006 / ISO 6935-2:1991 "Прокат арматурний для залізобетонних конструкцій. Загальні технічні умови".
4. ДБН В.1.2-14-2009 "Загальні принципи забезпечення надійності та конструктивної безпеки будівель, споруд, будівельних конструкцій та основ" / К.: Мінрегіонбуд України, 2009. - 40 с.
5. ДСТУ Б В.2-6-53:2008 "Плити перекриттів залізобетонні багатопустотні для будівель і споруд. Технічні умови" / К.: Мін-во регіон. розвитку та буд-ва України, 2009. - 29 с.

Today we have touched only on the basic nuances. However, it is essential to note that the verification under bending moment, although important (if not the most important), is not the only one. Let's not forget about the shear forces, crack stability, and deformation.

It is also crucial to pay attention to units of measurement. Remember that only quantities of the same dimension can be compared with each other.

For the preparation of explanatory notes, I recommend using ready-made drawings and other media content from Dystlab. This will significantly save you time!

We will discuss these and other nuances in our next meetings. Good luck!{/lang}

Vitalii Artomov

"I am working to make «Made in Ukraine» a global symbol of quality and style"

CEO, co-founder of Dystlab, developer of TechEditor. Engineer, scientist, Ph.D. with over 20 years of experience in structural analysis and automation of engineering calculations. I advise engineering companies in Ukraine, Europe, and North America.

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