Calculating long-term deflection and crack width for concrete slabs [WEBINAR RECORDING]

Posted on September 15th, 2021 in Webinars

Summary

This technical webinar introduces MasterSeries 2021's new features for concrete slab design, focusing on the complex calculations for long-term deflection and crack width. The discussion emphasizes the various influencing factors on deflection, such as early-age loading, creep, shrinkage, and cracking, which are often overlooked in traditional design. It highlights the importance of detailed planning and understanding of loading events throughout a slab's life cycle, providing insights into how the MasterSeries software helps engineers assess and validate these critical serviceability aspects of concrete structures in accordance with Eurocode standards

Key Concepts

• Concrete Slab deflections
• Crack Width Calculations
• Early age Loading
• Creep and Shrinkage
• Deflection check limits

Description

This source provides a detailed technical overview of a new feature in MasterSeries 2021 for MasterKey Slab Design program: the calculation of long-term deflections and crack widths in concrete reinforced slabs. The focus is primarily on deflections due to their complexity, with crack width calculation being a secondary, though related, issue.

Here's a summary of the key aspects discussed:

• Scope and Standards

    ◦ The feature is implemented to Eurocode EN 1992-1-1:2004, specifically sections 7.4.3 for long-term deflection and 7.3.4 for crack control.

    ◦ The Concrete Society Technical Report No. 58 (TR-58) is highlighted as an excellent publication that fills the void of limited Eurocode guidance on long-term deflection, offering detailed insights into complex calculations and the influence of various parameters.

    ◦ Currently, the software deals with deflections of flat slabs only, with long-term creep or shrinkage deflection for beams still under development.

• Accuracy and Validation

    ◦ Real-world deflection measurements of slabs have shown a wide range of errors (15% greater to 30% less) compared to calculated values, due to variations in software implementation and lack of precise real-world data.

    ◦ MasterSeries's method was validated against the BRE Cardington test concrete building, achieving a maximum error of 5.9%. This validation benefited from detailed information about concrete properties, humidity, and loading events that are often unavailable to designers.

• Key Factors Influencing Long-Term Deflection The calculation is a complex numerical exercise that includes many components:

    ◦ Concrete Creep

        ▪ Defined as the increase in strain over time under constant stress. Concrete subject to a constant compressive force will continue to compress, with increasing strains over time.

        ▪ Accounted for by calculating a phi creep modification factor and applying it to the 28-day Young's modulus to get an effective Young's modulus for numerical calculations.

        ▪ The creep coefficient varies over time and is influenced by cement type, relative humidity, ambient air temperature, and slab thickness. These are factors often not considered in traditional slab design but can significantly affect the coefficient.

        ▪ Since different loads are applied at different times, the software calculates a compound value of Young's modulus for each finite element at a specific time, based on stresses from various loading events.

    ◦ Concrete Shrinkage

        ▪ Includes drying shrinkage (loss of moisture) and autogenous shrinkage (chemical reaction of water hydrating with cement), both leading to volumetric changes and added together for a final shrinkage strain.

        ▪ Develops over time, tapering off at a constant value.

        ▪ Influenced by concrete grade, cement type, humidity, and slab depth.

        ▪ Causes a moment in the section due to unequal reinforcement at the top and bottom, which exacerbates normal deflection and can contribute as much as 25% to overall deflection.

        ▪ Implemented by applying shrinkage strains to produce an equivalent moment post-cracking and creep, taking into account the slab's partially cracked state.

        ▪ Shrinkage restraint (from surrounding structures like shear walls) can be input as a percentage (not less than 50% recommended) and directly affects the concrete's tensile capacity.

    ◦ Cracking

        ▪ Major influencing factors include reinforcement (primarily tension), its cover, and the strength of the concrete (fctm), which also depends on the age of the concrete.

        ▪ Tension stiffening accounts for the concrete in tension that has not yet ruptured, contributing to slab stiffness. This is represented by a distribution coefficient (zeta) that balances cracked and uncracked section properties.

        ▪ Once a crack occurs, it is permanent and non-recoverable; early cracking due to early striking or loading will follow the slab throughout its life cycle.

        ▪ The software applies stiffness modification to each finite element based on cracking assessment in principal directions.

        ▪ Effects of axial force are included in cracking analysis, which can be significant for in-plane membrane action and load transfer.

        ▪ Cracking leads to significant redistribution of forces, requiring a non-linear iterative analysis for convergence.

        ▪ A compound beta factor (distribution coefficient) is calculated for each finite element, considering multiple loads and their proportions.

• Importance of Loading Events and Construction Sequence

    ◦ Accurate deflection calculation requires detailed planning and knowledge of slab loading events, particularly at the early stage of construction.

    ◦ Early Age Loading: Applying loads when the slab has not reached its full capacity (e.g., striking at 2-3 days when concrete tensile strength is only 50% of 28-day strength) can cause significant stresses and early cracking.

    ◦ Slabs Above and Backpropping:

        ▪ Casting slabs above (e.g., at day 12) applies significant load to the slab below via backpropping.

        ▪ With one level of backpropping, 70% of the load from the slab above can transfer to the slab below. This is due to elastic shortening of props.

        ▪ Two levels of backpropping may only reduce this to 65% on the immediate slab, distributing the rest to lower levels.

        ▪ These construction stage loads can be the most significant events the slab experiences at a time of reduced strength, leading to non-recoverable early stage cracking.

    ◦ Designers need to liaise with contractors to agree on and specify strike times, backpropping levels, and other key events to minimize final deflections.

• Software Capabilities for Deflection and Crack Width Checks

    ◦ MasterSeries analyzes two loading cases: quasi-permanent and optionally frequent.

    ◦ Deflection checking is done using "check lines" drawn between support points, allowing application of multiple criteria (e.g., span over 250, or relative to columns).

    ◦ A useful feature is calculating differential deflection between two points in time (e.g., between partition installation and long-term), crucial for assessing impact on partitions and other elements.

    ◦ Users can easily vary parameters like strike time, restraint percentage, cement type, and humidity to analyze their impact on deflection and cracking.

    ◦ The software provides contour outputs for deflections at different loading events, creep coefficients, crack ratios (zeta), and the time at which the first crack occurs for each element.

    ◦ Crack widths are calculated purely from the Eurocode (section 7.3.4), independent of the cracking ratio used for deflection, though informed by service stress in the reinforcement, which is influenced by slab stiffness and cracking.

• Recommended Reading

    ◦ TR-58 (Concrete Society)

    ◦ The Concrete Centre's "How to Design Concrete Structures to Eurocode 2 Section 8: Deflection Calculations"

    ◦ "Temporary Works Toolkit Part Four: An Introduction to Backpropping of Slabs" (Structural Engineer, Dec 2016) for backpropping load distribution.