Deflection in Reinforced Concrete Structures

Introduction

Deflection

Reinforced concrete is used in modern construction as a reliable and affordable material for suspended flooring. Reinforced concrete slabs and beams and considerably durable, however, they deflect over time. A crucial part of the structural design of reinforced concrete elements is to prevent deflections from reaching intolerable levels known as deflection limits.
In addition to being unsightly, excessive deflection can make building occupants uncomfortable and also can cause cracks to non-structural elements such as partitions as these elements won’t likely be flexible enough unless they are articulated.

Reinforced concrete is the most common material being used in multi-story structures in Australia. It is a durable material and is considered suitable for Australia’s aggressive environmental conditions. Its behaviour in case of fire is acceptable if designed properly. This material also has disadvantages such as the propensity for cracking due to flexure, drying shrinkage, and thermal effects, as well as deflections brought on by shrinkage and creep.
When designing a structure, structural engineers and architects must take these factors into account and, where practical, provide the necessary accommodations. These accommodations may include concrete control joints, brickwork articulation joints, and stronger reinforced concrete parts.
Structural engineers must consider the parameters below when designing reinforced concrete elements:

1. Design actions as per Australian Standards AS1170 series.
2. Slab, beam, wall and column sizes to satisfy fire rating requirements nominated by BCA and Australian Standard AS3600.
3. Slab thickness to satisfy long-term total deflection and incremental deflection limits as per Australian Standard AS3600.

Since cracking, shrinkage, creep, and construction loads all have complex impacts, designing reinforced concrete members for long-term deflection is considered complicated and requires experience and expertise.

Post-tensioned concrete

Post-tensioned concrete has been used to create economical floor slabs in a variety of designs, including flat plate, flat slab, and banded slab. It is crucial to take both initial and long-term slab shortening into account when designing PT slabs, especially at joints and around the slab’s perimeter. As an example, contraction joints placed at 40 m intervals have shown gaps up to widths of 40 mm, and movements of up to 20 mm at the slab perimeter!
Long-term deflection also occurs in post-tensioned concrete beams and slabs and design for allowable serviceability deflection is crucial in PT design.

The Deflection Process

Initial Deflection

Initial deflection happens when the props are removed from a model slab in a lab. The slab should experience elastic deflection at low load levels. High load levels should cause flexural cracking, which should lead to cracks in some slab cross-sections; this portion of the first deflection is not totally elastic.
Hence: i = i_el + increase due to cracking
Due to shrinkage and creep and increased cracking, the initial deflection under relatively constant load will increase in the long-term. The slab will deform in regions where there are uneven amounts of top and bottom reinforcement due to concrete drying shrinkage. Mid-panel zones frequently lack top reinforcement, which causes them to sag and contribute to long-term deflection. The length of the warping and its severity are directly related to how much the utilised concrete shrank during free drying. The long-term deflection which is independent of load continues at a diminishing rate over time for several years. For several years after pouring, concrete creep under an effectively constant sustained load also contributes to long-term deflection at a diminishing rate. Both compressive and tensile creep can occur.
With more extensive slab cross-sectional cracking, deflection grows. Tensile stress, which is brought on by simultaneous heat, shrinkage, and flexure effects, causes cracking when it exceeds the concrete’s tensile strength at any one point in time. It is reasonable to anticipate that cracking will get worse over time as the concrete dries out and contracts more. Over time, additional fractures will form in concrete when a high amount of tensile stress (over the proportionate limit) is maintained. Therefore, a slab that is largely uncracked at the time of stripping will progressively become more cracked thus the effective moment of inertia will diminish, and this will lead to long-term deflection, as illustrated in Fig. 1.

Hence: l_t = i + shrinkage + creep + long-term cracking
Studies have shown that the long-term deflections in reinforced concrete flat plates can be as high as eight times the initial deflection over a period of three years 3. This was “mainly a result of the loss of stiffness owing to time-dependent cracking under the combined pressures of transverse stress and drying shrinkage.

Long-Term Deflection

For as long as five to nine years after stripping, the deflection of slabs and beams can continue (Figure 1). The rate and magnitude of the increase in long-term deflection depend on factors such as design, construction, material and environmental conditions.
Standards requirements have a significant impact on structural design, but it’s critical that both the architect and the engineer understand the likely long-term deflection behaviour of flexural elements and account adequately for the expected movements. This is because simply following the standards may not prevent long-term deflection failures.
The creep and shrinkage due to the properties of the concrete mix and the specification of an appropriate construction technique, requiring lengthy stripping periods, adequate propping, efficient curing, and stringent on-site supervision, will require extra attention from structural designers.

Incremental deflection

Incremental deflection is defined as the deflections that occur after the installation of brittle elements (superimposed dead load) which is done after stripping. In other words, the subtraction of initial deflection (after stripping) due to dead load and superimposed dead load from the total long-term deflection.
There are several methods of calculating incremental deflections described as below:

1. K_cs as per Australian Standard AS 3600:2018
   The k_cs method approximates the effects that long-term effects of creep and shrinkage will have on the slab deflection by increasing the dead and live load by some factor (k_cs factor). The amount of the factors and hence the increase/decrease in deflection are dependent on the ratio of the compressive steel (A_sc) to the tensile steel (A_st).
   The k_cs factors are calculated to AS 3600 – 2018 Cl 9.4.4 which states:
   
   • Long Term, Total Deflections: (1.0 + k_cs)g + (ψ_s + k_cs ψ_l )q
   • Long Term, Incremental Deflections: k_cs g + (ψ_s + k_cs ψ_l ) q
     k_cs is determined in accordance with Clause 8.5.3.2 and ψ_s and ψ_l are given in AS/NZS 1170.0
     where kcs is determined to AS 3600 -2009 Clause 8.5.3.2 and the short term and long term loading factors, ψ_s and ψ_l are given in AS/NZS 1170.0
     k_cs = [2 – 1.2 (A_sc / A_st)] ≥ 0.8
2. Eurocode2
   In this method, incremental deflection is calculated by subtracting Long Term Total Deflection from deflection due to self-weight, (Long Term – SW). The K_cs method as outlined above subtracts both the self-weight and the superimposed dead load. For EC2 Long Term Incremental Deflections it is assumed that the superimposed dead load is applied after the attachment of the masonry partition or the brittle finish. This will produce more conservative Long Term Incremental Deflection results when comparing with K_cs method.

Suspended Floor Slab

To guarantee the serviceability of concrete slabs during the design life of any structure, AS 3600 suggests limits for long-term deflection. Long-term deflection is the governing design criteria for residential and commercial RC slabs.
Serviceability issues develop when the long-term deflection causes cracks on walls and the buildings become aesthetically unpleasant. When insufficient tolerances for long-term deflections have been allowed, problems with structural steelwork, glass facades, and reinforced concrete wall panels supported on exterior beams will occur. Stormwater ponding is another issue brought on by excessive deflection on external suspended slabs. That is why it is crucial to consider long-term total as well as incremental deflections when designing falls and drainage outlet locations.
Due to the brittle nature of masonry and lightweight walls, cracks to these elements as a result of deflections to the supporting slab are inevitable. Although technical publications and rules for concrete buildings suggest limitations for projected long-term incremental deflection of as small as L/1000, such a restriction is insufficient to guarantee that floor slabs will sustain non-articulated, masonry partitions without cracking. Such a restriction, which is constrained by realistic economic considerations, can only regulate the length and widths of the masonry cracks; it will not prevent their occurrence.
Concrete structures standard AS 3600 also recommends limits for the calculated total deflection as well as incremental deflections of floors. This recommendation can be found in table 2.3.2 of AS 3600:2018 (Table 1).

The maximum mid-span deflection of a beam spanning either between columns or, in a two-way beam system, between its supporting beams is limited by the AS 3600:2018 – Concrete Structures.
Because the supporting beams also deflect, the effect of this additional deflection on the structure must be considered
It is important to consider the effect of additional deflection of supporting beams when calculating the total deflection of the structure. This is crucial when designing flat slabs or plates where the mid-panel deflection relative to the supporting columns is the sum of the column strip deflection and the two-way panel deflection.

Serviceability

As explained earlier, the long-term deflection of RC slabs or beams is dependent on factors such as materials supply, construction techniques, loading history, weather and time.
Because the long-term deflection performance will dictate the structural design, it is crucial that the structural designer employs a trustworthy and moderately accurate calculation process to estimate the deflection performance of the floor slab at any moment. It is also important to specify the use of materials and construction procedures that will control those factors that are critical to deflection. The slab must be serviceable during the life of the structure. Excessive deflection can cause issues such as an alarm to occupants, problems with the fixtures and furniture, unacceptable wall movement and/or cracking, aesthetically offensive effects, etc.

Increasing the stiffness of the slab to match that of the partitions is not economically feasible, despite the desire to prevent rotation, separation, and cracking of partitions. As a result, articulation should be used to lessen the stiffness of the partition.
The long-term deflections of the exposed beams should be kept within acceptable tolerances as these elements can be viewed from outside of the building. The sag in a member “will normally become visible if the deflection reaches L/250,” according to BS8110: Part 2: 1985. A limit of L/300 was recommended by Blakey, F.A., “Australian Experiments with Flat Plates”,. AS 3600 recommends an absolute maximum of L/250 for the deflection of flexural components but makes no mention of appearance. The ultimate maximum for pre-camber should be L/250 when it is utilised to manage appearance or serviceability.
Contractors doing fit-out activities, such as installing partitions and heavy furniture, are aware of the existence of surface imperfections, cambers, and sags in a floor. The majority of the pre-camber may be present at fit-out since it is often done during the building phase, which occurs early in the long-term deflection of a floor slab. When building partitions, there may be issues with light-weight partition alignment and uneven bed joints in masonry walls if the pre-camber is severe. Pre-camber must thus be used sparingly. Additionally, pre-cambering in-situ concrete components necessitate a high level of site management to guarantee that beam and slab design depths are met during construction.

Floor Slope Perception

It is challenging to evaluate how building occupants perceive deflection. The floor surface of a typical office building with carpeted flooring slopes differently in different places due to surface finish defects and long-term deflections. The slope of the floor affects how much camber or sag is perceived, and only a large amount of deflection may generate a slope that is noticeable to a person walking on a carpet. Walking across the floor would often not reveal a floor slope of 1/100 or less, indicating that substantial deflections can happen and go undetected. The behaviour of furniture and fixtures, such as the appearance of wall cracks, the opening up of partition joints, the sliding of desk drawers, the jamming of cupboard and partition doors, the sliding of compactus units, and the movement of objects on horizontal surfaces, is more likely to cause occupants to notice floor slopes.

Conclusion

In conclusion, deflection is a critical aspect of reinforced concrete structures that needs careful consideration during the design and construction process. Excessive deflection can lead to aesthetic issues, discomfort for building occupants, and even damage to non-structural elements. As a leading structural engineering firm, Prime Consulting Engineers understands the complexities involved in designing reinforced concrete elements to control deflection within acceptable limits.

Deflection in reinforced concrete structures is influenced by factors such as materials, construction techniques, loading history, weather, and time. Structural engineers must carefully assess these factors to ensure the long-term performance and serviceability of the structure. Post-tensioned concrete, with its economical benefits, also requires careful consideration of initial and long-term slab shortening to prevent future problems.

Our team of experienced and knowledgeable structural engineers is well-equipped to handle the challenges of designing for deflection in reinforced concrete structures. We follow Australian Standards and regulations, including AS 3600, to optimize slab, beam, wall, and column sizes for fire ratings and to control long-term deflection. We also provide expertise in calculating incremental deflections, considering factors like creep, shrinkage, and construction loads.

At Prime Consulting Engineers, we prioritize both functionality and aesthetics, ensuring that your reinforced concrete structure remains safe, stable, and visually appealing over its design life. With a focus on quality and attention to detail, we deliver exceptional structural engineering solutions that meet your project’s unique requirements. Trust us to be your reliable partner in constructing durable and well-designed reinforced concrete structures.

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