## Properties, Strength, and Behaviour

Beams are defined as a horizontal structural member that primarily carry axial loadings. Beams experience axial, torsional and beam loadings (Rossman & Dym, 2008). Beams are classified depending on their mode of support. Support can be a fixed, roller or pin. A simply supported beam is one in which the transverse member lies on singular support at each end. Beams extending beyond the their support are known as an overhanging beam, while the beams that have more than two supports are known as continuous beams. Lastly, a beam that has one end fixed and the other free is known as a cantilever beam (Mubeen, 2011). Loading imposed on a beam can either be a point load or distributed load. Point loads are applied at a definite point on the beam. Distributed load is applied continuously along the beam and can either be a varying or uniform.

Deep Beams are defined as those beams whose depth is significantly large compared with the length of the span. For a continuous beam, if the ratio of the span to depth is below 2.5 it is regarded to be a deep beam. In the case of simply supported beam, a span depth ratio of less than 2 represents a deep beam. However, it is important to note that there is no proven precise point at which beam behaviour changes from the ordinary to deep beam behaviour but design purposes, that point can be taken to be when the span depth ratio is around 2.5 (Kong & Chemrouk, 2002). They have application in foundations, high-rise building, and offshore structure. These type of structures are found in transfer girders and load bearing walls. In certain types of building systems, the transfer girder is subjected to large amounts of stress hence the section is designed with a much larger depth. Typical examples of deep beams include floor slabs exposed to lateral loadings and beams with short spans that are expected to sustain heaver loading.

Brunswick Building: A deep beam on top of the ground Columns

One of the differences between the ordinary beams and deep beams is the analysis. Due to their enormous size, deep beams behaviour my be studied in 2 dimensions rather than the one dimension in the ordinary beams. In an ordinary beam, an assumption is made that the section remains plane after deformation but this isn’t true for deep beams

## Strut and Tie

Figure 1Deep Beam example: Transfer girder in a bridge

Bridge with deep beam(Jakway Part Bridge, Buchanan County, Iowa

“The behavior of continuous deep beams is varies considerably from that of simply supported deep beams. Huge amounts shear and moments exist in the shear span in continuous beams which have an effect in the occurrence of cracks. Consequently, the effective strength of concrete strut(the part that mainly transfers load in deep beams)is reduced considerably.” (Rashwan, ZaherElsayed, Abdala, & Hassanean, 2014).

Regions of structural members that experience bending are categorized as;

- The area where there is linear distribution of the strain also known as the Bernoulli region
- The area where there is non linear distribution of the strain. This section is known as the distributed region.

In tall buildings, deep beams act as transfer girders. The beams have a high stiffness while the deflection is negligible. Their analysis are complex since the assumption of plane area remaining plane does not hold. Linear elastic method of analysis is not applicable in these types of beams (Raj & Gangolu, 2015). Rational methods have however been developed so that designers can come up with acceptable designs. Some of the models include the strut and tie and the softened truss.

This method is used to design the distributed and Bernoulli region instead of the empirical formulae. This method is flexible and intuitive. The stress flow patterns in cracked deep beams are complex. As a solution, the strut and tie method uses the truss members to approximate the stress flows hence analysis and design can be done by use of simple structural mechanics. When a simply supported deep beam is loaded with a point load at the centre, the tensile stresses will tend to act in the direction parallel to the horizontal plane that bisects the beam while the compressive stresses will tend to act in the direction of the line linking the support and load.

For a simply supported deep beam carrying a uniformly distributed load, cracks will occur a shown above. On the left is the truss model that would be used in the design. Several observations can be made. Fist, with the load hanging from below, the trajectories of the compression stresses tend to form an arch. The reinforcement transfers force upwards as shown in the pattern of cracking. The arch then transfers the force to the supports below. Secondly, The longitudinal load that acts on the tension ties will remain the same through the span of the deep beam. This therefore necessitates the anchorage of steel members at the joints above the supports.

These are the most commonly used type of deep beams especially in the form of foundation, transfer girders and pile caps. The process of determining the strength of deep beams is quite complex but there exists some design methods that are simple and enable designers to come up with design that are economical in terms of material usage. Continuous deep beams differ from simply supported ones and if attention is not paid during the designing process, the resultant structure may be susceptible to unexpected cracking which would have been avoidable if due consideration was given. Due to their unique truss behaviour, the detailing process that is appropriate to design of shallow deep beams cannot be suitable for continuous deep beams.

## Continuous Deep Beams

There exists a similarity between continuous deep beams and simply supported beams i.e. both show that a reduction of the ratio of shear span to depth leads increased shear strength. The location of the maximum negative moment in continuous deep beams coincides with the location of the shear hence the design methods for simply supported deep beams cannot be used in the designing of continuous beams (Rogowosky, 2002).

Typical Building Elevation showing examples of continuous deep beams (Rogowosky, 2002).

Leonhardt and Walther (1966) conducted several tests on continuous deep beams. This test involve the use of a deep beam including a two span beam and varying the support conditions, different loadings and arrangement of reinforcement. Development of flexure cracking in deep beams tends to be little. When a deep beam is loaded, shear cracks occur immediately. The cracks depict a truss mode behaviour. Previous tests show that the diagonal cracks tend to form at a load that is nearly half of the ultimate load. Flexural cracks continue to form as the amount of load is increased. As the flexure reinforcement yields, significant deflection starts occurring. The deflection leads to rotation of the joints of the ‘truss’ which eventually leads to the failure of the concrete compression struts. The yield of the major flexural reinforcement dictates the strength of the designed section while the point of failure of the concrete determines the ductility of the section (Rogowosky, 2002).

Conditions of the support and the type of loading are fundamental aspects that should be put into consideration when one is designing continuous deep beams. These types of beams are sensitive to the movements of the support structures. Minimum reinforcement should be provided so as to make the section ductile and minimize behaviour variability. Normally, in the design of structural members, cracking resulting from application of service load is controlled by use of at least the minimum reinforcement required (Draycott & Bullman, 2009). More than the minimum prescribed reinforcement can be applied to control cracking in deep beams.

Deep Beams with Web openings.

Sometimes, when accessibility is needed and provision of basic services is a requirement, deep beams may have web openings. These openings on the web of the deep beam may affect the shear strength and behaviour of the beams. Information on the effects of having web openings in deep beams is still low hence the need for more research. Some of the factors that have effect on the performance and strength of deep beams are the ratio of shear pan to depth , span to depth ratio, quantity and position of longitudinal bars, properties of concrete and reinforcements, loading type and its position on the beam, the shape, magnitude and position of the web openings (Ray, 2002).

## Deep Beams with Web Openings

Ray carried out investigations on the general performance of deep beams having web openings in shear failure under two point loading. It was established that he variation of the strain in the concrete make the beam behave elastically before cracking occurs. As load is increased on the beam, the number of neutral axes reduce to only one at the ultimate state. Under service loads, cracks and deflection occur but pose no threat.

Deep Beam with Web Opening (Ray, 2002)

The web openings can either be circular or rectangular. For rectangular openings, cracks begin to form at the corners of the opening and at the support bearing regions at a load 36-55% of the ultimate load. As the load is increased, the cracks propagate diagonally. At a load 50-97% of the ultimate, long diagonal cracks tend to form. Continued loading after these cracks have formed will definitely lead to failure of the structure (Ray, 2002). For Circular openings, cracks also begin to form at the corners of the opening and at the support bearing regions at a load 36-55% of the ultimate load. This is similar to that of rectangular web openings. In circular web openings, cracks which begin to form at bottom most diametrical point in the shear region extend to the point of support (Ray, 2002).

The location of the web openings has an effect on the behaviour and performace of deep beams. Web openings that are positioned in the exterior or interior of the shear span leads to a decrease in the shear strength capacity of the section (Rashwan, ZaherElsayed, Abdala, & Hassanean, 2014). Reinforcement should be provided in the area around the web openings so as to avoid premature failure of the beam. It has shown that the use of glass fibre reinforced polymers as a strengthening material has a significant effect only when the web opening is positioned in the shear region (Rashwan, ZaherElsayed, Abdala, & Hassanean, 2014).

Typical deep beam crack patterns at failure with rectangular openings under two-point loading (Ray, 2002)

Typical deep beam crack patterns at failure with circular openings under two-point loading (Ray, 2002)

The introduction of web openings does not lead to a change in the trajectories that is the compression struts. The most important aspect that influences the overall capacity of the beam is the depth of the web opening. The depth should not be greater than 20% of beam depth so that the reduction in the capacity of the beam doesn’t go beyond 10% of the solid beam i.e. with no opening (Mohamed, Shoukry, & Saeed, 2014).

Deep beams may fail from shear compression, diagonal tension, yielding of tie reinforcement, flexural failure, shear compression, bearing failure local crushing at the loading point or the support, and failure of the supporting column (Raj & Gangolu, 2015).

In the figure below, the cracks that form at the mid-span (labeled as1) represent flexure cracks. Flexure cracks occur when the tension stress in the concrete is more than the tensile strength of concrete (Mohammadhassani, Jumaat, Ashour, & Jameel, 2011). These cracks occur because concrete is weak in tension. Flexure cracks are not dangerous unless the reinforcement provided is not is not less than the minimum provide by the design codes.

Typical crack pattern of deep beams with two point loading (Mohammadhassani, Jumaat, Ashour, & Jameel, 2011)

Most deep beam fail due to shear failure. The compression struts in deep beams usually formed between the load and the support are responsible of transmitting loads directly to the support. This process of transferring load leads to shear failure. Failure occurs when the diagonal shear cracks widen and concrete crushing (Mohammadhassani, Jumaat, Ashour, & Jameel, 2011). The shear and inclined cracks occur at 46%-92% of ultimate load. Appearance of these cracks is not dependent on the on the tension reinforcement and web reinforcement bars.

Crack Pattern (Mohammadhassani, Jumaat, Ashour, & Jameel, 2011)

Here, both shear and flexural cracks occur. The figure below shows that as the load is increased, diagonal cracks occur at the terminus of vertical cracks. At ultimate load, these cracks occur as failure cracks.

Combined Shear and Flexural Cracks (Mohammadhassani, Jumaat, Ashour, & Jameel, 2011)

From the figure above, it can be seen that inclined cracks occur vertical to the strut compression trajectory that leads to the failure of the support.

In the figure below, it can be seen that local failure occurs at the regions of support and at the point of application of load( represented by 5).

Typical crack pattern of deep beams with two point loading (Mohammadhassani, Jumaat, Ashour, & Jameel, 2011)

This type of failure occurs when the compressive stress is high in the point load region and support. Local failure is not desirable because it is regarded as early failure. It occurs when the compressive stress is greater than the compressive strength of concrete.

Compression failure is as a result of the strain in the compression zone being more than the ultimate strain . This makes the concrete to explode in the zone of compression. This type of failure is not common as the depth of the beam is large hence concrete under tension may not reach the maximum strain.

Compression Cracks (Mohammadhassani, Jumaat, Ashour, & Jameel, 2011)

References

Draycott, T., & Bullman, P. (2009). Structural elements Design Manual: Working with Eurocodes (2nd ed.). 0xford, United Kingdom: Butterwoth-Heinemman.

Kong, F. K., & Chemrouk, M. (2002). Reinforced Concrete Deep Beams. In F. K. Kong (Ed.), Reinforced Concrete Deep Beams (pp. 1-2). New York, New York, United States of America: Van Nostrand Reinhold.

Mohamed, A. R., Shoukry, M. S., & Saeed, J. M. (2014, June). Prediction of the behaviour of reinforced concrete deep beams with web openings using the finite element method. Alexandria Engineering Journal, 42(5), 1138-1162.

Mohammadhassani, M., Jumaat, M. Z., Ashour, A., & Jameel, M. (2011, August 4). Failure Modes and Serviceability of High Strength Self Compacting Concrete Deep Beams. Engineering Failure Analysis, 2272-2281.

Mubeen, A. (2011). Mechanics of solid (2nd ed.). New Delhi: Pearson Education.

Raj, J. L., & Gangolu, A. R. (2015). Failue Modes of RC Deep Beam Panels. THE 17TH ASIA PACIFIC YOUNG RESERCHERS AND GRADUATES SYMPOSIUM. Kuala Lumpur.

Rashwan, M. M., ZaherElsayed, A. A., Abdala, A. M., & Hassanean, M. A. (2014, September). Behaviour of High Performace Continous R.C. Deep Beams with Openings and its Strength. Journal of Engineering Sciences-Assuit University, 42, 1138-1162.

Ray, S. P. (2002). Deep Beams with Web Openings. In F. K. Kong (Ed.), Reinforced Concrete Deep Beams (pp. 76-91). New York, New York, United States of America: Van Nostrand.

Rogowosky, D. (2002). Continuous Deep Beams. In F. k. Kong (Ed.), Reinforced Concrete Deep Beams (pp. 93-135). New York, New York, United States of America: Van Nostrand Reinhold.

Rossman, S. J., & Dym, C. L. (2008). Introduction to Engineering Mechanics: A Continous Approach. Boca Raton, Florida, United States of America: CRC Press.

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