Kyle Conway
Designing rectangular concrete reinforced beams made easy with this comprehensive guide for Australian structural engineers, covering AS 3600:2018 code requirements and calculations.
Reinforced concrete beams are used in structures where a horizontal load path is required. They typically support floor elements (usually concrete slabs) but can be used in a range of applications.
This article will explore the use cases and advantages of reinforced concrete beams in concrete design. We'll also provide an overview of the relevant design standard in Australia (AS 3600:2018), highlight its changes from previous versions, and discuss fundamental principles, calculations, and methods for reinforced concrete design to achieve both strength and serviceability.
Additionally, we'll provide some tips on best practices for design, formwork, construction, and quality assurance.
Table of Contents:
Reinforced concrete beams are constructed from a combination of both concrete and steel.
Figure 1: Example of reinforced concrete beams (Reference)
The part of a structure that has a tensile force acting on it is called a Tie, and the part that has a compressive force acting on it is called a Strut. Concrete naturally acts as a Strut.
Figure 2: Illustration of forces acting on reinforced concrete beams
The steel reinforcement provides all the tensile strength where concrete is in compression, and the two materials act together in resisting forces. Reinforced concrete beams are used where the loads/spans are too great to use timber or steel beams, and a stronger and larger section size is required.
The following are some of the benefits of using reinforced concrete in construction:
Reinforced concrete beams are widely used in the construction of buildings, highways, roads, traffic, precast structures, floating structures, Hydro-power tunnels, irrigation canals, and drains, among other conceivable structures.
Australian standard AS 3600:2018 provides guidelines for designing and constructing concrete structures in Australia.
The scope of the standard includes the design of reinforced and prestressed concrete structures, including beams, columns, walls, slabs, and footings. The standard also covers the design of concrete structures subjected to fire, earthquake, and wind loads.
The changes from the previous version of the standard include:
The changes aim to address issues in beam design for shear and torsion, increase the capacity reduction factors, and improve the calculation of shear capacity.
The Concrete Institute of Australia presented a symposium titled “The New AS3600-2018 Concrete Structures Code – What Impact Will It Have On You?” to discuss the changes and their impact on structural design for slabs, beams, and walls from previous versions.
The fundamental design principles specified in AS 3600 for reinforced concrete beams include the following:
The first step in the design of a reinforced concrete beam is determining the structural actions.
The load combinations for strength and serviceability design can be found in AS 1170.0 Section 4.
Strength Design:
Note: When computing Uniformly Distributed Loads (UDL’s), use the span-to-span length.
Serviceability Design: Long-Term: Short-Term:
Dead Load (): Weight of structure itself and any installed equipment Live Load (): Loads for various uses and occupancies
AS 3600 Clause 6.10.2.2 to 6.10.2.4 may be used for the calculation of design bending moments and shear forces for strength in continuous beams and one-way spanning slabs of reinforced concrete construction (note: = uniformly distributed load per unit length factored for strength).
Figure 3 & Figure 4 diagrammatically demonstrate the appropriate coefficients to multiply by () to determine the moment action in the beam using the simplified method.
Figure 3: Simplified Method Coefficients for Two Spans
Figure 4: Simplified Method Coefficients for Multiple Spans
Next the structural capacity for strength needs to be determined. Let’s start by checking the moment capacity of a reinforced concrete beam. The design of beams for strength and serviceability is covered in AS 3600:2018 Section 8.
There are two scenarios that occur when determining the moment capacity of a reinforced concrete beam.
Scenario 1. Calculate the design force/moment for a given reinfoced concrete section where the reinforcement area of the cross section () is known which is quite easy following the below steps;
Scenario 2. Calculate the beam size and amount of steel reinforcement (Ast) for a given design moment (structural action) where ( is unknown) which is more difficult and follows the below steps.
By Force Equilibrium we can deduce:
Assuming , then we can solve for the neutral axis parameter ().
Note the main assumption is positive bending (beam sagging) (with the compressive reinforcement () on top and tensile reinforcement () on bottom). However, if it is a negative bending moment (beam hogging) these should be switched.
Note: Always assume tension side has yielded (hence the fsy). However, we do not know if compression side has yielded so we need to do a check.
As per the requirements of AS 3600:2018 Section 8.1.3 the maximum strain in the extreme compressive fibre () is 0.003.
Using this we can check our assumption for using the strain diagram below:
If , then the assumption is correct and the moment capacity as determined by force equilibrium is shown below.
If , then a recalculation of and is Required:
By force equilibrium above we deduced:
We can substitute in,
To give,
The above equation can be solved for the neutral axis parameter (ku), and then we can calculate, which gives the moment capacity as below.
The steps to determine the shear capacity of a reinforced concrete beam are below.
Step 1: Determine the Maximum Ultimate Shear Strength () in accordance with AS 3600:2018 Section 8.2.3.3.
Take and .
Note: If (determined in Section 3.1) then increase the dimensions of the beam.
Step 2: Transverse Shear Reinforcement (Vus) shall be provided in regions where , or if the depth of the member is greater than 750mm
Where (determined in Section 3.1) in accordance with AS 3600:2018 Section 8.2.4
As per AS 3600:2018 Section 8.2.5, the area of transverse reinforcement () and stirrup spacing () can then be determined by iterating the below equation.
Step 3: If but the Overall Depth of Member ≥ 750 mm, provide minimum transverse reinforcement area ()
Deflection Modes:
As per AS 3600:2018 Section 8.5.3.1:
Short-Term Deflection at Mid-Span (Simply Supported Beam):
Short-Term Deflection at Mid-Span (Continuous Beam):
Where: = uniformly distributed service load, = effective length, = modulus of elasticity, =effective second moment of area, =midspan moment, =moment at support , = moment at support .
As per AS 3600:2018 Section 8.5.3.2:
Long-Term Deflection:
Where: = factor used in serviceability design to take account of the long-term effects of creep and shrinkage.
Example:
For a singly reinforced simply supported rectangular section with:
Determine the amount of reinforcement required when a 6000mm interior span beam is subjected to a uniformly distributed dead load of 10kN/m. Consider moment as the critical loading.
As per part 3.1 of this article, the load combinations for strength and serviceability design can be found in AS 1170.0 Section 4.
Strength Design:
For a simply supported beam:
As we have a given design moment (structural action) where (Ast is unknown) which should follow the below steps as per Case 2 in Section 3.2.
Step 1: Use force equilibrium (Compression=Tension) across the rectangular stress block to develop the below two equations
Step 2: Solve simultaneously for the neutral axis parameter (ku) and the required reinforcement area of the cross section (Ast)
fsy=500MPa, d=500mm, b=250mm, f’c=50MPa, capacity reduction factor = 0.85 as per AS 3600:2018 Table 2.2.2
As per AS 3600:2018 Section 8.1.3: 𝛾=0.97-(0.0025*f’c)>0.67=0.845, 𝛼2=0.85-0.0015f’c>0.67=0.775
By solving the above two equations simultaneously we yield: ku=0.0499, Ast=402mm^2
We can use 2 N16 bars as bottom tensile reinforcement to achieve the 402mm^2 required area of tensile reinforcement.
Note: Shear should be checked as per Section 3.3 of this article and deflection should be checked as per Section 3.4 of this article. It is always imperative to verify hand calculations using software.
Using ClearCalcs Concrete Beam Calculator to AS 3600:2018, we can greatly speed up the design process and even improve a conforming design to be more structurally efficient.
First, we input the key properties of the problem as per the below.
Based on these inputs, we can check the structural adequacy of the tensile reinforcement being 2 N16 bars using the traffic light checks for moment, shear and deflection utilisation of the beam.
We can see that the design is conforming, but at only 62% utilisation, we could seek to make the design even more efficient, by reducing the beam size or reinforcement area to save money during construction or we could achieve a longer span for the beam which may be more architecturally pleasing.
ClearCalcs provides instantaneous feedback to any changes made to the inputs rather than having to perform all the calculations again!
Concrete beams can be under-reinforced, over-reinforced, or balanced-reinforced, depending on the design criteria which determines the failure mechanism.
To ensure a gradual ductile failure (which will show signs of fatigue and allow occupants to safely leave the building before failure), the beam must be under-reinforced.
This can be satisfied by setting a limit on the depth of neutral axis factor () to be less than that corresponding to a balanced failure state: < . According to AS 3600, < 0.36. This will result in an adequate ductility provided in the beam. Over-reinforced beams where > can experience brittle failure that results in instantaneous collapse.
Note: Satisfying 𝑘𝑢 ≤ 0.36 is equivalent to 𝑝 ≤ 𝑝𝑚𝑎𝑥 where p is the reinforcement ratio.
There are minimum strength requirements in AS 3600:2018 Section 8.1.6 that denote the minimum amount of flexural reinforcement that must be checked during the design (excerpt below).
Crack control of beams is covered in AS 3600:2018 Section 8.6. Some key steps are summarised below.
Step 1: Check Concrete Cover and Bar Spacing: Cover<100mm & >40mm, Spacing<300mm
Step 2: Check Tension Stress in Bars
Using the moment capacity in service of the reinforcement.
Assume:
< 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑆𝑡𝑟𝑒𝑠𝑠 where, $𝑀𝑠 = 𝐺 + 0.7𝑄$$
Check against the Tables in AS 3600:2018 Section 8.6.2.2
Table 8.6.2.2 in AS 3600:2018 for maximum steel stress for tension or flexure in reinforced beams
AS 3600:2018 Section 8.3 details the requirements for detailing of reinforcement and should be referred to after calculating the amount of flexural and shear reinforcement.
Some of the key requirements for flexural reinforcement are summarised below.
For the negative bending force at supports:
Unequal spans:
For the positive bending force at midspan:
Regarding shear requirements:
These rules ensure proper placement and lengths of reinforcing bars to support the beams and meet necessary strength criteria. There are a range of detailing requirements for shear and torsional reinforcement in the standard that also need to be adhered to.
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