Designing a Concrete Beam Using the New AS3600:2018 - Webinar Slides - ClearCalcs

Designing a Rectangular
Concrete Beam Using AS3600-
2018
Understanding the design process using the
newly-updated standard
Brooks H. Smith, CPEng, PE, MIEAust, NER, RPEQ
brooks.smith@clearcalcs.com

Outline
• Introduction
• Overview of Major Changes
• Designing a Rectangular Beam
• Flexural Capacity
• Shear Capacity
• Deflection
• Stability Checks
• Crack Control
• Example Beam Calculations
• Conclusion & Questions
218 October 2018 ClearCalcs.com | FEA Structural Design in the Cloud

Introduction – About the Presenter
• Chartered Professional Engineer
• MCivE, MIEAust, NER, RPEQ, P.E. (USA)
• Currently the lead engineering developer for ClearCalcs
• Recently released concrete beam calculator for AS3600-2018
• 8 years of previous experience in:
• Forensic structural engineering, specialising in reinforced and PT concrete
• Research fellowship in system behaviour of thin-walled steel
• Structural engineering R&D consulting, specialising in cold-formed steel
3
Brooks H. Smith

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Intro Video Hyperlink

Introduction – Today’s Goals
• To be able to design a rectangular reinforced concrete beam to
AS3600-2018
• No torsion forces
• No prestressing or post-tensioning
• I’ll point out important points where T-beams differ
• Differences to 2009 code will only be broadly addressed
• Detailing will only be broadly addressed
• Provisions are very prescriptive and depend on precise geometries and layout
• We’ll distribute this slide deck and video after the webinar
• Please ask quick questions as I go – best to answer while on the
topic
• I’ll save involved questions until the end

Outline
• Introduction
• Shear Capacity
• Deflection
• Crack Control

Overview of Major Changes
• Phi factors are revised
• Mostly simplified, increased
• Shear procedure significantly redone
• New methodology for shear strength of concrete
• Rectangular stress block formulas modified
• Deflection calculations modified
• Alternative method & effective moment of inertia changes
• Shrinkage & creep calculations heavily revised
• Simplifying conservative assumptions
• Also: Punching shear, SFRC, some detailing, fatigue, diaphragms
• Though these are outside the scope of this webinar

Phi Factors Updated (Table 2.2.2)
• Many limit states increased by 0.05
• Shear and torsion for most members with Class N reo: 0.7 → 0.75
• Tension with Class N reo: 0.8 → 0.85
• Compression: 0.6 → 0.65
• Bending without axial increased:

Shear Procedure Redone (Cl 8.2)
• Procedure almost completely redone
• Forget all the equations you previously learned
• Largely adopted the United States ACI procedure
• Generally simpler
• Explicit alternate (simplified) clauses for non-prestressed beams
• Torsion (formerly Section 8.3) merged into shear (Section 8.2)

Rectangular Stress Block Formulas (Cl
8.1.3)
• Formulas for the rectangular stress block assumed in flexural
loading have been modified
• Strength of the concrete has less effect on shape of block
• Already modified in 2009’s A1 revision, further modified in 2018

Deflection Calculations Modified (Cl 8.5)
• Effective moment of inertia equation modified
• 2009’s A2 added in alternative (simpler) non-prestressed
equations
• 2018 fixes an important mistype in there, but otherwise unchanged
since A2
• Parentheses are important!

Shrinkage & Creep Revised (Cl 3.1.7-8)
• Shrinkage
• Same equations, but factors simplified, made a little more conservative
• Adelaide and Perth, you are no longer lumped into “elsewhere”!
• Creep
• Was completely revised in 2009’s A2 revision
• 2018 further adds a k6 factor to account for non-linear creep at high
stress

Outline
• Introduction
• Shear Capacity
• Deflection
• Crack Control

Designing a Rectangular Concrete Beam
• Calculate your demands by AS1170.X
• Limit states which must be checked:
• Positive moment flexural capacity (midspans)
• Negative moment flexural capacity (supports)
• Shear capacity
• Deflection
• Stability
• Crack control

Geometric Derivatives
• First, make sure you’ve calculated some of your basic geometry:
• Ast = total area of tension steel
• d = depth to centroid of outer layer of tension steel
• Asc = total area of compression steel
• dsc = depth to centroid of outer layer of compression steel
• Asv = total area of transverse steel (shear reinforcement)
• n = ratio of elastic modulus of steel to elastic modulus of concrete
• Ig = gross second moment of area / moment of inertia
• Ag = gross cross-sectional area

Flexural Capacity - Uncracked Beam
Analysis
• Essentially an elastic composite beam calculation using
mechanics
• Needed later for minimum bending strength calculations
16
𝐴𝐴𝑠𝑠𝑠𝑠,𝑡𝑡𝑡𝑡 = 𝑛𝑛 − 1 𝐴𝐴𝑠𝑠𝑠𝑠
𝐴𝐴𝑠𝑠𝑠𝑠,𝑡𝑡𝑡𝑡 = 𝑛𝑛 − 1 𝐴𝐴𝑠𝑠𝑠𝑠
𝑑𝑑𝑛𝑛,𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 =
∑ 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 ∗ [𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐]
∑[𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎]
𝐼𝐼𝑔𝑔,𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 = 𝐼𝐼𝑔𝑔 + 𝐴𝐴𝑔𝑔 𝑑𝑑𝑛𝑛,𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 −
𝐷𝐷
2
2
+𝐼𝐼𝑠𝑠𝑠𝑠,𝑡𝑡𝑡𝑡 + 𝐴𝐴𝑠𝑠𝑠𝑠,𝑡𝑡𝑡𝑡 𝑑𝑑𝑛𝑛,𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 − 𝑑𝑑𝑠𝑠𝑠𝑠
2
+𝐼𝐼𝑠𝑠𝑐𝑐,𝑡𝑡𝑡𝑡 + 𝐴𝐴𝑠𝑠𝑐𝑐,𝑡𝑡𝑡𝑡 𝑑𝑑𝑛𝑛,𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 − 𝑑𝑑𝑠𝑠𝑐𝑐
2
𝑍𝑍 =
𝐼𝐼𝑔𝑔,𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢
min(𝑑𝑑𝑛𝑛,𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢, 𝐷𝐷 − 𝑑𝑑𝑛𝑛,𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢)

Flexural Capacity – Ultimate (Cl 8.1.3)
• Based upon rectangular stress block theory
• Assuming steel will yield (usually desired)
17
𝑘𝑘𝑢𝑢 =
𝐴𝐴𝑠𝑠𝑠𝑠 𝑓𝑓𝑠𝑠𝑠𝑠
𝛼𝛼2 𝑓𝑓𝑐𝑐
′
𝛾𝛾𝛾𝛾𝛾𝛾 + 𝐴𝐴𝑠𝑠𝑠𝑠 𝑓𝑓𝑠𝑠𝑠𝑠
𝛼𝛼2 𝑓𝑓𝑐𝑐
′
𝛾𝛾𝑘𝑘𝑢𝑢 𝑑𝑑
𝑑𝑑𝑛𝑛 = 𝑘𝑘𝑢𝑢 𝑑𝑑
𝑀𝑀𝑢𝑢 = 𝐴𝐴𝑠𝑠𝑠𝑠 𝑓𝑓𝑠𝑠𝑠𝑠 ∗ 𝑑𝑑 −
𝛾𝛾𝑘𝑘𝑢𝑢 𝑑𝑑
2
Stress Strain

Flexural Capacity – Minimums (Cl 8.1.6)
• Minimum moment capacity required:
• …unless failure will not lead to reduced collapse load or sudden collapse
• For reinforced beams, this means a minimum quantity of tensile steel:
• In other words, you must meet one of the two above equations
18
with no prestressing → 𝑀𝑀𝑢𝑢,𝑚𝑚𝑚𝑚 𝑚𝑚 = 1.2 𝑍𝑍 𝑓𝑓𝑐𝑐𝑐𝑐.𝑓𝑓
′

Flexural Capacity – Finalising (Cl 8.1)
• Check that concrete will not crush (Cl 8.1.3 / 8.1.5)
• Calculate your ɸ (capacity) factor:
19
𝜀𝜀𝑐𝑐 =
⁄𝑓𝑓𝑠𝑠𝑠𝑠 𝐸𝐸𝑠𝑠 𝑘𝑘𝑢𝑢
1 − 𝑘𝑘𝑢𝑢
≤ 0.003
18 October 2018
Final Capacity = 𝜙𝜙𝑀𝑀𝑢𝑢
ClearCalcs.com | FEA Structural Design in the Cloud

Shear Capacity – General (Cl 8.2.1-3)
• For most flexural beams, may design by Sectional Design
Method
• Unless near discontinuities (see Cl 8.2.2, not yet included)
• Calculate your effective shear depth
• 𝑑𝑑𝑣𝑣 = max(0.72𝐷𝐷, 0.9𝑑𝑑)
• Make sure you use the correct 𝑑𝑑 – based on tension reo! (Cl 8.2.1.9)
• 𝑏𝑏𝑣𝑣 = 𝑏𝑏𝑤𝑤 = 𝐵𝐵 for rectangular beams
• Shear fitments / ligatures required if 𝑉𝑉∗ > 𝜙𝜙𝑉𝑉𝑢𝑢𝑢𝑢 or if 𝐷𝐷 ≥ 750𝑚𝑚𝑚𝑚
• And the minimum cross-sectional area of fitments is the following:

Shear Capacity – Concrete (Cl 8.2.4)
• Main equation:
• Can usually use a simplified method to calculate 𝑘𝑘𝑣𝑣 (Cl 8.2.4.3)
• For reo with 𝐹𝐹𝑠𝑠𝑠𝑠 ≤ 500𝑀𝑀𝑀𝑀𝑀𝑀, 𝑓𝑓𝑐𝑐
′ ≤ 65𝑀𝑀𝑀𝑀𝑀𝑀, maximum aggregate size ≥ 10mm
• Mandatory sanity checks (Cl 8.2.4.4-5):
• If creep, shrinkage, differential temperature > 10% of stress, must consider
• If load reversal can cause cracking, then 𝑉𝑉𝑢𝑢𝑢𝑢 = 0

Shear Capacity – Steel (Cl 8.2.5)
• 𝛼𝛼𝑣𝑣 = angle of shear fitments, 𝜃𝜃𝑣𝑣 = 36°
• (these are the same equation)
• Can only include steel strength if you have at least minimum
fitments
• 𝐴𝐴𝑠𝑠𝑠𝑠 ≥ 𝐴𝐴𝑠𝑠𝑠𝑠,𝑚𝑚𝑚𝑚 𝑚𝑚

Shear Capacity – Finalising (Cl 8.2.1-3)
• Check that concrete will not crush:
• Total shear capacity:
• 𝑉𝑉𝑢𝑢 = min(𝑉𝑉𝑢𝑢𝑢𝑢 + 𝑉𝑉𝑢𝑢𝑢𝑢, 𝑉𝑉𝑢𝑢.𝑚𝑚𝑚𝑚𝑚𝑚)
• Calculate your 𝜙𝜙 factor:
• That is: 𝜙𝜙 = 0.75 if 𝐴𝐴𝑠𝑠𝑠𝑠 ≥ 𝐴𝐴𝑠𝑠𝑠𝑠.𝑚𝑚𝑚𝑚 𝑚𝑚 and 𝑉𝑉𝑢𝑢 < 𝑉𝑉𝑢𝑢.𝑚𝑚𝑚𝑚𝑚𝑚

Deflection – General (Cl 8.5)
• Three methods:
1. Refined – take all strain properties and staged construction into account
2. Deemed-to-conform – set span-to-depth ratios, etc
3. Simplified – our method, likely your most common
• Short-term deflection based on effective second moment of area:
• 𝑏𝑏𝑒𝑒𝑒𝑒 = 𝑏𝑏𝑤𝑤 = 𝐵𝐵 for rectangular beams

Deflection – Long-Term (Cl 8.5.3.2)
• Two methods:
1. Calculate shrinkage and creep by Cl 3.1.7-8 – often a tedious process
2. Estimate factor – our method, likely your most common
• Additional long-term deflection factor:
• 𝛿𝛿𝑙𝑙𝑙𝑙 = 𝛿𝛿𝑠𝑠𝑠𝑠 + 𝑘𝑘𝑐𝑐𝑐𝑐 𝛿𝛿𝑠𝑠𝑠𝑠
• Calculated at midspan for interior spans, and at supports for cantilevers

Stability Checks (Cl 8.9)
• May use either:
• Full stability analysis
• Deemed-to-conform – our method
• Interior spans:
• 𝐿𝐿1 = distance between lateral restraints
•
𝐿𝐿1
𝑏𝑏𝑒𝑒𝑒𝑒
≤ min
180𝑏𝑏𝑒𝑒𝑒𝑒
𝐷𝐷
, 60
• Cantilevers:
• 𝐿𝐿𝑛𝑛 = clear projection of cantilever
•
𝐿𝐿𝑛𝑛
𝑏𝑏𝑒𝑒𝑒𝑒
≤ min
100𝑏𝑏𝑒𝑒𝑒𝑒
𝐷𝐷
, 25

Crack Control (Cl 8.6)
• Usually only need to meet:
• For beams that will be fully enclosed in the building after construction,
and cracking will not affect beam’s function, then:
27
≤ 100mm ≤ 300mm
a)
b)

Shrinkage & Creep (Cl 3.1.7-8)
• Shrinkage (Cl 3.1.7):
• Sum of autogenous strain (𝜀𝜀𝑐𝑐𝑐𝑐𝑐𝑐)
+ drying strains (𝜀𝜀𝑐𝑐𝑐𝑐𝑐𝑐)
• May typically simply look up in table:
• Creep (Cl 3.1.8):
• 𝜎𝜎0 = stress due to sustained loads
• 𝐸𝐸𝑐𝑐 = �
𝜌𝜌1.5
∗ 0.043 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐, 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐 ≤ 40𝑀𝑀𝑀𝑀𝑀𝑀
𝜌𝜌1.5
∗ 0.024 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐 + 0.12, 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐 > 40𝑀𝑀𝑀𝑀𝑀𝑀

Outline
• Introduction
• Shear Capacity
• Deflection
• Shrinkage, Creep, etc

Example Beam #1 – Simply Supported
30
3500 mm
3x N12
130mm
300mm
50mm
• Office building floor beam
• No transverse shear reinforcement
• Load width of 1000mm
• 𝑓𝑓𝑐𝑐
′
= 32𝑀𝑀𝑀𝑀𝑀𝑀
G = 0.9 kPa
Q = 1.5 kPa
18 October 2018
Showing methods and formulas
using ClearCalcs’s new reinforced
concrete calculator

Example Beam #2 – Complex Beam
31
3x N10
130mm
300mm
50mm
2x N12
30mm
2x N10
3x N12
Positive Moment Regions Negative Moment Regions
G = 0.9 kPa
Q = 1.5 kPa
• Retail building floor beam
• R6 shear reinforcement @ 200mm
near supports
• Load width of 1500mm
• 𝑓𝑓𝑐𝑐
′
= 32𝑀𝑀𝑀𝑀𝑀𝑀
3500 mm 4500 mm 2000 mm
18 October 2018
Ex #1 Beam @ 7000mm

Outline
• Introduction
• Shear Capacity
• Deflection
• Shrinkage, Creep, etc

Summing It Up
• Major updates in 2018 include:
ɸ factors • Shear • Rectangular stress block • Deflection •
Shrinkage/Creep
• Beam design checks at all sections include:
• Flexure: Uncracked analysis → Rectangular stress block → Minimum
checks
• Shear: Concrete contribution → Steel contribution → Maximum check
• Deflection: Effective 2nd moment of area → Long-term factor
• Stability: Maximum span-to-breadth ratios
• Crack Control: Minimum steel & maximum reo spacings
• We performed examples with simply supported and complex
beams

Questions?
3418 October 2018
Explore our broad range of calculations
at clearcalcs.com
Already available:
- Timber
- Steel
- Concrete
- Connections
- Retaining walls
In development:
- Cold-formed steel
- Advanced connections
- Foundations
- Retaining walls
And watch for more free webinars
upcoming on designing other types of
members and connections!
Q: Will you be adding C sections
A: We will be implementing these, starting with cold formed
steel C sections. Hot rolled will be added at a later point
Q: Is % reinforcement available in ClearCalcs?
A: If you click Details > on the top right of the calculation, and
then toggle from “Summary” to “Detail” additional info.
Q: Has 2009 requirement to include shear steel if V*>Vu been
changed?
A: yes, it has been replaced in 2018. You only need to include
shear steel if V* exceeds phi factor * contribution from concrete
Q: Can you calculate the beam’s reinforcement using any type
of load?
A: Yes, you can calculate using any type of load (e.g. wind,
seismic) and may include triangular, point load, or moments.

Appendix
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Designing a Concrete Beam Using the New AS3600:2018 - Webinar Slides - ClearCalcs

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