Reinforced Concrete Moment Curvature – Development over time

I recently noticed that in the RC Design Functions spreadsheet the TimeCurve function had stopped working.  The function calculates the development of reinforced concrete section curvature over time, and was previously presented in Reinforced Concrete Moment-Curvature – 3; Restrained Shrinkage and Creep and Reinforced Concrete Moment-Curvature – 4; Development of curvature over time.

In the course of fixing the problem I took the opportunity to add some further refinements:

  • The function previously did not allow for changes in the cracking stress over time, or for the effect of creep on the cracking strain.  It now either calculates a cracking strain, which may include a proportion of the creep strain, or a cracking strain can be specified for each time step.
  • The tension-stiffening factor calculation has been revised to take account of the effect of creep and shrinkage on the cracking moment.
  • The output table has been rearranged and extended to include:
    • The virtual prestress stress, as well as strain.
    • The adjusted concrete elastic modulus.
    • The cracking moment.
    • The depth of the Neutral Axis
    • The concrete stress at the top and bottom face
    • The concrete strain including creep at the top and bottom face, and the cracking strain.

The updated spreadsheet (including full open-source code) may be downloaded from:

 RC Design Functions spreadsheet

Examples of the function results, compared with experimental data, will be included in the next post on this subject.  The screen-shots below show input and results for a typical beam loaded to just below the cracking moment, with cracking occurring as a result of the combined action of shrinkage and creep.  Click any image for a full-size version:

Function input documentation:

Typical section properties input and output graph:

Time related data input:

Note that the function may be used anywhere in the spreadsheet.  To display all the results it must be entered as an array function, using Ctrl-Shift-Enter. See Using Array Functions and UDFs for details.
Output results columns 1 to 9:

Output results columns 10 to 17:


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More from the path dug-less:

Douglas H on having no head (where H = both Harding and Hofstadter):

On Having No Head

The Incredible String Band on Douglas Traherne Harding:

(Douglas Harding’s middle name was not really Traherne, it was Edison)



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A Loopy Link (and three more)

For some reason Doug Glancy’s Excel Blog has escaped my attention up till now, but having a browse today, I discovered this loopy animation:

which would not have been out of place in Douglas Hofstadter’s “I am a Strange Loop

I really should have sent Doug G. a copy of this letter: A Tail of Two Letters …

But anyway, the Blog Roll now includes Sumbuddy.

And three more links from Alfred Vachris:

A VBA multi-threading tool.

Financial Modelling

Real Statistics Using Excel

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There is No Planet B

My latest (and final) President’s column from the Concrete in Australia Magazine:

Some responsibilities of engineers are universally recognised. Everyone accepts that we have a duty to carry out design and construction so that structures will be serviceable, strong and stable, and will be safe at all stages of construction and throughout their life. There may be debate about how this end is best achieved, indeed I will be discussing this question at the Concrete 2015 Conference in September, but there is no argument about the basic principles.

Then there is sustainability. Too often this is seen as not real engineers’ business. Something that we will incorporate if we can, to keep the architect happy, or to provide the client with some PR material, but not something that should be allowed to interfere with good engineering design.   In my opinion this approach fails to recognise that using and providing sustainable products is as fundamental a part of an engineer’s responsibilities as any other. In 1828 Thomas Tredgold, one of the founders of the profession of Civil Engineering, described it as “the art of directing the great sources of power in Nature for the use and convenience of man”. Implicit in this statement is the requirement that we should consider the effects of what we do on all humanity, including future generations. If we recognise that the use of materials cannot be sustained in the long term, or that our current practices may have a significant adverse effect on the environment, now or in the future, then we have a duty to do what we can to change these practices. Far from being antithetical to a good engineering approach, a consideration for the future effects of what we do simply requires a process of design optimisation, but one that includes allowance for hidden and future costs.

Fortunately, there is plenty of scope for changing the way we do things. New materials and new design and construction techniques provide great opportunities for innovation. These will combine with changing financial and political pressures to result in widespread changes to current standard practice. Future commercial success will demand a readiness to accept change on a wide scale. Examples of innovation of this sort that will be illustrated at the Concrete 2015 Conference include the use of ultra-high strength concrete in bridge structures, the use of geo-polymer concrete in buildings and airport pavements, and the extension of the life of old structures through remediation and strengthening. These innovations, and many others, demand the transition from academic research into industrial application. This is the theme of this year’s Concrete Conference, and I recommend attendance to all interested in maximising their future opportunities.

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Concrete 2015


This year the 27th biennial Conference of the Concrete Institute of Australia will be held in Melbourne from 31st August to 2nd September, in conjunction with RILEM Week.

Concrete 2015

On behalf of the organising and technical committees, we cordially invite you to join us at Concrete 2015. Concrete 2015 will be the 27th Biennial National Conference of the Concrete Institute of Australia in conjunction with the 69th RILEM Week conference.  This historic joint event will provide national delegates with valuable exposure to cutting edge research and development exchanges in the international forum of RILEM Week.

Concrete 2015 will focus on the theme Research into Practice. The conference is dedicated to bringing together global leaders in the concrete industry, covering all aspects of concrete design improvements, research, construction, maintenance and repair of concrete projects. Concrete 2015 will offer participants from around the world the opportunity to connect face to face and share innovative and interesting ideas on valuable research outcomes and latest construction practices.

The multidisciplinary theme of Concrete 2015 provides an excellent forum for networking and education and an opportunity to meet and interact with practitioners, engineers, scientists, researchers, academics, practitioners and professionals, and also to engage with international delegates from RILEM technical committees. Whether you attend technical sessions, sit in on multiple committee meetings, or network with friends and colleagues this conference will provide you with ample opportunity for professional growth.

On behalf of the Organising Committee, we look forward to meeting you at Concrete 2015 in Melbourne, Australia. 

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