Reinforced Concrete Design (With Flowchart)

Reinforced Concrete Design (with Flowchart) – Concrete Beam with Tension Reinforcement Only April 14, 2014 by Andy Lin 3 Comments

Have you heard of Mu/4d? That’s something I learned at work from one of my bosses who has been a licensed SE since 1984! It’s basically a quick way to check your numbers for concrete flexure (which I will show you later in the post). Apparently that’s how engineers used to do quick checks – there’s no reasons why we can’t still use the same technique today.

In this post, you will learn how to design a reinforced concrete beam step-by-step, with my “simple-to-follow” flowchart. By creating and using the flowchart, I was able to recall the info needed without having to memorize anything which I hope I can help you do the same.

The Goals There a few things that I want to help you achieve by the end of the post: 

To be able to come up with the required reinforcement without having to “re-read” anything.



Recall how to design without memorizing.



A step-by-step procedure that can be easily followed so that you don’t miss all the little “fine-prints” such as minimum/maximum reinforcement requirement…etc.

Note that the flowchart mainly addresses the design of a rectangular beam (not T-beams) with tension reinforcing only. T-beam design will come in a later post.

Assumptions I want to point out that since you are taking the SE exam, you most likely have some idea about all of the concrete properties (brittle) and the design theories (compression zone…etc.) so I am not going to elaborate too much about them. If you do need more info though, please let me know – I am more than happy to help. Another thing I want to mention is that there are many many ways to do the same design and this is just the one that I am most familiar with. OK let’s get to this!

Flowchart The flowchart itself is pretty self-explanatory (maybe because I created it?) but I am going to give you a quick rundown anyway. Please do not hesitate to let me know if you got any questions. Click Here to get the Flowchart What’s Given? Usually, you should already have something to get started with on your design:



Mu: Factored design moment based on the worst case from your load combinations.



f’ c: Specified compressive strength. This is typically 3000, 4000, or 5000 psi.



fy: Specified yield strength of reinforcement. Usually 60,000 psi for new buildings and 40,000 psi for older buildings.



b: Width of the beam.



d: Usually the total beam depth – cover – 1/2 of the rebar diameter. I am going to assume you know what this is.

What Are We Trying to Determine? Ultimate goal is of course to find the reinforcements you need that makes the beam work. Quick Check

Before you do anything, it’s a good idea to do this first. Like I mentioned in the beginning, it’s a very quick way to get a rough number for the reinforcement you need. I know the units don’t make sense but just go with it and test it out. You want to make sure the unit for your “Mu” is [kip-ft] and “d” is [in]. The result will be in [in2]. I’ll show you an example at the end. Step-by-Step Explanations #

Equation

1

Action

Notes/Explanation

Calculat e

You are going to calculate this number a lot. It’s used for determining the factor which you can see in the next item.

2

Use Appendix A Table (of the SE Reference

Determi

This basically tabulates

the equation

so that you don’t have to plug in the numbers. For example, if you had calculated , Manual)

3

4

ne

Calculat e

Calculat e (make sure your units are in psi)

using the table, you get =0.259. Pretty handy.Let me know if you don’t have the table, I can create one and post it when I get a chance. You can also solve the equation using quadratic formula if needed. This is basically the reinforcement ratio you need. You still need to verify min/max and …etc. This is the minimum reinforcement ratio required. I have tabulated the number for the most common case: if and , then .

Calculat e

This will be used in a couple of equations later.

Calculat e

This is the maximum reinforcement ratio which was derived from the requirement of minimum net tensile strain at nominal strength.

Calculat e

After comparing these three numbers, we should now know how much reinforcement is needed that meets both the minimum and maximum requirements.PS: I wrote it in this format because I am used to writing like this in Excel functions which I assume you might be as well.

Calculat e

This is for checking to see if the beam is “tension controlled” or “compression controlled”. See below.

9

Compare

If the statement is true, then we know that the beam is “tension controlled”.

10

Calculat e

5

6

7

8

This simply converts the ratio to an actual number so that you can decide on the number of bars and the size of bars.Note

that this number is based on a tension controlled section and has already accounted for .

Calculat e

11

This is the size of the compression block (see diagram on the very top). We need this to calculate the location of neutral axis and the corresponding factor if the section is compression controlled.

12

Calculat e

13

Calculat e

Calculat e

14

Concrete Beam Design Example Now let’s run through this flowchart with an actual example. Given 

Location of neutral axis from the top fiber. Corresponding factor as mentioned earlier. Revised (increased) reinforcement required since the section is “compression controlled” which has lower .











(say cover is 1-1/2″ and we are using #8 bar: )

Quick Check

This is the quick and dirty way to check the required reinforcement. We’ll come back to verify when we have an actual solution. Flowchart #

Equation

1

2

Results

Notes/Explanation

0.1875

Use Appendix A Table (of the SE Reference Manual)

0.243

Use the table, the number listed that is closest to 0.1875 is 0.1874 – which corresponds to .

3

0.0122

4

0.0033

5

0.85

6

0.0155

7

0.0122

8

0.0136

9

Yes; therefor e tension governs .

10

2.9171 in2

Compare to the quick calc we did above (2.8125 in2), we are fairly close! Therefore, we know that we didn’t make any computational errors.Based on this, we will need 4-No.8 bars (0.79 in2 x 4 = 3.16 in2).Note that if the As you use is significantly larger than As.req, you should repeat steps 7 and 9 to ensure that you didn’t exceed the maximum reinforcing and to ensure

that tension still governs.For example:

It is still less than the max so we are OK.

Tension still governs – we are OK here as well.

Not really necessary if tension governs but it is useful later if you want to calculate out the actual capacity. I can demonstrate how this works in a future post.

11

5.720 in

12

6.729 in

13

–

Not applicable since tension governs.

14

–

Not applicable since tension governs.

And done!

Now if you change Mu to 300 kip-ft, you can see how it works if compression governs (I won’t demonstrate here).

Determine the Capacity of a Reinforced Concrete Beam with Tension Reinforcement May 27, 2014 by Andy Lin 0 Comments

In the last post, I talk about how to determine the required reinforcing for a rectangular beam. To elaborate more on the same topic, I am going to show you how to actually calculate out the capacity (using my handy dandy flowchart). This most likely is just a refresher for many of you but it doesn’t hurt to get more familiar with the calculation (especially if you haven’t designed concrete for awhile).

The Goal To determine the moment capacity,

, without having to memorize anything – you just

need to follow the flowchart.

Flowchart This flowchart also includes the stress/strain distribution diagram shown above. Click Here to Get the Flowchart Given 

(or

)

Provided reinforcing steel (or steel ratio).



Specified compressive strength. This is typically 3000, 4000, or 5000 psi.



Specified yield strength of reinforcement. Usually 60,000 psi for new buildings and 40,000 psi for older buildings.



Width of the beam.



Usually the total beam depth – cover – 1/2 of the rebar diameter.

Determine



Moment capacity of the section.

Quick Check I’ve demonstrated the following “quick check” in an earlier post:

If we set

and rearrange the equation, we get:

where the units for

is [in²] and

is [in].

Step-by-Step #

Equation

Action

Notes/Explanation

Calculate

This calculates the size of the compression stress block.

Calculate

This is the ratio between the TC moment arm and d. It’ll be used in step [8] to obtain the moment capacity.

3

Calculate

Location of the neutral axis from top fiber. See previous post/flowchart step [5] for the calculation of .

4

Calculate

This is the strain in the tension reinforcement.

1

2

This checks whether the section is tension or compression controlled per er ACI 318, 9.3.2.2.

5

Check

6

Calculate if answer in [5] is no (i.e., compression controls).

If compression controls, you have to reduce the factor

7

Calculate if answer in [5] is yes (i.e., tension controls).

This is the

8

Calculate

based on this formula. factor for

tension controlled section. The moment capacity. This is the reinforcement ratio that will cause “balanced strain condition” which is when these two events occur at the same time: 1. Tension reinforcement yields.

9

Calculate (Optional)

2. Strain in the concrete reaches 0.003. In terms of design, you just want to make sure that your reinforcement ratio is less than this calculated value to prevent brittle failures.

Example Given 

(4-No.8)









Quick Check

Remember that this quick check is just an estimate. The point is just to make sure that we didn’t mess up the actual calculation somewhere along the way. We’ll verify the real capacity in the table below. Use the Flowchart #

Equation

Results

1

6.1961 in

2

0.8451

Notes/Explanation

is calculated to be 0.85 for 3

7.2895 in

4

0.0052

5

Yes, tension

.

controls. 6

Not applicable

7

0.90

8

240 kip-ft

This is pretty close to the quick check (253 kip-ft) which means we probably didn’t screw up arithmetically. Compares with , balanced

9

0.0214

reinforcement ratio is greater; therefore we will not get brittle failure which is good.

Done! There you have it. Is this helpful? Let me know in the comments below.

Retaining Wall Design Let’s actually talk about designing retaining walls now! Since both masonry and concrete retaining walls are likely to appear on the exam, I will only focus on the general design requirements for retaining walls. For the design specific calculations and details of each retaining wall design, I leave up to the reader for their own studying. If you’re taking the SE exam, you should make sure to practice at least one design of each type of retaining wall. I’m also going to only briefly touch on each area without going into too much detail. There are plenty of other good references on retaining wall design that will do a much better job than I can on explaining the detailed design of a retaining wall. The goal of this section is to familiarize yourself with the basic principles and make sure you cover all the bases during your studies.

Typical retaining wall types, courtesy Wikipedia Retaining walls generally have little vertical load other than self-weight and weight of any soil on a footing. However, this isn’t the case if the retaining wall is also a bearing wall. If the retaining wall is, for example, the basement foundation wall of a building, then it likely has a beam or other lateral support at the top as well as the cantilevered support at the bottom. Thus, the wall acts somewhere between a simple span beam and a fixed cantilever. With the above in mind, let’s limit our discussion to non-bearing walls for the remainder of this article (the principles are similar for both bearing and non-bearing retaining walls). Either way, the design will likely be one of the four structures shown above: gravity wall, piling wall, cantilever wall, and an anchored wall. Of note, I would consider cantilever walls to be a subsection of gravity walls. This is important because the SE exam specifications list three types of walls that may show up on the exam: 

Gravity walls



Anchored walls



Basement walls for buildings

You may also see some mentioning of piling walls or mechanically stabilized earth walls but they aren’t specifically called out in the exam specification so I believe you can reasonably

ignore these during your studies. I’d just be aware that they exist and understand the fundamentals of how those retaining structures work prior to the exam.

Loads and Reactions on Retaining Walls Loads on a retaining wall are generally as follows: 

Self-weight of the retaining wall.



Vertical weight of the soil, both in front and behind the wall (as applicable).



Lateral soil load, generally modeled as an equivalent fluid pressure. (Note: If the backfill is sloped there will be a vertical component to this load as well.)



Surcharge loads from adjacent structures or loads near the wall.

Reactions on a retaining wall depend on the type of wall being designed but will generally include some of the following: 

Vertical base soil pressure reaction, in response to overturning moments.



Passive soil pressure on the front of the wall and footing (sometimes ignored).



Friction forces between the footing of the wall and the soil.



Anchorage forces from any soil anchors in the wall.

Loads and Reactions on Retaining Walls (Photo credit: Structural Engineering Reference Manual by Alan Williams)

I’ve borrowed the image above from Alan Williams’ excellent Structural Engineering Reference Manual. Copyright? What’s that? Just kidding, fair-use laws are good to know and I was too lazy to redraw it, so be quiet. In the above image we can see all the loads on a cantilevered retaining wall. Many of these loads are applicable to all types of retaining walls. I’ve listed the loads below: 

F is the frictional force at the underside of the wall bearing surface.



HA is the total active earth pressure behind wall (HA may also include a hydrostatic component but note that any hydrostatic load will reduce the active earth pressure ).



HL is the total pressure behind the wall due to live load surcharge (if present).



HP is the total passive earth pressure in front of the wall.



WB is the weight of the base.



WK is the weight of the key (if present).



WL is the weight of the surcharge (if present).



WS is the weight of the backfill.



WW is the weight of wall stem.

The primary method to solve these problems is statics: sum of the forces and sum of the moments equal to zero. With that you can solve for all of the forces on a retaining wall. Often you will be given the retaining wall geometry and the soil properties of the backfill. You then usually are tasked with finding the resulting bearing pressures under the retaining wall. Or perhaps you have to find the length of the heel of the retaining wall (LH in the image above). Some design of the structural components will also likely be involved. The easiest way to speed up the analysis of a retaining wall is to break the vertical weights into rectangular sections, as the above image has done. You can quickly calculate and tabulate the centroid and weight of each section based on given densities and dimensions. After that, you can then sum the moments about a “point” to obtain the total moment in the wall. The “point” typically chosen is the furthest forward, lowest part of the toe of the wall’s footing (bottom left corner for the example image above); but any point will serve as long as you’re consistent. I often choose the typical “point” such that the vertical loads will cause a clockwise moment (in the wall orientation shown above) and the soil pressures will cause a counter-clockwise

moment. See the picture below from the 2008 CRSI Handbook for details, note they have separated the overturning moment Mo and the resisting moment Mr as you are often given one and must design for the other.

Overturning moment, resisting moment, and soil pressure (Picture credit: 2008 CRSI Handbook) After tabulating these moments you can then calculate the required length of heel for overturning resistance, the soil pressure from the soil below the footing of the wall, and any anchorage forces required, depending on the wall type being designed. Anchorage loading for an anchored wall should be much simpler to calculate so I’ll leave that for another time. For cantilevered and other gravity walls, you have to first calculate the centroid of the required soil bearing force (see “e” in the picture above). If it is outside of the kern (middle third of the footing) then you will have the soil pressure truncated to zero at some point on the footing. This will require a more complicated analysis and should be avoided if possible due to the time required for analysis. Remember that soil is typically assumed to have zero tensile capacity, though some very small amount does exist. Once the centroid is determined, you can then calculate the pressure distribution using the equations shown on page 2-1 of the Structural Engineering Reference Manual. After that, you can compare soil pressure demand v.s. capacity. If the exam question asks you to size the footing, most likely you will need to do an iterative analysis to come up with a satisfactory soil pressure. (Note: if you run into an iterative design like this, don’t focus on an efficient design unless required to.) For example, sure you think you can make the foundation work with only a 4-foot long heel but what if you find it needs 4.5 feet? You just wasted 10 minutes writing out a design that’s no good. Instead, just find a rough idea of what will work (remember those CRSI tables I mentioned?) and then exceed it. As far as I know you don’t lose points for an inefficient design unless they specifically mention it. Watch out for wording that might read something like “find the smallest bar diameter that can adequately reinforce the wall”. You’ll note that I have not discussed passive soil resistance so far. This is because of two very important reasons. The first being that it’s unreliable. In practice, some engineers (and myself) tend to ignore it as it may not exist in certain circumstances (unless the soil report specifically indicates it). For instance, if the wall toe is excavated for repairs or future construction then there will be no passive soil resistance to sliding or overturning. Additionally, it’s possible for the wall to “push” the soil away leaving a gap or at least a reduced passive soil pressure. Passive soil is a real force though so it can be included if required for a design to work. For example, if a shear key is added below the wall for sliding resistance then passive soil is almost certainly being used. In the case of a shear key, excavation is unlikely and the weight of the wall confining the soil will help ensure that the passive soil pressure is likely to be present. The other issue with passive soil is it’s generally not required. Frictional forces below a wall can often be sufficient to resist sliding and are very quick to calculate. Thus, not including passive soil can speed up your design process. This can save precious time during the exam.

In the end, both in real practice and on the exam, only use passive soil pressure if you require it and understand its limitations.

Structural Design of Wall Components After you’ve calculated the forces on the wall you can then design the individual components for the loads on them. Sum the forces and moments on each member in a freebody diagram and find the internal forces that need to be resisted. Typically it’s all cantilevers but you’ll see others as well. For example, a counterfort retaining wall spans continuously between the counterforts, assuming no construction joints. From here, you will design the components typically as reinforced concrete, reinforced masonry, or steel structural members, whichever is applicable. Most of these will be simple designs in nature and should be of little difficulty. Note that shear in the walls will likely not control but don’t forget to check it as some minimal shear reinforcement may be required. If possible, break the retaining wall up into 12 inch sections. This will simplify your design and loads mathematically. Further details about design of the wall components is highly dependent of the material of the retaining wall and I leave it up to the reader to study those further. See the previous blog post from Andy regarding design of reinforced concrete members for a quick refresher as much of that will apply to a concrete retaining wall. Note that the governing section of the codes for masonry and concrete will be the wall and foundation sections of those codes. Make sure to check their sections for specific requirements for walls and foundations.

Final Thoughts There’s much more to cover but I fear that this blog post is getting too long as it is. I will conclude this by broadly addressing some of the other items the reader should be familiar with regarding retaining walls. Remember that if there is a sloped backfill there will be both a vertical and horizontal component to the active pressure from the backfill (where there was just horizontal with a level backfill before). Also, remember that if they don’t give you soil data for lateral soil loads (which is unlikely), then in ASCE 7, chapter 3, there are minimum soil and hydrostatic pressure loads. Glance over Table 3-1 Design Lateral Soil Loads on page 7 and be familiar with that table and the footnotes given there. Under AASHTO most retaining walls that are subject to vehicle loads require some amount of additional “backfill” to be included to simulate a vehicle surcharge load. Bearing pressure and other service related design aspects are typically done with unfactored loads under LRFD. Some other service failures that must be checked are sliding of the

wall, lateral deflection of the wall, lateral tilt of the wall due to differential settlement, and crack control. However, I would expect that any question regarding serviceability failures will likely be related to “how would one fix it” and not include much in the way of actual design. This is entirely my own opinion, though – be prepared either way. Finally, remember that retaining walls are just spread footings that are trying to tip over. Much of the same design applies to both, and both will likely be encountered in either a large or small portion of the exam. Shear in the footings, anchorage of the reinforcement, flexure in the walls, temperature and shrinkage reinforcement, these are all going to be similar in both retaining walls and typical footings and foundations. Make sure you can do these sorts of problems quickly because any unfamiliarity will cause issues during both morning and afternoon portions of the exam. Foundation problems require much tabulation and multiple simple calculations at each step. Thus, being able to rapidly solve these sorts of problems through familiarity with the design steps is crucial to success. I hope you’ve enjoyed this blog post. It took me a little longer to finish it than I hoped but that was partly due to my lax attitude to beginning my own studies for the exam. However, that time is upon us and study we must. I plan to study hard over the next few months to pass this exam and I hope you will too. Don’t let good opportunities to study pass you by; you will miss them as October gets closer. Thanks for reading.

Standard disclaimer: The above blog post is offered as a helpful reference for studying for the NCEES Structural Engineering exam. However, no warranty is given or implied for the accuracy or correctness of the information presented and any use of this material is at the users own risk. I am not a licensed engineer in any state nor a subject matter expert in the areas discussed. I write these blogs for Andy Lin and Engineering HQ to allow myself and others to better prepare for the SE exam in the hope that we can all learn to be better engineers together.