How do you calculate air volume in a concrete problem?
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NJHHEngineer P.E.
Got a bridge to sell ya.
Take a look at the two questions again, you'll see you're solving for two different things.
In the first, you're looking for the unit weight. They are not calculating the air volume, but the total mix volume WITH air (I mean, in a sense they are calculating the air volume and adding it to the total solids, but specific calculation not required). Air has no mass, but occupies volume, so your unit weight is the total weight of components divided by the total volume INCLUDING the air.
In the second, you are looking for the volume of fine aggregate, in what I assume is 1 CY (27 CUFT). So given the weight and SG of cement you calculate the volume in CU FT, the apparent previously calculated CU FT volume of coarse, and W/C ratio (calculate based on given info) used to calculate volume of water in CU FT, and the volume occupied by air (total 27 CU FT, 4% is air, therefore 96% is "solids"). Sum that up (3.11+9.66+4.31+1.08) and you get 18.16 CU FT. That's comprised of the cement, coarse, water and air. So, the total volume of fine aggregate is then 27 CU FT - 18.16 CU FT.
In the first, you're looking for the unit weight. They are not calculating the air volume, but the total mix volume WITH air (I mean, in a sense they are calculating the air volume and adding it to the total solids, but specific calculation not required). Air has no mass, but occupies volume, so your unit weight is the total weight of components divided by the total volume INCLUDING the air.
In the second, you are looking for the volume of fine aggregate, in what I assume is 1 CY (27 CUFT). So given the weight and SG of cement you calculate the volume in CU FT, the apparent previously calculated CU FT volume of coarse, and W/C ratio (calculate based on given info) used to calculate volume of water in CU FT, and the volume occupied by air (total 27 CU FT, 4% is air, therefore 96% is "solids"). Sum that up (3.11+9.66+4.31+1.08) and you get 18.16 CU FT. That's comprised of the cement, coarse, water and air. So, the total volume of fine aggregate is then 27 CU FT - 18.16 CU FT.
civilrobot PE etc etc
The Beyonce of Construction
@rodr
In the first problem, you need to solve for the total yield of concrete (Volume) in order to solve for the unit weight (Weight/Volume). The total yield is not given. Instead, you can solve for the volume for the cement, sand, coarse aggregate, and water. You know that 3% of the total yield is air. So, you set up the equation to say:
1. Volume of Cement + Volume of Sand + Volume of Coarse Aggregate + Volume of Water = (1-0.03)x <--x = total yield of concrete here
2. In your case, you get 3.46=0.97x
3. Then solve for the total yield of concrete, x = 3.567 ft^3
In the second problem, you can assume that the total yield is 1 yd^3 because the problem isn't asking you to find the total yield or the unit weight. So in this case, you know that the Volume of Air is 4% of the total yield.
I hope this helps. It took me a while to figure it out too. I actually scribbled down this equation in my binder somewhere because it stumps me every now and again. The mental gymnastics can be frustrating.
In the first problem, you need to solve for the total yield of concrete (Volume) in order to solve for the unit weight (Weight/Volume). The total yield is not given. Instead, you can solve for the volume for the cement, sand, coarse aggregate, and water. You know that 3% of the total yield is air. So, you set up the equation to say:
1. Volume of Cement + Volume of Sand + Volume of Coarse Aggregate + Volume of Water = (1-0.03)x <--x = total yield of concrete here
2. In your case, you get 3.46=0.97x
3. Then solve for the total yield of concrete, x = 3.567 ft^3
In the second problem, you can assume that the total yield is 1 yd^3 because the problem isn't asking you to find the total yield or the unit weight. So in this case, you know that the Volume of Air is 4% of the total yield.
I hope this helps. It took me a while to figure it out too. I actually scribbled down this equation in my binder somewhere because it stumps me every now and again. The mental gymnastics can be frustrating.
NJHHEngineer P.E.
Got a bridge to sell ya.
And exhausting...even in my head I still can't do a back flip.
civilrobot PE etc etc
The Beyonce of Construction
Right? When you're sitting for the exam, and see something like this, it's frustrating because you know it's simple but your brain is tired and can't make it over the hump to solve it. lol
Maybe I'll feel differently after I pass, but the more I study this thing, the more I think that it should be split up into 2 days. I've been in the work force for 18 years and I've NEVER had a day where I need to think through this many different areas of civil engineering for 8 hours straight. It's not realistic. But anyway... that's not my business. I just need to pass.
@civilrobot @NJHHEngineer thank you both for your explanations. The difference between the problems seems so subtle. I always thought that of they didn't give you the volume then you should assume 1 cy. But it sounds like it is more based off what they are asking for.
So is it as simple as thinking that if they ask for unit weight then we cannot assume the volume is 1 cy?
I'll take a look at these problems again today to make sure it's all clear now. I've spent a lot of time on this section and felt pretty confident besides this part. Thanks
So is it as simple as thinking that if they ask for unit weight then we cannot assume the volume is 1 cy?
I'll take a look at these problems again today to make sure it's all clear now. I've spent a lot of time on this section and felt pretty confident besides this part. Thanks
civilrobot PE etc etc
The Beyonce of Construction
Samir from EET said the rule of thumb is if they don't provide it, you should assume that the total yield is 1 cy. But you bring up a valid question. I wouldn't make a hard and fast rule, but I've noticed that typically in my practice problems, it's been clearly articulated. But now I need to go back and look.
NJHHEngineer P.E.
Got a bridge to sell ya.
I had this EXACT thought in my prep. I understand the purpose of the exam is to test competency in the engineering principles (and practice). But to me, beating a dead horse for 8 hours isn't necessarily going to prove that said examinee is competent (or incompetent). The 8 hours turns more of a test of mental endurance, not necessarily knowledge or competency. You've just proven that someone could answer questions on a test. I've been out of college now and working for ~10 years, and not once in my career have I had someone with a gun to my head say "You have 6 minutes to determine this X,Y,Z and tipping moments and Factor of Safety used etc. or else" - Sure I've had maydays from the field requiring immediate attention, but even those it turns more into initial damage control and then the engineering is for the future solution.
BUT, I understand they do need some kind of barometer of measure, so the test is a necessary evil.
@rodr, you're very welcome. One piece of advice i can offer is, READ the questions SLOWLY, and COMPLETELY. Understand what the question is asking. Don't just bomb into solving it. Sometimes one word difference or caveat turns the whole question upside down. Sometimes the solution is much simpler than it appears. Also, everyone says "Solve problems. Solve Problems. Solve more problems". While I agree you need to solve several different style problems, make sure that you're not becoming robotic and actually understand the WHY behind the solving. The exam is not all plugging numbers and solving equations. Make sure you understand the theory behind it as well. My particular exam was very heavy on the conceptual style. I think that caught a lot of people off guard (myself included).
NJHHEngineer P.E.
Got a bridge to sell ya.
An Also also, if you're taking the EET course, those binders are your #1 resource. If you take the time to watch the lectures, do all of the practice problems, and the exams they give at the end...you will be fine. I took the class as well and would recommend it 1000%. AND don't be afraid to email and ask questions. Samir and team are extremely helpful and responsive. Not sure where you are time zone wise in relation to them but that seemed to be the only real factor in their "delay" response. I'm east coast, they're west coast. 90% of my questions were emailed at ~ 5:30am ish here when I got to work. I'd usually get an answer from them by the end of that day, maybe the next day.
