cive.3100 e m assignment concrete mix...

CIVE.3100 ENGINEERING MATERIALS ASSIGNMENT #8: CONCRETE MIX PROPORTIONING

CIVE.3100 2016 Assignment 08 Solution of 14

PROBLEM #1: GIVEN: Concrete is required for a pavement slab that will be exposed to moderate freeze-thaw climate as well as deicing chemicals. A specified compressive strength of 4,000 psi is required at 28 days. Cement: Use Type I cement with a specific gravity of 3.15. Coarse Aggregates: 1” Nominal Maximum Size; Bulk Specific Gravity (oven-dry) = 2.67; Dry-Rodded Unit Weight = 102.5 lb/ft3; Total Moisture = 2.6%; Absorption = 1.2%. Fine Aggregates: Sand - Bulk Specific Gravity (oven-dry) = 2.65; Fineness Modulus (F.M.) = 2.70; Total Moisture = 3.2%; Absorption = 1.4%. Air Entraining Admixture: Use Euclid Chemical Eucon Air 30 (if needed). Determine the materials required for one cubic yard of concrete using the absolute volume method. REQUIRED: Determine the materials required for one cubic yard of concrete using the absolute volume method. SOLUTION (Determined using the PCA Design and Control of Concrete Mixtures 14th Edition. All figures and tables are referenced from this document unless otherwise noted): Step 1: Determine Strength (f′cr) Using Table 9-1 (page 150), concrete exposed to freezing and deicers requires a minimum design concrete compressive strength (f′c) of 4,500 psi. Therefore, the design f′c of 4,000 psi is too low. Use f′c = 4,500 psi in your calculations.



No statistical data available. Using Table 9-11 (PCA Design and Control of Concrete Mixtures): f′cr = f′c + 1,200 psi = 4,500 psi + 1, 200 psi = 5,700 psi Therefore f′cr = 5,700 psi.

Step 2: Determine w/c Ratio Using Table 9-1 for the given conditions, the maximum water-cementitious material ratio you could use is 0.45. Using f′cr = 5,700 psi (see previous calculations), Table 9-3, and interpolating, for air-entrained concrete the required w/c = 0.34 ← Use this w/c instead of maximum value from Table 9-1.



Step 3: Determine Coarse Aggregate Size: This is given (1 inch). There is no additional data provided to check if this is acceptable (i.e. no reinforcing steel spacing or pavement thickness information is provided). Step 4: Determine Air Content: Using Table 9-5 (PCA Design and Control of Concrete Mixtures), for 1 inch coarse aggregate and severe freeze-thaw conditions, use an air content of 6.0%. Add an additional 1% to cover -1% to + 2% range (see class example). Therefore, use air content = 7.0% (although 6.0% is also acceptable – no calculations are provided for this air content).



For an air content of 7.0%, the volume of air = 0.07 x (27ft3) = 1.89 ft3. Step 5: Determine Slump: For pavements, slumps are recommended to vary between 1-3 inches (see Table 9-6). Select a slump = 2 inch (middle of range). A slump between 1-3 inches is acceptable. However, no calculations are provided for additional slumps.



Step 6: Determine Water Content: Using Table 9-5 and a slump of 2 inches, air entrained concrete, and 1 inch aggregate, water = 270 lb/yd3. This takes up a volume of 270 lb/(62.4 lb/ft3) = 4.33 ft3. As discussed in class, you do not need to reduce water content for subangular aggregate or crushed particles. Step 7: Determine Cement Content: For a w/c = 0.34 (see Step 2), 2 inch slump, and 270 lb/yd3 of water, you will need 794 lb/yd3 of cement. This takes up a volume of 794 lb/(3.15 x 62.4 lb/ft3) = 4.04 ft3. Step 8: Determine Coarse Aggregate Content: Using Table 9-4, 1 inch aggregate, and a FM = 2.8 for the fine aggregate, the bulk volume of coarse aggregate per unit volume of concrete = 0.68. Therefore, the weight of the course aggregate = 0.68 x (27ft3/yd3) x (102.5 lb/ft3) = 1,882 lb/yd3. This takes up a volume of 1,882 lb/(2.67 x 62.4 lb/ft3) = 11.30 ft3.

Step 9: Determine Fine Aggregate Content: summary of the volumes of Air, Water, Cement, and Coarse Aggregates from Steps 1-5 is presented in Table A. The fine aggregates = 27 ft3 – (the sum of air, water, cement, and coarse aggregate volumes).



Table A. Summary of Steps 1-5.

Mix Part Volume (ft3)

Air 1.89

Water 4.33

Cement 4.04

Coarse Aggregate (C.A.) 11.30

Fine Aggregate (F.A.) 5.44

The weight of the fine aggregate = (Volume)x(Specific Gravity)x(Unit Weight of Water). For 3 inch slump: Weight (Fine Aggregate) = (5.44 ft3)(2.65)(62.4lb/ft3) = 900 lb. Step 10: Determine Admixture Amount: According to the Euclid Chemical Eucon Air 30 specifications, a rate of 0.5 to 1.0 oz per 100 lbs (30 to 60 mL per 100 kg) of total cementitious material is used to entrain 3% - 6% air content. Therefore, for 7% air content, you would use 1.17 oz per 100 lbs cement. Since you have 794 lbs of cement, you would use 9.3 oz of Euclid Chemical Eucon Air 30. Step 11: Apply Moisture Correction: Weight of Wet C.A. required for 1 yd3 of concrete = 1882 lbs (1.026) = 1931 lb Weight of Wet F.A. required for 1 yd3 of concrete = 900 (1.032) = 929 lb Free Moisture in C.A. = (0.026 – 0.012) 1882 = 26 lb Free Moisture in F.A. = (0.032 – 0.014) 900 = 16 lb Water contributed by the aggregates = 42 lb Actual amount of water to be added = 270 lb – 42 lb = 228 lb A summary of the final batch weight corrected for moisture is presented in Table B.



Table B. Summary of Final Batch Weight corrected for Moisture.

Mix Part Weight/Cubic Yard

(lbs)

Air 7.0%

Water 228 lb

Cement 794 lb

Admixture 9.3 oz

Coarse Aggregate (C.A.) 1931 lb

Fine Aggregate (F.A.) 929 lb

PROBLEM #2: GIVEN: Determine the materials required for one cubic yard of concrete for SCDOT Class 4000 structural concrete using the absolute volume method. The project will be in Charleston, SC and you will be using the concrete for a bridge abutment. You have the following coarse and fine aggregates available: Coarse Aggregates: ¾ inch Nominal Maximum Size (ASTM C33) gravel, Bulk Specific Gravity (oven-dry) = 2.68; Absorption = 0.75% (SSD – Saturated Surface Dry), and an oven-dry rodded bulk density (unit weight) = 103 lb/ft3; Lab trail batching moisture content = 2.70%. Fine Aggregates: Sand - Bulk Specific Gravity (oven-dry) = 2.65; Fineness Modulus (F.M.) = 2.50; Total Moisture = 4.2%; Absorption = 0.8%. Air Entraining Admixture: Use Euclid Chemical Eucon Air 30 (if needed). REQUIRED: Determine the materials required for one cubic yard of concrete for SCDOT Class 4000 structural concrete using the absolute volume method. SOLUTION (Determined using the PCA Design and Control of Concrete Mixtures 14th Edition and the SCDOT 2007 Standard Specifications. All figures and tables are referenced from these documents unless otherwise noted): Read the Specifications!



SCDOT Standard Specifications, Table from Section 701.2.12.2:

SCDOT Standard Specifications, Section 701.2.5 (Air Entrained Concrete): Unless otherwise specified, use a design mix for air-entrained concrete based on 4.5% (± 1.5%) entrained air, except for prestressed concrete. If the concrete is pumped, then the entrained air will be acceptable at 5.5% (± 1.5%) measured at the truck. So, the specifications state you need to use air-entrained concrete. Now use the PCA Design and Control of Concrete Mixtures Book. Step 1: Determine Strength (f′cr) For SCDOT Class 4000 structural concrete: f′c = 4,000 psi. No statistical data available. Using Table 9-11 (PCA Design and Control of Concrete Mixtures):

f′cr = f′c + 1,200 psi. Therefore f′cr = 5,200 psi.



Step 2: Determine w/c Ratio How often does it freeze in SC? Here is some historical data:

It doesn’t typically freeze in Charleston, SC. Therefore, using Table 9-1, you see that you don’t have requirements for maximum w/c and minimum f′c.

Using f′cr = 5,200 psi (see previous calculations), Table 9-3, and interpolating, for air-entrained concrete the required w/c = 0.34.



Step 3: Determine Coarse Aggregate Size: This is given (¾ inches). There is no additional data provided to check if this is acceptable (i.e. no reinforcing steel spacing or pavement thickness information is provided). Step 4: Determine Air Content: As previously noted, SCDOT Standard Specifications, Section 701.2.5 (Air Entrained Concrete) states to use air content of 5.5% (± 1.5%). Use 6.5% (5.5% + 1%) for batching (+1% same as previous and in class example). Using 6.5% air content, the volume of air = 0.065 x (27ft3) = 1.76 ft3. Note you could use 5.5% or anything in the range, but you would want to avoid the exteremes. Step 5: Determine Slump: SCDOT Standard Specifications, Section 701.4.6 (Slump) notes a maximum slump of 4 inches for all concrete except Class 2500 or unless otherwise specified. Use a slump = 4 inches (although 3 inches is acceptable). Step 6: Determine Water Content: Using Table 12-5 and a slump of 4 inches, air entrained concrete, and ¾ inch aggregate, water = 305 lb/yd3. This takes up a volume of 305 lb/(62.4 lb/ft3) = 4.89 ft3.



As discussed in class, you do not need to reduce water content for subangular aggregate or crushed particles. Step 7: Determine Cement Content: For a w/c = 0.34 (see Step 2), 4 inch slump, and 305 lb/yd3 of water, you will need 897 lb/yd3 of cement. Select Type I cement (no reason to select another Type). Use a specific gravity of 3.15 for Type I (See Problem #1). This takes up a volume of 897 lb/(3.15 x 62.4 lb/ft3) = 4.56 ft. Step 8: Determine Coarse Aggregate Content: Using Table 9-4, ¾ inch aggregate, and a FM = 2.7, the bulk volume of coarse aggregate per unit volume of concrete = 0.65. Therefore, the weight of the course aggregate = 0.65 x (27ft3/yd3) x (103 lb/ft3) = 1,808 lb/yd3. This takes up a volume of 1,808 lb/(2.68 x 62.4 lb/ft3) = 10.81 ft3.

Step 9: Determine Fine Aggregate Content: A summary of the volumes of Air, Water, Cement, and Coarse Aggregates from Steps 1-5 is presented in Table C. The fine aggregates = 27 ft3 – (the sum of air, water, cement, and coarse aggregate volumes).



Table C. Summary of Steps 1-5.

Mix Part Volume (ft3)

Air 1.76

Water 4.89

Cement 4.56

Coarse Aggregate (C.A.) 10.81

Fine Aggregate (F.A.) 4.98

The weight of the fine aggregate = (Volume)x(Specific Gravity)x(Unit Weight of Water). For 4 inch slump: Weight (Fine Aggregate) = (4.98 ft3)(2.65)(62.4lb/ft3) = 823 lb. Step 10: Determine Admixture Amount: According to the Euclid Chemical Eucon Air 30 specifications, a rate of 0.5 to 1.0 oz per 100 lbs (30 to 60 mL per 100 kg) of total cementitious material is used to entrain 3% - 6% air content. Therefore, for 6.5% air content, you would use 1.08 oz per 100 lbs cement. Since you have 897 lbs of cement, you would use 9.7 oz of Euclid Chemical Eucon Air 30. Step 11: Apply Moisture Correction: Weight of Wet C.A. required for 1 yd3 of concrete = 1808 lb (1.027) = 1857 lb Weight of Wet F.A. required for 1 yd3 of concrete = 823 lb (1.042) = 867 lb Free Moisture in C.A. = (0.027 – 0.0075) 1808 = 35 lb Free Moisture in F.A. = (0.042 – 0.008) 823= 28 lb Water contributed by the aggregates = 65 lb Actual amount of water to be added = 305 – 65 = 240 lb A summary of the batch weight corrected for moisture is presented in Table D.



Table D. Summary of Batch Weight corrected for Moisture.

Mix Part Weight/Cubic Yard

(lbs)

Air 6.5%

Water 240 lb

Cement 897 lb

Admixture 9.7 oz

Coarse Aggregate (C.A.) 1857 lb

Fine Aggregate (F.A.) 867 lb

Does it meet specifications? Cement Content: 897 lbs/yd3 > 611 lb/yd3 (minimum) – CHECKS! Water to Cement Ratio: w/c ratio = 0.34 < 0.40 (maximum) – CHECKS! Percent Fine to Coarse Aggregate: SCDOT Specification Section 701.2.12.1 – Base the sand/stone ratio on volume. 31.5% Fine: 68.5% Coarse ≠ 34% Fine: 66% Coarse – DOES NOT CHECK Note SCDOT Specifications Section 701.2.12.1 states that you can vary this ratio to obtain good workability. Try a trial batch BEFORE adjusting! If you iterated to find a solution, hopefully you will read the specifications in the future. PROBLEM #3: Could the concrete mix you determined from Problem #2 be used for a similar project for the Massachusetts Department of Transportation (MassDOT)? Briefly explain your answer. Read the Specifications! Section M4.02.00: Concrete subjected to severe exposure will have a minimum f′c of 30 MPa (~4,350 psi) with 7.0% (± 1.0%). CHECKS! Section M4.02.01: Type I cement ok since nine is specified. CHECKS! Section M4.02.02: FM = 2.5 is OK. CHECKS!



Section M4.02.06.B.2: Slump = 100mm (4 inches) is OK. CHECKS! Section M4.02.06.B.4: Air content table not provided. Cannot check. In general, the mix design from Problem #2 can be used for MassDOT projects, but you should get it approved first.

cive.3100 e m assignment concrete mix...

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